Tüm alıştırma soruları

In the system of equations below, what is the value of $x$ ?

3x - y = 7

x + y = 5

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The value of

x

is

3

.

Adding the two equations eliminates

y

, resulting in

4x = 12

. Dividing by

4

gives

x = 3

.

Adım Adım Çözüm

1

Add the two equations to eliminate

y

.

4x = 12

Adding the equations

(3x - y) + (x + y) = 7 + 5

eliminates

y

because

-y + y = 0

.

2

Solve for

x

.

x = 3

Divide both sides of the equation

4x = 12

by

4

.

Anahtar Kavram

Solving a system of linear equations by elimination.

Soru 982Soru →

In the mid-nineteenth century, critics of the newly emerged medium of photography debated its status as a fine art. Many argued that because a camera mechanically records images, a photograph lacks the subjective expression of a painting; others contended that the photographer's choices of framing and lighting constitute a distinct creative ________ the latter perspective eventually gained widespread acceptance as photography exhibitions entered major museums.

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

act, indeed,

act indeed

act; indeed,

act, but

Cevabı ve açıklamayı göster

Cevap: act; indeed,

Cevap

The correct answer is the option that links the clauses using a semicolon and the transition word 'indeed' followed by a comma.

The correct option correctly uses a semicolon to separate the two independent clauses. The first independent clause ends with the word 'act', and the second independent clause begins with the transition 'indeed'. Using a semicolon is the standard way to connect these clauses since no coordinating conjunction is present. Additionally, the conjunctive adverb 'indeed' is followed by a comma, which is the correct convention when introducing an independent clause.

Adım Adım Çözüm

1

Analyze the structure of the passage to identify the main clauses.

The text contains two main independent clauses: one asserting that critics contended the choices of framing and lighting constitute a creative act, and the second stating that this perspective eventually gained acceptance.

Understanding clause boundaries is essential for choosing the correct punctuation and conjunctions.

2

Determine the relationship between these two independent clauses.

The second clause reinforces and confirms the statement in the first clause, so an intensifying transition like 'indeed' is appropriate.

Identifying the semantic relationship ensures we select the correct linking word or conjunction.

3

Select the punctuation that conforms to Standard English conventions for joining independent clauses.

A semicolon must be used to separate the independent clauses because they are not joined by a coordinating conjunction. The conjunctive adverb 'indeed' should begin the second clause and be followed by a comma.

Semicolons are used to link related independent clauses without coordinating conjunctions, and conjunctive adverbs starting a clause are set off by commas.

Anahtar Kavram

Clause Boundaries and Linking

Soru 983Soru →

If $3(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1$ , what is the value of $2x - 3$ ?

-\frac{19}{2}

\frac{7}{2}

\frac{9}{2}

\frac{13}{4}

Cevabı ve açıklamayı göster

Cevap: $\frac{7}{2}$

Cevap

The value of the expression is

\frac{7}{2}

.

The correct answer is

\frac{7}{2}

. Distributing the constants on both sides of the equation

3(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1

yields

3x - 6 - 8 + 4x = 3x - 2 + 1

. Combining like terms on both sides gives

7x - 14 = 3x - 1

. Subtracting

3x

from both sides and adding

14

to both sides results in

4x = 13

, which simplifies to

x = \frac{13}{4}

. Substituting this value into

2x - 3

gives

2\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}

.

Adım Adım Çözüm

1

Distribute the constants on both sides of the equation.

3x - 6 - 8 + 4x = 3x - 2 + 1

To simplify the linear terms and constants before isolating the variable.

2

Combine like terms on both sides of the equation.

7x - 14 = 3x - 1

To reduce the equation to a simpler form with one variable term and one constant term on each side.

3

Isolate the variable term by subtracting

3x

from both sides and adding

14

to both sides.

4x = 13

To group all variable terms on one side and constant terms on the other.

4

Solve for

x

by dividing both sides by

4

.

x = \frac{13}{4}

To isolate the variable

x

.

5

Substitute the value of

x

into the expression

2x - 3

.

2\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}

To calculate the final value requested by the question.

Anahtar Kavram

Solving linear equations in one variable by distributing terms, combining like terms, isolating the variable, and evaluating algebraic expressions.

Soru 984Soru →

If $\frac{3}{5}p - 4 = 8$ , what is the value of $p$ ?

Cevabı ve açıklamayı göster

Cevap: 20

Cevap

20

To solve the equation

\frac{3}{5}p - 4 = 8

, we perform inverse operations to isolate

p

. First, add 4 to both sides of the equation to get

\frac{3}{5}p = 12

. Next, multiply both sides by the reciprocal of the coefficient of

p

, which is

\frac{5}{3}

. This gives

p = 12 \times \frac{5}{3} = 20

. Substituting 20 back into the original equation confirms it is the correct solution.

Adım Adım Çözüm

1

Add 4 to both sides of the equation.

\frac{3}{5}p = 12

To isolate the term containing the variable

p

.

2

Multiply both sides of the equation by

\frac{5}{3}

.

p = 20

To solve for

p

by multiplying by the reciprocal of its coefficient.

Anahtar Kavram

Solving one-variable linear equations using inverse operations.

Soru 985Soru →

The Titan arum _______ emits a foul odor resembling decaying meat to attract carrion beetles and flesh flies for pollination.

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

, a giant flowering plant native to the rainforests of Sumatra—

—a giant flowering plant native to the rainforests of Sumatra—

—a giant flowering plant native to the rainforests of Sumatra,

a giant flowering plant native to the rainforests of Sumatra,

Cevabı ve açıklamayı göster

Cevap: —a giant flowering plant native to the rainforests of Sumatra—

Cevap

—a giant flowering plant native to the rainforests of Sumatra—

The correct answer uses a matching pair of em dashes to properly set off the nonessential appositive phrase describing the Titan arum. Nonessential elements in a sentence must be set off by matching punctuation marks, such as two commas, two parentheses, or two em dashes.

Adım Adım Çözüm

1

Identify the nonessential element in the sentence.

The phrase 'a giant flowering plant native to the rainforests of Sumatra' is an appositive that provides extra information about the subject 'Titan arum'. It is nonessential because removing it leaves the main clause grammatically complete: 'The Titan arum emits a foul odor...'

Recognizing the boundaries of a nonessential element is necessary to determine where the setting-off punctuation must be placed.

2

Check the options for matching punctuation pairs.

The nonessential element must be enclosed by identical punctuation marks at its start and end. The only option that offers a matching pair is the one enclosed by em dashes.

Standard English conventions require nonessential elements to be set off by matching pairs of punctuation (e.g., two commas or two em dashes) rather than mixed punctuation.

Anahtar Kavram

Nonessential elements must be set off from the rest of the sentence using matching punctuation marks: two commas, two em dashes, or two parentheses.

Soru 986Soru →

Throughout the 1870s, naturalist Charlotte Wheeler kept meticulous records of the exotic flora in her conservatory. In her diaries, Wheeler—who frequently shared her observations with other botany enthusiasts—often noted that by the time a rare orchid species finally bloomed in her greenhouse, she _______ its developmental stages for months, documenting each subtle shift in leaf coloration and stem length. Which choice conforms to the conventions of Standard English?

has been tracking

had been tracking

is tracking

will track

Cevabı ve açıklamayı göster

Cevap: had been tracking

Cevap

had been tracking

The past perfect progressive verb phrase 'had been tracking' is correct because it indicates that an action began in the past and continued over a period of time ('for months') up until another event in the past ('bloomed'). This matches the past-tense framework established by the verbs 'kept' and 'noted' in the passage.

Adım Adım Çözüm

1

Identify the temporal framework of the passage by looking at neighboring verbs.

The verbs 'kept,' 'noted,' and 'bloomed' establish a past-tense framework for events occurring in the 1870s.

Verb tenses within a passage must remain consistent unless there is a clear chronological shift.

2

Analyze the relationship between the target verb and the other events in the sentence.

The phrase 'by the time a rare orchid species finally bloomed' indicates that the tracking occurred prior to the blooming. The phrase 'for months' indicates a duration of time leading up to that point.

An action that began and continued over a period of time prior to another past action requires the past perfect or past perfect progressive aspect.

3

Select the option that conforms to this past perfect progressive aspect.

The verb phrase 'had been tracking' is the correct past perfect progressive form.

It maintains tense consistency and correctly expresses the completed duration before a past point.

Anahtar Kavram

Maintaining verb tense consistency and selecting the correct aspect (past perfect progressive) to show the chronological relationship between past events.

Tahmini Süre:1m 30s

Soru 987Soru →

The passage below contains a blank indicating a missing punctuation mark. Read the passage and identify the punctuation mark that should fill the blank to correctly set off the nonessential element. What punctuation mark should be placed in the blank?

Aşağıdaki boşlukları doldurun

In his 1967 masterpiece *One Hundred Years of Solitude*, Colombian author Gabriel García Márquez introduced readers to the fictional town of Macondo. This setting, which was closely modeled on the author’s childhood home of Aracataca served as a metaphorical microcosm of Latin American history. The novel’s success popularized the literary style known as magical realism.

Cevabı ve açıklamayı göster

Cevap

A comma (,) must be placed in the blank to match the comma that opens the nonessential clause.

A comma is the correct punctuation mark because the nonessential relative clause 'which was closely modeled on the author’s childhood home of Aracataca' begins with a comma after the word 'setting'. To maintain grammatical symmetry, the clause must also end with a comma before the verb 'served'.

Adım Adım Çözüm

1

Identify the nonessential element in the sentence.

The clause 'which was closely modeled on the author’s childhood home of Aracataca' is a nonessential relative clause that modifies the noun 'setting'.

Nonessential elements provide descriptive details that can be omitted without changing the core meaning or grammatical integrity of the sentence.

2

Observe the punctuation used to introduce the nonessential element.

A comma is placed after 'setting' to open the clause.

Punctuation setting off nonessential elements must be symmetrical (comma-comma, dash-dash, or parenthesis-parenthesis).

3

Determine the punctuation mark needed to close the nonessential element.

A comma must be placed in the blank before the main verb 'served'.

Since a comma was used to introduce the nonessential element, a matching comma must be used to close it.

Anahtar Kavram

Punctuation of Nonessential Elements

Soru 988Soru →

In the equation below, $k$ is a constant.

\frac{1}{3}(2kx - 9) - \frac{5}{6}(x + 4) = \frac{11}{2}

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

Cevabı ve açıklamayı göster

Cevap: 1.25

Cevap

1.25 (or 5/4)

The correct answer is 1.25 (or 5/4). A linear equation in one variable of the form

Ax + B = C

has no solution if the variable terms on both sides of the equation are equal (meaning

A = 0

) and the constant terms are unequal (

B \neq C

). Expanding the left side of the given equation yields

\frac{2}{3}kx - 3 - \frac{5}{6}x - \frac{10}{3} = \frac{11}{2}

. Combining the constant terms gives

\left(\frac{2}{3}k - \frac{5}{6}\right)x - \frac{19}{3} = \frac{11}{2}

. Setting the coefficient of

x

to

0

yields

\frac{2}{3}k - \frac{5}{6} = 0

. Solving for

k

gives

k = \frac{5}{6} \times \frac{3}{2} = \frac{5}{4}

, which is equivalent to 1.25. Since the remaining constant terms are unequal (

-\frac{19}{3} \neq \frac{11}{2}

), the equation has no solution when

k = 1.25

.

Adım Adım Çözüm

1

Expand the expression on the left side of the equation

\frac{2}{3}kx - 3 - \frac{5}{6}x - \frac{10}{3} = \frac{11}{2}

Apply the distributive property to remove the parentheses.

2

Group the

x

terms and combine the constants on the left side

\left(\frac{2}{3}k - \frac{5}{6}\right)x - \frac{19}{3} = \frac{11}{2}

Simplify the equation by combining like terms:

-3 - \frac{10}{3} = -\frac{9}{3} - \frac{10}{3} = -\frac{19}{3}

.

3

Set the coefficient of the

x

term equal to

0

\frac{2}{3}k - \frac{5}{6} = 0

For a linear equation to have no solution, the variable terms on both sides of the equation must cancel out (meaning the coefficient of the variable must be

0

), while the remaining constant terms must not be equal (

-\frac{19}{3} \neq \frac{11}{2}

).

4

Solve the resulting equation for

k

k = 1.25

Add

\frac{5}{6}

to both sides to get

\frac{2}{3}k = \frac{5}{6}

, then multiply by the reciprocal of

\frac{2}{3}

, which gives

k = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} = 1.25

.

Anahtar Kavram

Conditions for a linear equation in one variable to have no solution

Soru 989Soru →

A rectangle has a length of $2x + 5$ centimeters and a width of $x - 2$ centimeters. If the perimeter of the rectangle is $42$ centimeters, what is the value of $x$ ?

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

6

The correct answer is 6. The perimeter of a rectangle is calculated using the formula

P = 2l + 2w

. Substituting the given expressions for length and width yields the linear equation

2(2x + 5) + 2(x - 2) = 42

. Distributing the 2 gives

4x + 10 + 2x - 4 = 42

. Combining like terms on the left side simplifies this to

6x + 6 = 42

. Subtracting 6 from both sides yields

6x = 36

. Finally, dividing both sides by 6 gives the value

x = 6

.

Adım Adım Çözüm

1

Write the perimeter equation in terms of

x

.

2(2x + 5) + 2(x - 2) = 42

The perimeter of a rectangle is the sum of all its sides, represented by the formula

P = 2l + 2w

.

2

Distribute the 2 into the parentheses.

4x + 10 + 2x - 4 = 42

Applying the distributive property yields

2(2x + 5) = 4x + 10

and

2(x - 2) = 2x - 4

.

3

Combine like terms on the left side.

6x + 6 = 42

Grouping the variable terms gives

4x + 2x = 6x

, and grouping the constant terms gives

10 - 4 = 6

.

4

Subtract 6 from both sides of the equation.

6x = 36

This isolates the variable term on the left side of the equation.

5

Divide both sides of the equation by 6.

x = 6

Dividing by the coefficient of

x

solves for the variable.

Anahtar Kavram

Solving linear equations in one variable by applying the distributive property and combining like terms.

Soru 990Soru →

Located roughly 500 light-years from Earth in the constellation Ophiuchus, Barnard 68 is a dark absorption nebula consisting of a high concentration of dust and molecular gas. Known for its extreme density and cold temperature, _______

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

astronomers find that the molecular cloud Barnard 68 absorbs almost all visible light from the stars behind it.

visible light from background stars is almost completely absorbed by the molecular cloud Barnard 68.

the absorption of visible light from background stars occurs within the molecular cloud Barnard 68.

the molecular cloud Barnard 68 absorbs almost all visible light from the stars behind it.

Cevabı ve açıklamayı göster

Cevap: the molecular cloud Barnard 68 absorbs almost all visible light from the stars behind it.

Cevap

the molecular cloud Barnard 68 absorbs almost all visible light from the stars behind it.

The introductory modifying phrase 'Known for its extreme density and cold temperature' must describe the molecular cloud Barnard 68. The correct option begins with this noun phrase, ensuring that the modifier is logically and grammatically connected to the subject it describes.

Adım Adım Çözüm

1

Identify the introductory modifying phrase in the sentence.

The phrase is 'Known for its extreme density and cold temperature'.

This phrase sets up a description that must apply to the noun that immediately follows the comma.

2

Determine the logical subject that is described by the modifying phrase.

The entity known for extreme density and cold temperature is the molecular cloud Barnard 68, not the astronomers, the visible light, or the absorption.

Correct grammatical construction requires the modifying phrase to be placed directly next to the noun it modifies.

3

Select the option that begins with the logical subject.

The option beginning with 'the molecular cloud Barnard 68' is correct, as it avoids a dangling or misplaced modifier.

This establishes proper subject-modifier agreement.

Anahtar Kavram

Subject-Modifier Agreement

Tahmini Süre:1m 0s

Soru 991Soru →

A line in the $xy$ -plane has the equation $3y - 2x = 12$ . What is the slope of this line?

\frac{3}{2}

4

\frac{2}{3}

-\frac{2}{3}

Cevabı ve açıklamayı göster

Cevap: $\frac{2}{3}$

Cevap

The slope of the line is

\frac{2}{3}

.

To find the slope, the equation

3y - 2x = 12

is rewritten in slope-intercept form (

y = mx + b

). Adding

2x

to both sides gives

3y = 2x + 12

. Dividing by

3

yields

y = \frac{2}{3}x + 4

. The slope is the coefficient of

x

, which is

\frac{2}{3}

.

Adım Adım Çözüm

1

Isolate the term containing

y

by adding

2x

to both sides of the equation.

3y = 2x + 12

To express the equation in slope-intercept form (

y = mx + b

).

2

Divide all terms in the equation by

3

to solve for

y

.

y = \frac{2}{3}x + 4

To isolate

y

and identify the slope,

m

, which is the coefficient of

x

.

Anahtar Kavram

Finding the slope of a line from its linear equation by rewriting it in slope-intercept form.

Soru 992Soru →

In 1974, farmers digging a well near Xi'an, China, unearthed fragments of a clay figure, a discovery that eventually led to the excavation of the Terracotta Army. Since then, archaeologists ______ thousands of life-sized clay soldiers, horses, and chariots buried near the tomb of Emperor Qin Shi Huang. Which choice completes the text so that it conforms to the conventions of Standard English?

uncovered

uncover

have uncovered

had uncovered

Cevabı ve açıklamayı göster

Cevap: have uncovered

Cevap

have uncovered

The present perfect tense 'have uncovered' is correct because the introductory phrase 'Since then' establishes a timeframe that begins in the past (1974) and continues up to the present. The present perfect tense is specifically used to describe actions that span from the past to the present.

Adım Adım Çözüm

1

Analyze the sentence structure and locate temporal cues in the text.

The phrase 'Since then' refers back to the initial discovery in 1974 and establishes a time frame that extends from that past point up to the present day.

Identifying the temporal context determines the correct verb tense and aspect.

2

Evaluate the verb forms to find the one that matches a past-to-present time frame.

The present perfect tense ('have uncovered') is the standard English convention for actions that started in the past and continue into or remain relevant to the present.

Selecting the verb form that maintains tense consistency and aspect logic is necessary to complete the sentence.

Anahtar Kavram

Verb Tense, Aspect, and Mood

Tahmini Süre:1m 0s

Soru 993Soru →

The following passage is missing a word. Write a word in the blank that conforms to the conventions of Standard English parallel structure. Which word best completes the passage to maintain this structure?

Aşağıdaki boşlukları doldurun

In a recent study of deep-sea ecosystems, oceanographers observed that hydrothermal vent communities depend on chemosynthetic bacteria to convert toxic chemicals into usable energy. To survive in these extreme environments, endemic species rely on adapting to intense hydrostatic pressure, cultivating symbiotic relationships with the bacteria, and the high concentration of heavy metals in the surrounding water.

Cevabı ve açıklamayı göster

Cevap

A gerund (a verb form ending in -ing, such as 'tolerating' or 'withstanding') that is parallel to the preceding gerunds 'adapting' and 'cultivating'.

The correct answer must be a gerund (a verb form ending in -ing, such as 'tolerating' or 'withstanding') because it is the third item in a parallel list of actions following the preposition 'on'. The first two items in the list, 'adapting' and 'cultivating', are gerunds, so the third item must also be a gerund to maintain parallel structure.

Adım Adım Çözüm

1

Analyze the sentence to identify the list of parallel elements.

The sentence lists three elements that species rely on: 'adapting...', 'cultivating...', and '{{blank_1}}...'.

Identifying the parallel elements allows us to determine the grammatical pattern that must be maintained.

2

Determine the grammatical form of the first two elements in the list.

The words 'adapting' and 'cultivating' are both gerunds (verb forms ending in -ing) acting as objects of the preposition 'on'.

The form of the initial elements determines the required form for the final element in a parallel series.

3

Apply the rule of parallel structure to the final element.

The blank must be filled with a gerund (a verb form ending in -ing).

All items in a list coordinated by 'and' must share the same grammatical structure to be parallel.

4

Select a semantically fitting verb in the gerund form.

Words like 'tolerating', 'withstanding', or 'enduring' fit the context of surviving heavy metal concentrations.

The chosen word must not only be grammatically parallel but also logically make sense in the context of the passage.

Anahtar Kavram

Parallel Structure

Soru 994Soru →

A solar energy company offers two payment plans for installing solar panels. Under Plan A, the customer pays a one-time installation fee of $1,200 and a monthly maintenance fee of$ 25. Under Plan B, there is no installation fee, but the customer pays a monthly maintenance fee of $45 for the first 12 months, and$ 35 per month for each month thereafter. If a customer chooses Plan A, after how many months of service will the total cost of Plan A be exactly equal to the total cost of Plan B?

24

66

108

132

Cevabı ve açıklamayı göster

Cevap: 108

Cevap

The correct answer is 108 months.

The correct answer is 108. Setting the total cost of Plan A,

1200 + 25m

, equal to the total cost of Plan B,

45(12) + 35(m-12)

, yields the linear equation

1200 + 25m = 120 + 35m

. Isolating

m

by subtracting

25m

and

120

from both sides gives

10m = 1080

, which simplifies to

m = 108

.

Adım Adım Çözüm

1

Set up the total cost expression for Plan A.

\text{Cost}_A = 1200 + 25m

Plan A has a fixed setup fee of

1,200 plus a recurring cost of

25 for each of the

m

months.

2

Set up the total cost expression for Plan B, assuming the number of months

m > 12

.

\text{Cost}_B = 45(12) + 35(m - 12) = 540 + 35m - 420 = 120 + 35m

Plan B charges

45 per month for the first 12 months and

35 per month for the remaining

m - 12

months.

3

Equate the two expressions and solve for

m

.

1200 + 25m = 120 + 35m \Rightarrow 1080 = 10m \Rightarrow m = 108

Setting the two costs equal allows us to isolate the variable

m

by subtracting

25m

and

120

from both sides.

Anahtar Kavram

Formulating and solving multi-step linear equations in one variable from real-world word problems.

Tahmini Süre:2m 30s

Soru 995Soru →

If $5 - 3(2x - 4) = 2(x + 3) - 5$ , what is the value of $4x - 3$ ?

5

-7

2

6

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5

The correct answer is the value of the expression when the linear equation is solved correctly. Distributing the terms on both sides of the equation yields

5 - 6x + 12 = 2x + 6 - 5

. Simplifying each side gives

17 - 6x = 2x + 1

. Adding

6x

to both sides and subtracting

1

from both sides results in

16 = 8x

, which means

x = 2

. Substituting

x = 2

into the expression

4x - 3

gives

4(2) - 3 = 5

.

Adım Adım Çözüm

1

Distribute the constants on both sides of the equation.

5 - 6x + 12 = 2x + 6 - 5

To eliminate the parentheses so that like terms can be combined.

2

Combine like terms on both sides of the equation.

17 - 6x = 2x + 1

To simplify the linear expression on each side.

3

Isolate the variable

x

by adding

6x

to both sides and subtracting

1

from both sides.

16 = 8x

, which simplifies to

x = 2

To find the value of

x

that satisfies the equation.

4

Substitute the value of

x

into the target expression

4x - 3

.

4(2) - 3 = 5

To find the final value requested by the question.

Anahtar Kavram

Solving linear equations in one variable by distributing constants, combining like terms, and evaluating expressions.

Soru 996Soru →

In the 1940s, geneticist Barbara McClintock conducted pioneering research on maize chromosomes, eventually discovering transposable elements—segments of DNA that can move within the genome. Although mainstream scientists initially dismissed her findings as anomalies, subsequent research in the 1960s and 1970s ______ her theories, ultimately leading to her receiving the Nobel Prize in Physiology or Medicine in 1983.

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

validates

validated

will validate

had validated

Cevabı ve açıklamayı göster

Cevap: validated

Cevap

validated

The correct answer is the simple past tense verb 'validated.' The passage establishes a past-tense temporal framework with verbs like 'conducted' and 'dismissed.' Since the action in the target clause occurred in a specific past period (the 1960s and 1970s), the simple past tense is required to maintain consistency with the rest of the timeline.

Adım Adım Çözüm

1

Identify the temporal framework of the sentence by looking at contextual clues.

The verbs 'conducted' and 'dismissed' indicate a past-tense timeline, and the specific timeframe 'in the 1960s and 1970s' refers to a completed period in the past.

This establishes that the verb filling the blank must be in the past tense.

2

Evaluate the options to find the correct past-tense verb form.

The simple past tense verb 'validated' correctly fits the sentence, whereas present, future, and past perfect tenses do not align chronologically.

The simple past tense is used for completed actions in the past, maintaining tense consistency.

Anahtar Kavram

Verb Tense Consistency

Tahmini Süre:1m 0s

Soru 997Soru →

In his influential mid-century essays, literary critic Northrop Frye argued that literature does not merely reflect the external world, but rather organizes human experience into coherent archetypal patterns. According to Frye, a literary work's significance is derived not from its correspondence to actual historical events, but from _______

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

relating the work to other works within the literary universe.

to relate the work to other works within the literary universe.

its relationship to other works within the literary universe.

how the work relates to other works within the literary universe.

Cevabı ve açıklamayı göster

Cevap: its relationship to other works within the literary universe.

Cevap

The correct option is the one that uses a parallel noun phrase structure: 'its relationship to other works within the literary universe.'

The correct answer maintains parallel structure by matching the noun phrase pattern of the first element in the comparison ('its correspondence to actual historical events'). The phrase starting with 'its relationship to other works' successfully uses a possessive pronoun followed by a noun and a prepositional phrase, aligning with the grammatical structure of the first compared element.

Adım Adım Çözüm

1

Identify the grammatical construction and the elements being compared or listed in the sentence.

The sentence uses the comparison structure 'derived not from [Element A], but from [Element B]'.

To satisfy the conventions of parallel structure, Element A and Element B must share the exact same grammatical form.

2

Analyze the grammatical structure of Element A.

Element A ('its correspondence to actual historical events') is a noun phrase composed of a possessive pronoun ('its'), a noun ('correspondence'), and a prepositional phrase ('to actual historical events').

Identifying the structure of the first element dictates the required structure of the second element.

3

Evaluate the choices to find the one that matches this noun phrase structure.

The phrase 'its relationship to other works within the literary universe' successfully matches the structure of possessive pronoun + noun + prepositional phrase.

Only this choice maintains the necessary parallelism to make the sentence grammatically correct.

Anahtar Kavram

Parallel Structure

Tahmini Süre:1m 30s

Soru 998Soru →

In the equation below, $c$ is a constant.

\frac{3c(2x - 1) - 2(x + 4c)}{5} = 2x - 3

If the equation has no solution for $x$ , what is the value of $c$ ?

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

The correct answer is 2.

To find the value of

c

that results in no solution, we first clear the fraction by multiplying both sides of the equation by 5, giving

3c(2x - 1) - 2(x + 4c) = 10x - 15

. Next, we expand the terms to get

6cx - 3c - 2x - 8c = 10x - 15

, and group the

x

terms and constant terms:

(6c - 2)x - 11c = 10x - 15

. For a linear equation to have no solution, the coefficients of

x

on both sides must be equal while the constant terms must be different. Setting the coefficients equal gives

6c - 2 = 10

, which solves to

c = 2

. Checking the constant terms when

c = 2

, we get

-11(2) = -22

on the left and

-15

on the right. Since

-22 \neq -15

, the equation has no solution, confirming

c = 2

is correct.

Adım Adım Çözüm

1

Multiply both sides of the equation by 5 to eliminate the denominator.

3c(2x - 1) - 2(x + 4c) = 10x - 15

Clearing the denominator simplifies the equation into standard polynomial terms.

2

Distribute the terms on the left side of the equation.

6cx - 3c - 2x - 8c = 10x - 15

Applying the distributive property expands the expression so terms can be grouped.

3

Group the

x

terms and constant terms on the left side.

(6c - 2)x - 11c = 10x - 15

Putting the equation in the standard form

Ax + B = Cx + D

allows us to easily set up the conditions for no solution.

4

Set the coefficients of

x

on both sides equal to each other.

6c - 2 = 10

, which simplifies to

6c = 12

, and thus

c = 2

.

For the equation to have no solution, the variable terms on both sides must cancel each other out.

5

Verify that the constant terms are not equal when

c = 2

.

The left-side constant is

-11(2) = -22

, and the right-side constant is

-15

. Since

-22 \neq -15

, the equation has no solution.

If the constant terms were equal, the equation would have infinitely many solutions instead of no solution.

Anahtar Kavram

Identifying conditions for a linear equation in one variable to have no solution.

Alternatif Yöntem

Instead of clearing the fraction first, write the left side of the equation as

(\frac{6c - 2}{5})x - \frac{11c}{5}

. For there to be no solution, the coefficient of

x

on the left side,

\frac{6c - 2}{5}

, must equal the coefficient of

x

on the right side, which is 2. Solving

\frac{6c - 2}{5} = 2

gives

6c - 2 = 10 \implies c = 2

.

Tahmini Süre:2m 30s

Soru 999Soru →

The following passage is about photosynthesis. Complete the passage by entering the punctuation mark that should replace the blank to correctly join the two independent clauses.

Aşağıdaki boşlukları doldurun

Photosynthesis is the process by which green plants convert light energy into chemical energy this biological pathway is essential for sustaining life on Earth.

Cevabı ve açıklamayı göster

Cevap

A semicolon (;), colon (:), or dash (—) can correctly join the two independent clauses.

A semicolon, colon, or em dash is correct because it successfully links two independent clauses without a coordinating conjunction. The first clause ('Photosynthesis is the process...') and the second clause ('this biological pathway is...') are both complete thoughts that can stand alone as sentences.

Adım Adım Çözüm

1

Analyze the clause preceding the blank.

The clause 'Photosynthesis is the process by which green plants convert light energy into chemical energy' is independent because it contains a subject and a verb and expresses a complete thought.

Identifying the clause structure is necessary to apply correct punctuation rules.

2

Analyze the clause following the blank.

The clause 'this biological pathway is essential for sustaining life on Earth' is also independent because it contains a subject and a verb and expresses a complete thought.

Establishing the relationship between the two clauses determines the valid punctuation options.

3

Select a punctuation mark that can link two independent clauses without a coordinating conjunction.

A semicolon, colon, or dash can be used to join the two independent clauses, whereas a comma alone cannot.

Joining two independent clauses directly requires a stronger mark of punctuation than a comma to avoid a comma splice.

Anahtar Kavram

Using semicolons, colons, or dashes to join independent clauses.

Soru 1000Soru →

In the 1940s, geneticist Barbara McClintock conducted pioneering research on the inheritance patterns of maize plants. Her work focused on transposons ______ which challenged the prevailing scientific consensus that genomes are rigid and unchanging. Although her findings were initially met with skepticism from the scientific community, McClintock's discoveries eventually earned her a Nobel Prize in 1983.

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

, genetic elements that can move to different positions within a genome—

—genetic elements that can move to different positions within a genome,

—genetic elements that can move to different positions within a genome—

, genetic elements that can move to different positions within a genome

Cevabı ve açıklamayı göster

Cevap: —genetic elements that can move to different positions within a genome—

Cevap

The choice that begins and ends the appositive phrase with matching em dashes is correct.

The correct choice uses a pair of matching em dashes to set off the nonessential appositive phrase 'genetic elements that can move to different positions within a genome'. In English grammar, nonessential elements must be set off from the rest of the sentence using matching punctuation marks, such as two commas, two em dashes, or parentheses.

Adım Adım Çözüm

1

Identify the nonessential element within the sentence structure.

The phrase 'genetic elements that can move to different positions within a genome' functions as an appositive that defines 'transposons' but is not essential to the main clause of the sentence.

Locating the boundaries of the nonessential element helps determine where punctuation must be placed.

2

Apply the punctuation rule for nonessential elements.

Nonessential elements must be set off by matching punctuation marks: either two commas, two em dashes, or parentheses.

Mixing different punctuation marks (such as a comma and an em dash) to set off a single phrase is grammatically incorrect.

3

Evaluate the punctuation pairs in the choices.

Only the option using matching em dashes on both sides of the appositive phrase maintains punctuation symmetry.

Selecting this option ensures the sentence conforms to Standard English conventions.

Anahtar Kavram

Punctuation of Nonessential Elements

Tahmini Süre:1m 0s

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

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Anahtar Kavram

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Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm