Tüm alıştırma soruları

Soru 1121Soru →

The following passage is adapted from a history of science text. Which punctuation mark should replace the blank to correctly join the clauses?

Aşağıdaki boşlukları doldurun

In the nineteenth century, geologists debated whether Earth's features were shaped by sudden, catastrophic events or by slow, gradual processes. Catastrophists argued that massive floods and earthquakes formed mountains and canyons almost instantly uniformitarians, conversely, maintained that these same features resulted from millions of years of steady erosion.

Cevabı ve açıklamayı göster

Cevap

A semicolon (;)

A semicolon is correct because it links two independent clauses ('Catastrophists argued...' and 'uniformitarians, conversely, maintained...') that are closely related. Because these two complete thoughts are not joined by a coordinating conjunction, a semicolon is required to connect them grammatically.

Adım Adım Çözüm

1

Analyze the clause preceding the blank.

The clause 'Catastrophists argued that massive floods and earthquakes formed mountains and canyons almost instantly' is grammatically independent because it contains a subject and verb and forms a complete thought.

Identifying if the preceding clause is independent is necessary to determine which punctuation marks can link it to the following text.

2

Analyze the clause following the blank.

The clause 'uniformitarians, conversely, maintained that these same features resulted from millions of years of steady erosion' is also grammatically independent.

Identifying if the following clause is independent narrows the punctuation choices to those that can join two complete sentences.

3

Determine the logical relationship between the two independent clauses.

The two clauses present contrasting ideas (instantaneous catastrophic formation vs. gradual uniformitarian erosion), connected by the conjunctive adverb 'conversely'.

This relationship helps determine whether an explanatory punctuation mark (like a colon) or a coordinating mark (like a semicolon) is appropriate.

4

Select the correct punctuation mark.

A semicolon is the correct punctuation mark to join two independent clauses without a coordinating conjunction.

A semicolon correctly links the clauses while avoiding a comma splice or an incorrect explanatory colon.

Anahtar Kavram

A semicolon is used to join two closely related independent clauses when they are not connected by a coordinating conjunction (for, and, nor, but, or, yet, so).

Tahmini Süre:1m 30s

Soru 1122Soru →

If $-2(x - 5) \geq 4$ , what is the maximum possible value of $x$ ?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

3

Distributing the

-2

on the left side of the inequality

-2(x - 5) \geq 4

yields

-2x + 10 \geq 4

. Subtracting

10

from both sides gives

-2x \geq -6

. Dividing both sides by

-2

and reversing the inequality sign results in

x \leq 3

. The maximum possible value is therefore 3.

Adım Adım Çözüm

1

Distribute

-2

to the terms inside the parentheses.

-2x + 10 \geq 4

Applying the distributive property simplifies the inequality.

2

Subtract

10

from both sides of the inequality.

-2x \geq -6

This isolates the variable term on the left side.

3

Divide both sides of the inequality by

-2

and reverse the inequality sign.

x \leq 3

Dividing both sides of an inequality by a negative number reverses the direction of the inequality.

Anahtar Kavram

Solving linear inequalities in one variable using the distributive property and division by negative numbers.

Soru 1123Soru →

In the early twentieth century, a dedicated group of female researchers at the Harvard College Observatory, led by the astronomer Edward Pickering, revolutionized the field of stellar spectroscopy. Although the ______ groundbreaking observations were initially undervalued by contemporary male colleagues, the extensive catalogs they compiled eventually laid the foundation for modern stellar classification systems.

Which choice completes the text so that it conforms to the conventions of Standard English?

researcher

researchers

researcher's

researchers'

Cevabı ve açıklamayı göster

Cevap: researchers'

Cevap

researchers'

The correct answer is the plural possessive form of the noun. The passage establishes that the observations belong to a group of researchers (plural possessive), which requires the spelling ending in an apostrophe after the plural 's'.

Adım Adım Çözüm

1

Analyze the context to determine if the noun should be singular or plural.

The text refers to 'a dedicated group of female researchers' and later uses the plural pronoun 'they' to refer to them, indicating that the noun must be plural.

Identifying the number of the noun ensures grammatical consistency with antecedent and pronoun references.

2

Analyze the syntactic role of the noun to determine if it should be possessive.

The noun modifies the phrase 'groundbreaking observations,' showing that the observations belong to the researchers. Therefore, a possessive form is required.

Possessive forms are necessary when a noun acts as a modifier indicating ownership of another noun.

3

Determine the correct spelling and punctuation for a plural possessive noun.

For a regular plural noun ending in 's' (researchers), the possessive is formed by adding an apostrophe after the 's', resulting in 'researchers'.

Applying standard punctuation rules for plural possessive nouns.

Anahtar Kavram

Plural and Possessive Nouns

Tahmini Süre:1m 0s

Soru 1124Soru →

The following passage is from a biology text. Which punctuation mark must be inserted into the blank to ensure the sentence conforms to the conventions of Standard English?

Aşağıdaki boşlukları doldurun

First discovered in 1998 off the coast of Sulawesi, the mimic octopus—a highly intelligent cephalopod capable of dynamic mimicryis able to impersonate toxic species such as lionfish and sea snakes to deter predators.

Cevabı ve açıklamayı göster

Cevap

An em dash (—) is required to correctly close the nonessential element.

The sentence contains a nonessential appositive phrase ('a highly intelligent cephalopod capable of dynamic mimicry') that interrupts the flow between the subject ('the mimic octopus') and the verb ('is able'). Because this nonessential element is introduced with an em dash, it must also close with an em dash to maintain punctuation symmetry.

Adım Adım Çözüm

1

Identify the nonessential element in the sentence.

The phrase 'a highly intelligent cephalopod capable of dynamic mimicry' is a nonessential appositive phrase modifying 'the mimic octopus'.

This phrase can be removed without changing the core grammatical structure of the sentence.

2

Examine the punctuation introducing the nonessential element.

An em dash ('—') is used immediately before the phrase.

Nonessential elements must be set off by matching pairs of punctuation marks: two commas, two em dashes, or a pair of parentheses.

3

Determine the punctuation mark needed to close the nonessential element.

An em dash ('—') must be placed in the blank.

Using any other punctuation mark would cause punctuation asymmetry, which violates Standard English conventions.

Anahtar Kavram

Punctuation of Nonessential Elements

Soru 1125Soru →

During the Baroque period, Italian painter Artemisia Gentileschi achieved widespread renown for her dramatic and emotionally charged depictions of biblical narratives. She frequently utilized a technique known as chiaroscuro, which creates stark contrasts between light and dark ______ deliberate stylistic choice heightened the psychological tension of her compositions and influenced generations of subsequent artists.

Which choice completes the text so that it conforms to the conventions of Standard English?

; this

, this

this

, but this

Cevabı ve açıklamayı göster

Cevap: ; this

Cevap

The semicolon followed by the pronoun 'this'

The correct answer utilizes a semicolon to properly join two independent clauses. A semicolon is grammatically sufficient to connect closely related independent clauses without the need for a coordinating conjunction.

Adım Adım Çözüm

1

Identify the clause structures in the sentence.

The text before the blank is an independent clause, and the text starting with the blank's pronoun and ending with 'artists' is also an independent clause.

Determining the grammatical status of the clauses helps establish how they should be linked.

2

Rule out choices that violate standard punctuation conventions for connecting independent clauses.

The choice using a comma alone creates a comma splice, and the choice with no punctuation creates a run-on sentence.

Independent clauses cannot be joined by a comma alone or by no punctuation at all.

3

Evaluate the remaining options for logic and grammatical correctness.

The choice with a semicolon correctly links the clauses, whereas the choice with the coordinating conjunction 'but' introduces an incorrect relationship of contrast.

A semicolon is a standard method to connect two independent clauses when the relationship is continuous and logical.

Anahtar Kavram

Clause Boundaries and Linking

Tahmini Süre:45s

Soru 1126Soru →

Complete the passage by filling in the blank with the noun or pronoun that ensures proper subject-modifier agreement.

Aşağıdaki boşlukları doldurun

Analyzing data from a newly constructed radio telescope in 1967, astrophysicist Jocelyn Bell Burnell noticed a series of extremely regular radio pulses. By carefully ruling out potential sources of terrestrial interference, proved that these signals originated from rapidly rotating neutron stars, which are now known as pulsars.

Cevabı ve açıklamayı göster

Cevap

Jocelyn Bell Burnell (or the pronoun 'she')

The introductory modifying phrase 'By carefully ruling out potential sources of terrestrial interference' describes an action that can only be logically performed by a person. In this context, the astrophysicist Jocelyn Bell Burnell is the individual who investigated the signals and ruled out interference. Thus, starting the main clause with 'Jocelyn Bell Burnell' or the pronoun 'she' establishes a correct and logical subject-modifier agreement.

Adım Adım Çözüm

1

Identify the introductory modifying phrase and determine what or who it logically describes.

The modifying phrase is 'By carefully ruling out potential sources of terrestrial interference'. The entity performing the action of 'ruling out' must be a logical, conscious agent.

In English grammar, modifiers must clearly and logically modify the subject that immediately follows them.

2

Identify the subject from the context that matches the modifier.

The context identifies astrophysicist Jocelyn Bell Burnell as the person analyzing the data. Therefore, she is the agent who ruled out the interference.

To avoid a dangling modifier error, the subject immediately following the modifying phrase must be the noun or pronoun representing the person who performed the action.

Anahtar Kavram

Subject-Modifier Agreement

Soru 1127Soru →

In the harsh environment of the Sahara Desert, the silver ant (*Cataglyphis bombycina*) utilizes unique physiological adaptations to forage during the hottest parts of the day. One such adaptation is its dense coating of triangular hairs_______ these hairs reflect visible and near-infrared light, keeping the ant's body cool.

Which choice completes the text so that it conforms to the conventions of Standard English?

hairs, these

hairs these

hairs; these

hairs; which

Cevabı ve açıklamayı göster

Cevap: hairs; these

Cevap

The choice containing a semicolon followed by the pronoun 'these' correctly links the two independent clauses.

The correct option correctly uses a semicolon to separate two independent clauses. The clause preceding the blank ('One such adaptation is its dense coating of triangular hairs') and the clause following the blank ('these hairs reflect visible and near-infrared light, keeping the ant's body cool') are both independent, meaning they can stand alone as complete sentences. A semicolon is a standard and appropriate way to link them without a coordinating conjunction.

Adım Adım Çözüm

1

Identify the structure of the clause preceding the blank.

'One such adaptation is its dense coating of triangular hairs' is an independent clause because it contains a subject and a verb and can stand alone as a sentence.

Determining the grammatical status of the first clause helps establish what punctuation is permitted.

2

Identify the structure of the clause following the blank.

'these hairs reflect visible and near-infrared light, keeping the ant's body cool' is also an independent clause.

Knowing that both clauses are independent means they must be separated by a terminal punctuation mark, a semicolon, or a comma with a coordinating conjunction.

3

Select the punctuation that correctly links two independent clauses.

A semicolon appropriately joins two independent clauses without any coordinating conjunction.

Applying standard punctuation rules resolves clause boundary requirements.

Anahtar Kavram

Semicolon usage to link independent clauses

Tahmini Süre:45s

Soru 1128Soru →

A company manufactures custom travel mugs. The daily cost $C$ , in dollars, to manufacture $n$ mugs is given by the formula $C = 1.25n + 250$ . The company sells each mug for $4.50. To make a profit of exactly$ 400$ in a day, how many mugs must the company manufacture?

Cevabı ve açıklamayı göster

Cevap: 200

Cevap

The company must manufacture 200 mugs to make a profit of exactly $400 in a day.

Subtracting the cost expression from the revenue expression gives the profit equation:

4.50n - (1.25n + 250) = 400

. Distributing the negative sign results in

4.50n - 1.25n - 250 = 400

, which simplifies to

3.25n - 250 = 400

. Adding 250 to both sides gives

3.25n = 650

. Dividing both sides by 3.25 yields

n = 200

.

Adım Adım Çözüm

1

Set up the profit equation

4.50n - (1.25n + 250) = 400

Profit is calculated as total revenue (

4.50n

) minus total cost (

1.25n + 250

).

2

Distribute the negative sign and simplify the equation

3.25n - 250 = 400

Subtracting the entire cost expression requires distributing the subtraction to both

1.25n

and

250

, yielding

4.50n - 1.25n - 250

.

3

Isolate the variable term by adding 250 to both sides

3.25n = 650

Adding 250 to both sides of the equation isolates the term containing

n

.

4

Solve for

n

by dividing both sides by 3.25

n = 200

Dividing 650 by 3.25 gives the number of mugs needed to achieve the target profit.

Anahtar Kavram

Solving linear equations in one variable derived from a real-world context.

Soru 1129Soru →

A linear relationship between $x$ and $y$ is defined by the values in the table below.

$x$	$y$
2	7
4	13
6	19

Which of the following equations represents this relationship?

y = 3x - 5

y = \frac{1}{3}x + \frac{19}{3}

y = 3x + 1

y = 6x - 5

Cevabı ve açıklamayı göster

Cevap: $y = 3x + 1$

Cevap

The equation representing the relationship is

y = 3x + 1

.

The correct equation is

y = 3x + 1

. The slope

m

of the linear function can be determined from the table values

(2, 7)

and

(4, 13)

as

\frac{13 - 7}{4 - 2} = \frac{6}{2} = 3

. Substituting the slope

m = 3

and the point

(2, 7)

into the slope-intercept form

y = mx + b

gives

7 = 3(2) + b

, which simplifies to

7 = 6 + b

, so

b = 1

. Therefore, the equation is

y = 3x + 1

.

Adım Adım Çözüm

1

Find the slope (

m

) of the linear relationship using the points

(2, 7)

and

(4, 13)

from the table.

m = 3

The slope is the ratio of the change in

y

to the change in

x

between any two points on the line:

m = \frac{13 - 7}{4 - 2} = \frac{6}{2} = 3

.

2

Use the slope

m = 3

and the point

(2, 7)

to find the

y

-intercept (

b

) of the line.

b = 1

Substituting the coordinates and slope into the slope-intercept equation

y = mx + b

gives

7 = 3(2) + b

, which simplifies to

7 = 6 + b

, leading to

b = 1

.

3

Substitute the slope and

y

-intercept into the slope-intercept form.

y = 3x + 1

Combining the slope of

3

and

y

-intercept of

1

yields the equation

y = 3x + 1

.

Anahtar Kavram

Determining a linear equation from a table of values

Tahmini Süre:45s

Soru 1130Soru →

In the system of equations below, $k$ is a constant.

kx - 3y = 4

(k-2)x - 5y = 8

If the system has no solution, what is the value of $k$ ?

-1

5

-3

3

Cevabı ve açıklamayı göster

Cevap: -3

Cevap

-3

To find the value of

k

for which the system of linear equations has no solution, we determine when the two lines represented by the equations are parallel and distinct. Parallel lines have equal slopes. We can express each equation in slope-intercept form,

y = mx + b

. For the first equation,

kx - 3y = 4

simplifies to

y = \frac{k}{3}x - \frac{4}{3}

, giving a slope of

\frac{k}{3}

. For the second equation,

(k-2)x - 5y = 8

simplifies to

y = \frac{k-2}{5}x - \frac{8}{5}

, giving a slope of

\frac{k-2}{5}

. Equating the two slopes yields

\frac{k}{3} = \frac{k-2}{5}

. Cross-multiplying gives

5k = 3(k-2)

, which simplifies to

5k = 3k - 6

. Subtracting

3k

from both sides gives

2k = -6

, and dividing by

2

results in

k = -3

. Since the y-intercepts

-\frac{4}{3}

and

-\frac{8}{5}

are distinct, the lines are parallel and do not intersect, meaning there is no solution.

Adım Adım Çözüm

1

Express both equations in slope-intercept form (

y = mx + b

) to find their slopes.

For the first equation,

kx - 3y = 4 \implies 3y = kx - 4 \implies y = \frac{k}{3}x - \frac{4}{3}

(slope is

\frac{k}{3}

). For the second equation,

(k-2)x - 5y = 8 \implies 5y = (k-2)x - 8 \implies y = \frac{k-2}{5}x - \frac{8}{5}

(slope is

\frac{k-2}{5}

).

A system of two linear equations has no solution if the lines are parallel (slopes are equal) and their y-intercepts are different.

2

Set the slopes equal to each other.

\frac{k}{3} = \frac{k-2}{5}

Since the lines must be parallel, their slopes must be equivalent.

3

Solve for

k

by cross-multiplying.

5k = 3(k-2) \implies 5k = 3k - 6 \implies 2k = -6 \implies k = -3

.

Cross-multiplication isolates the variable

k

. Since the y-intercepts (

-\frac{4}{3}

and

-\frac{8}{5}

) are different, this value of

k

guarantees the lines are parallel and distinct.

Anahtar Kavram

Determining parameters for a system of linear equations with no solution

Alternatif Yöntem

Alternatively, align the coefficients of

y

to eliminate the

y

terms. Multiply the first equation by

5

and the second equation by

-3

:

5(kx - 3y) = 5(4) \implies 5kx - 15y = 20

-3((k-2)x - 5y) = -3(8) \implies -3(k-2)x + 15y = -24

Adding these two equations yields:

(5k - 3(k-2))x = -4

(2k + 6)x = -4

For the system to have no solution, the coefficient of

x

must be

0

while the constant on the right side is non-zero (which it is,

-4

). Setting the coefficient of

x

to

0

:

2k + 6 = 0 \implies k = -3

Tahmini Süre:2m 0s

Soru 1131Soru →

A line in the $xy$ -plane is represented by the equation $3x - 4y = 24$ . What is the $y$ -coordinate of the $y$ -intercept of this line?

-6

6

8

\frac{3}{4}

Cevabı ve açıklamayı göster

Cevap: -6

Cevap

The

y

-coordinate of the

y

-intercept is

-6

.

The correct answer is

-6

. The

y

-intercept of a line is the point where it intersects the

y

-axis, which occurs when the

x

-coordinate is

0

. Substituting

x = 0

into the given equation

3x - 4y = 24

yields

-4y = 24

. Dividing both sides by

-4

gives

y = -6

.

Adım Adım Çözüm

1

Substitute

x = 0

into the equation to find the

y

-intercept.

3(0) - 4y = 24

By definition, the

y

-intercept of a line in the coordinate plane is the point where the line crosses the

y

-axis, which always has an

x

-coordinate of

0

.

2

Simplify the equation.

-4y = 24

Multiplying

3

by

0

yields

0

, leaving only the term containing

y

on the left side of the equation.

3

Solve for

y

by isolating the variable.

y = -6

Dividing both sides of the simplified equation by

-4

isolates

y

and gives the final coordinate value.

Anahtar Kavram

Finding the y-intercept of a linear equation in two variables by setting x = 0.

Tahmini Süre:45s

Soru 1132Soru →

For what value of the constant $k$ does the equation $\frac{1}{2}(2kx - 6) - \frac{2}{3}(9 - 3x) = 5x + 4$ have no solution for $x$ ?

3

7

1.5

-7

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The correct value of

k

is

3

.

To find the value of

k

for which the equation has no solution, we first distribute the coefficients on the left side of the equation to get

kx - 3 - 6 + 2x = 5x + 4

. Combining the like terms on the left side gives

(k + 2)x - 9 = 5x + 4

. Moving all the

x

terms to one side yields

(k - 3)x = 13

. For a linear equation of the form

Ax = B

to have no solution, the coefficient of the variable

A

must equal

0

while the constant

B

must be non-zero. Setting

k - 3 = 0

gives the correct value of

3

.

Adım Adım Çözüm

1

Distribute the fractional coefficients on the left side of the equation.

The term

\frac{1}{2}(2kx - 6)

simplifies to

kx - 3

, and the term

-\frac{2}{3}(9 - 3x)

simplifies to

-6 + 2x

.

Applying the distributive property simplifies the parenthetical expressions.

2

Substitute the simplified expressions back into the equation and group like terms.

The equation becomes

kx - 3 - 6 + 2x = 5x + 4

, which simplifies to

(k + 2)x - 9 = 5x + 4

.

Grouping terms allows us to isolate the variable.

3

Isolate the terms containing

x

on one side of the equation.

Subtract

5x

and add

9

to both sides, yielding

(k - 3)x = 13

.

This puts the equation into the standard linear form

Ax = B

.

4

Set the coefficient of

x

to

0

to find the value of

k

that yields no solution.

Setting

k - 3 = 0

gives

k = 3

. Since

13 \neq 0

, the equation

0x = 13

has no solution.

A linear equation of the form

Ax = B

has no solution if and only if

A = 0

and

B \neq 0

.

Anahtar Kavram

Determining the parameter value for which a linear equation in one variable has no solution.

Tahmini Süre:2m 0s

Soru 1133Soru →

Although the compilation of anonymous sixteenth-century ballads contains several verses celebrating the deeds of folk heroes, each of the poems in the collection, when analyzed closely for stylistic consistency, reveals ______ reliance on a single, highly skilled author rather than a succession of oral storytellers.

Which choice completes the text so that it conforms to the conventions of Standard English?

their

its

they're

its'

Cevabı ve açıklamayı göster

Cevap: its

Cevap

The pronoun 'its'

The singular possessive pronoun 'its' correctly matches the grammatical number of its antecedent, the singular indefinite pronoun 'each'.

Adım Adım Çözüm

1

Identify the grammatical antecedent of the pronoun needed in the blank.

The antecedent is the singular indefinite pronoun 'each' (the head of the subject phrase 'each of the poems in the collection').

The pronoun must agree in number with its true antecedent rather than any intervening nouns in prepositional phrases.

2

Determine the case and function of the pronoun required in the sentence.

The blank modifies the noun 'reliance', indicating a possessive pronoun is required.

A possessive pronoun is needed to show whose reliance is being discussed.

3

Select the option that is singular, possessive, and grammatically correct.

The singular possessive pronoun is 'its'.

'its' matches the singular antecedent 'each' and functions correctly as a possessive modifier.

Anahtar Kavram

Pronoun-Antecedent Agreement and Case

Alternatif Yöntem

Locate the main verb of the clause, 'reveals', which is singular. The subject must agree in number with the verb, confirming that the singular indefinite pronoun 'each' is the subject. Therefore, the pronoun that refers back to 'each' must also be singular.

Tahmini Süre:1m 15s

Soru 1134Soru →

During the eighth and ninth centuries, scholars at the House of Wisdom in Baghdad translated numerous classical Greek philosophical and scientific texts into Arabic. By the time European intellectuals rediscovered these manuscripts and initiated the Renaissance, the preservation of the Arabic translations ________ the survival of Aristotle's treatise on poetics for several centuries.

Which choice completes the text so that it conforms to the conventions of Standard English?

ensure

have ensured

had ensured

will ensure

Cevabı ve açıklamayı göster

Cevap: had ensured

Cevap

had ensured

The correct option is 'had ensured' because the past perfect tense is used to describe an action that was completed before another action in the past. The sentence establishes that by the time European intellectuals rediscovered the manuscripts (a past event), the preservation of the Arabic translations had already occurred and completed its role of securing the survival of Aristotle's treatise.

Adım Adım Çözüm

1

Analyze the temporal markers and verbs in the passage to establish the time frame.

The verbs 'translated,' 'rediscovered,' and 'initiated' establish that the passage is set entirely in the past.

Establishing the temporal framework is necessary to choose the correct verb tense.

2

Determine the relationship between the events described in the sentence containing the blank.

The blank describes an action (the preservation ensuring the survival of the treatise) that occurred and was completed prior to another past event ('By the time European intellectuals rediscovered...').

An action that is completed before another action in the past requires the past perfect tense (had + past participle).

3

Select the verb form that corresponds to the past perfect tense.

The past perfect form of 'ensure' is 'had ensured'.

This form correctly conveys the completed sequence of past events.

Anahtar Kavram

Verb Tense, Aspect, and Mood

Soru 1135Soru →

\begin{aligned} 3x - 5y &= 8 \\ kx + 10y &= -3 \end{aligned}

In the system of equations above, $k$ is a constant. If the system has no solution, what is the value of $k$ ?

-2

-6

-1.5

6

Cevabı ve açıklamayı göster

Cevap: -6

Cevap

-6

The correct answer is

-6

. A system of two linear equations has no solution when the equations represent parallel lines, meaning they have the same slope but different

y

-intercepts. Writing the first equation in slope-intercept form gives

y = \frac{3}{5}x - \frac{8}{5}

, so its slope is

\frac{3}{5}

. Writing the second equation in slope-intercept form gives

y = -\frac{k}{10}x - \frac{3}{10}

, so its slope is

-\frac{k}{10}

. Since the

y

-intercepts are different (

-\frac{8}{5} \neq -\frac{3}{10}

), the system will have no solution when their slopes are equal:

\frac{3}{5} = -\frac{k}{10}

. Solving this equation for

k

yields

k = -6

.

Adım Adım Çözüm

1

Convert the first equation to slope-intercept form (

y = mx + b

) to find its slope.

y = \frac{3}{5}x - \frac{8}{5}

, so the slope is

\frac{3}{5}

and the

y

-intercept is

-\frac{8}{5}

.

Expressing the line in slope-intercept form directly reveals its slope and

y

-intercept.

2

Convert the second equation to slope-intercept form to express its slope in terms of

k

.

10y = -kx - 3 \Rightarrow y = -\frac{k}{10}x - \frac{3}{10}

, so the slope is

-\frac{k}{10}

and the

y

-intercept is

-\frac{3}{10}

.

This allows comparison of the slope and

y

-intercept of the second line with the first line.

3

Set the slopes equal to each other and solve for

k

.

\frac{3}{5} = -\frac{k}{10} \Rightarrow 30 = -5k \Rightarrow k = -6

.

A system of two linear equations has no solution if and only if the lines are parallel (equal slopes) and have different

y

-intercepts (which

-\frac{8}{5}

and

-\frac{3}{10}

are).

Anahtar Kavram

Determining the number of solutions to a system of linear equations based on slope and intercept relationships.

Soru 1136Soru →

For decades, paleontologists operated under the assumption that all non-avian dinosaurs were strictly land-dwelling creatures, lacking the adaptations required for swimming. However, while studying the fossilized remains of the Cretaceous-era theropod *Spinosaurus* in Morocco, researcher Nizar Ibrahim realized that the dinosaur's dense, compact bones and unique paddle-like tail indicated an aquatic ______ conclusion that challenged the long-held scientific consensus regarding dinosaur habitats.

Which choice completes the passage so that it conforms to the conventions of Standard English?

lifestyle; a

lifestyle: a

lifestyle, it was a

lifestyle; it being a

Cevabı ve açıklamayı göster

Cevap: lifestyle: a

Cevap

lifestyle: a

The correct answer is 'lifestyle: a'. A colon is grammatically appropriate here because the clause preceding the colon is independent, and the phrase following it is an appositive noun phrase ('a conclusion...') that explains the significance of the preceding clause.

Adım Adım Çözüm

1

Analyze the grammatical structure of the clause preceding the blank.

The text before the blank forms a grammatically independent clause ('However, while studying... indicated an aquatic lifestyle').

This establishes whether the punctuation mark can be preceded by this clause.

2

Analyze the grammatical structure of the phrase following the blank.

The text after the blank ('conclusion that challenged...') is an appositive noun phrase and is not grammatically independent.

This determines what punctuation marks are eligible to connect the two parts.

3

Evaluate the options based on standard English conventions.

A colon is the correct punctuation mark to join an independent clause to an explanatory noun phrase, making 'lifestyle: a' correct.

To select the option that conforms to standard grammatical conventions.

Anahtar Kavram

Using colons to connect independent clauses to explanatory noun phrases, and avoiding semicolons or commas where they create fragments or comma splices.

Soru 1137Soru →

During the construction of early Gothic cathedrals in twelfth-century France, master builders encountered unprecedented structural challenges as they attempted to build taller vaults than ever before. To solve the problem of lateral thrust, they began incorporating pointed arches and ribbed vaulting to distribute weight more ______ this crucial architectural innovation allowed for thinner, lighter walls punctuated by expansive stained-glass windows.

Which choice completes the text so that it conforms to the conventions of Standard English?

efficiently,

efficiently

efficiently;

efficiently, although

Cevabı ve açıklamayı göster

Cevap: efficiently;

Cevap

efficiently;

The correct option correctly uses a semicolon to link the two independent clauses. Semicolons are standard punctuation marks for separating related independent clauses without the need for a coordinating conjunction.

Adım Adım Çözüm

1

Identify the two clauses in the sentence.

The first clause is 'To solve the problem of lateral thrust, they began incorporating pointed arches and ribbed vaulting to distribute weight more efficiently' and the second clause is 'this crucial architectural innovation allowed for thinner, lighter walls punctuated by expansive stained-glass windows.'

Analyzing sentence structure is necessary to identify where clause boundaries lie.

2

Determine if the clauses can stand alone.

Both clauses contain a subject and a verb and express a complete thought, meaning they are both independent clauses.

The type of punctuation or conjunction required depends on whether the clauses are independent or dependent.

3

Check the punctuation conventions for linking independent clauses.

Two independent clauses must be linked by a period, a semicolon, a colon, or a comma combined with a coordinating conjunction.

This step ensures the chosen punctuation conforms to Standard English conventions.

Anahtar Kavram

Clause Boundaries and Linking

Soru 1138Soru →

Complete the passage by entering the punctuation mark that correctly joins the two independent clauses.

Aşağıdaki boşlukları doldurun

In 1977, deep-sea explorers discovered hydrothermal vents on the ocean floor, revealing complex ecosystems that thrive in complete darkness. These vents spew superheated, mineral-rich water directly into the ocean strange organisms like giant tube worms use these minerals to generate energy. Because this process does not require sunlight, these ecosystems exist completely independent of solar energy.

Cevabı ve açıklamayı göster

Cevap

A semicolon (;) is the correct punctuation mark to join the two independent clauses.

A semicolon is used to connect two closely related independent clauses when no coordinating conjunction is present.

Adım Adım Çözüm

1

Identify the clause structures surrounding the blank.

The clause before the blank ('These vents spew superheated, mineral-rich water directly into the ocean') and the clause after the blank ('strange organisms like giant tube worms use these minerals to generate energy') are both independent clauses.

Each clause contains a subject and a verb and expresses a complete thought, meaning both could stand alone as separate sentences.

2

Determine the appropriate punctuation to join the two independent clauses.

A semicolon is required to link them because there is no coordinating conjunction (such as 'and' or 'but') connecting the two sentences.

Using a comma without a conjunction would result in a comma splice, and leaving them unpunctuated would create a run-on sentence.

Anahtar Kavram

Semicolons to link independent clauses

Soru 1139Soru →

In the $xy$ -plane, line $L_1$ is defined by the equation $ax + by = c$ , where $a$ , $b$ , and $c$ are non-zero constants. Line $L_2$ is perpendicular to line $L_1$ and has a $y$ -intercept that is twice the $y$ -intercept of line $L_1$ . If the $x$ -intercept of line $L_2$ is $d$ , which of the following expressions represents $d$ in terms of $a$ , $b$ , and $c$ ?

-\frac{2ac}{b^2}

\frac{2ac}{b^2}

-\frac{2bc}{a^2}

-\frac{2c}{a}

Cevabı ve açıklamayı göster

Cevap: $-\frac{2ac}{b^2}$

Cevap

The expression that represents

d

in terms of

a

,

b

, and

c

is

-\frac{2ac}{b^2}

.

The correct answer is found by first rewriting the equation of the first line in slope-intercept form to determine its slope,

-\frac{a}{b}

, and its

y

-intercept,

\frac{c}{b}

. The second line is perpendicular to the first, so its slope is the negative reciprocal,

\frac{b}{a}

. Its

y

-intercept is twice that of the first line, which is

\frac{2c}{b}

. Setting

y = 0

in the equation of the second line,

y = \frac{b}{a}x + \frac{2c}{b}

, and solving for

x

yields the

x

-intercept

d = -\frac{2ac}{b^2}

.

Adım Adım Çözüm

1

Rewrite the equation of line

L_1

in slope-intercept form.

y = -\frac{a}{b}x + \frac{c}{b}

To identify the slope and

y

-intercept of the first line.

2

Determine the slope and

y

-intercept of line

L_2

.

Slope of

L_2

is

\frac{b}{a}

;

y

-intercept of

L_2

is

\frac{2c}{b}

.

Line

L_2

is perpendicular to

L_1

(so its slope is the negative reciprocal of

-\frac{a}{b}

) and its

y

-intercept is twice that of

L_1

.

3

Write the equation of line

L_2

.

y = \frac{b}{a}x + \frac{2c}{b}

Using the slope-intercept form

y = mx + k

for the second line.

4

Find the

x

-intercept

d

of line

L_2

by setting

y = 0

.

d = -\frac{2ac}{b^2}

The

x

-intercept is the value of

x

when

y = 0

.

Anahtar Kavram

Linear Equations in Two Variables

Alternatif Yöntem

Instead of converting to slope-intercept form, one can use the general form relationships. For

ax + by = c

, the slope is

-a/b

and the

y

-intercept is

c/b

. A perpendicular line has slope

b/a

. With double the

y

-intercept, its equation can be written as

y - \frac{2c}{b} = \frac{b}{a}x

. Setting

y=0

directly gives

-\frac{2c}{b} = \frac{b}{a}d \implies d = -\frac{2ac}{b^2}

.

Tahmini Süre:2m 0s

Soru 1140Soru →

For decades, planetary scientists have debated the origins of the asteroid belt positioned between Mars and Jupiter. Many astronomers believe that the belt is a collection of fragments from a planet that shattered early in the solar system's history_______ others argue that the rocky debris represents primordial materials that were prevented from coalescing into a single planet due to Jupiter's intense gravitational pull.

Which choice completes the text so that it conforms to the conventions of Standard English?

history; others

history, others

history others

history; while others

Cevabı ve açıklamayı göster

Cevap: history; others

Cevap

history; others

The correct option correctly uses a semicolon to separate two independent clauses. The clause preceding the semicolon ('Many astronomers believe...') and the clause following the semicolon ('others argue...') are both grammatically complete and can stand alone as sentences, making a semicolon the appropriate punctuation mark to link them.

Adım Adım Çözüm

1

Analyze the grammatical structure of the clauses before and after the blank.

The clause before the blank ('Many astronomers believe that the belt is a collection of fragments from a planet that shattered early in the solar system's history') and the clause after the blank ('others argue that the rocky debris represents primordial materials that were prevented from coalescing into a single planet due to Jupiter's intense gravitational pull') are both independent clauses.

Identifying clause boundaries is necessary to determine the correct punctuation required to link them.

2

Determine the punctuation mark needed to join two independent clauses without a coordinating conjunction.

A semicolon is appropriate to separate two closely related independent clauses when no coordinating conjunction (such as 'and' or 'but') is present.

This avoids grammatical errors such as run-on sentences and comma splices.

3

Evaluate the choices to find the one that correctly applies a semicolon between the two independent clauses without introducing subordinate conjunctions.

The option containing 'history; others' correctly uses a semicolon to link the independent clauses. The option with 'history; while others' is incorrect because the addition of 'while' makes the second clause dependent, which cannot follow a semicolon in this context.

A semicolon must only connect two independent clauses, not an independent clause and a dependent clause.

Anahtar Kavram

Semicolons are used to link two independent clauses that are closely related in thought, provided no coordinating conjunction is used.

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

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Alternatif Yöntem

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Anahtar Kavram

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Alternatif Yöntem

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Cevap

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Anahtar Kavram

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Anahtar Kavram

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Anahtar Kavram

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Anahtar Kavram

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Anahtar Kavram

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Alternatif Yöntem