Tüm alıştırma soruları

A system of linear equations is shown below.

y = 2x - 7

3x - 2y = 11

What is the value of $x$ ?

8

-25

3

-3

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The correct value of

x

is 3.

The correct value of

x

is 3, which is found by substituting

2x - 7

for

y

in the second equation and solving for

x

.

Adım Adım Çözüm

1

Substitute the expression for

y

from the first equation into the second equation.

3x - 2(2x - 7) = 11

Since the first equation defines

y

in terms of

x

, substitution is a direct way to eliminate

y

and solve for

x

.

2

Distribute the

-2

to both terms inside the parentheses.

3x - 4x + 14 = 11

Applying the distributive property requires multiplying

-2

by both

2x

and

-7

, remembering that negative times negative is positive.

3

Combine the like terms on the left side of the equation.

-x + 14 = 11

Simplifying the expression by combining the

x

terms (

3x - 4x = -x

).

4

Isolate the variable term by subtracting 14 from both sides.

-x = -3

Using the subtraction property of equality to move the constant term to the right side.

5

Solve for

x

by multiplying or dividing both sides by

-1

.

x = 3

Finding the positive value of

x

.

Anahtar Kavram

Solving systems of linear equations using the substitution method.

Soru 1062Soru →

In the equation below,

p

and

q

are constants.

\frac{2}{p}(6x - 9) - \frac{3}{q}(4x + 2) = -2x - 9

If the equation has infinitely many solutions for

x

, what is the value of

p + q

?

1

5

9

-5

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

The value of

p+q

is

5

.

For the equation to have infinitely many solutions for

x

, the coefficients of

x

on both sides must be equal, and the constant terms on both sides must also be equal. Expanding the left side of the equation gives

\left(\frac{12}{p} - \frac{12}{q}\right)x - \left(\frac{18}{p} + \frac{6}{q}\right) = -2x - 9

. Equating the coefficients of

x

yields

\frac{12}{p} - \frac{12}{q} = -2

, which simplifies to

\frac{6}{p} - \frac{6}{q} = -1

. Equating the constant terms yields

-\frac{18}{p} - \frac{6}{q} = -9

, which simplifies to

\frac{18}{p} + \frac{6}{q} = 9

. Adding these two simplified equations eliminates the term with

q

, giving

\frac{24}{p} = 8

, which means

p = 3

. Substituting

p = 3

back into the first equation yields

2 - \frac{6}{q} = -1

, which simplifies to

\frac{6}{q} = 3

, meaning

q = 2

. Thus, the value of

p + q

is

3 + 2 = 5

.

Adım Adım Çözüm

1

Expand and group the terms on the left side of the equation.

\left(\frac{12}{p} - \frac{12}{q}\right)x - \left(\frac{18}{p} + \frac{6}{q}\right) = -2x - 9

To analyze the linear equation, we must group the coefficients of the variable

x

and the constant terms.

2

Set up a system of equations for

p

and

q

using the condition for infinitely many solutions.

\frac{12}{p} - \frac{12}{q} = -2

and

-\frac{18}{p} - \frac{6}{q} = -9

A linear equation in the form

Ax + B = Cx + D

has infinitely many solutions if and only if

A = C

and

B = D

.

3

Simplify the system of equations.

\frac{6}{p} - \frac{6}{q} = -1

(Equation 1) and

\frac{18}{p} + \frac{6}{q} = 9

(Equation 2)

Dividing Equation 1 by

2

and Equation 2 by

-1

simplifies the coefficients, making the system easier to solve.

4

Solve for

p

by adding Equation 1 and Equation 2.

\frac{24}{p} = 8 \implies p = 3

Adding the two equations eliminates the term containing

q

, allowing us to solve directly for

p

.

5

Substitute

p = 3

back into Equation 1 to solve for

q

.

\frac{6}{3} - \frac{6}{q} = -1 \implies 2 - \frac{6}{q} = -1 \implies \frac{6}{q} = 3 \implies q = 2

Using the value of

p

allows us to isolate and solve for

q

.

6

Calculate the sum of

p

and

q

.

p + q = 3 + 2 = 5

The question asks for the value of

p + q

.

Anahtar Kavram

Conditions for a linear equation in one variable to have infinitely many solutions, and solving systems of literal equations.

Soru 1063Soru →

A student is writing an essay about modern agricultural technology. Which word completes the passage so that it conforms to the conventions of Standard English and maintains a parallel structure?

Aşağıdaki boşlukları doldurun

In response to the challenges of traditional agriculture, researchers are developing modern vertical farming systems. These innovative indoor facilities are designed to conserve freshwater resources, reduce carbon emissions, and crop yields throughout the entire year. By stacking crops vertically and using controlled LED lighting, these systems optimize land use and minimize environmental impact.

Cevabı ve açıklamayı göster

Cevap

maximize (or a similar base verb such as increase, boost, improve, optimize, or enhance)

The sentence lists three functions of vertical farming systems following the phrase 'are designed to'. The first function is 'conserve' (a base verb) and the second is 'reduce' (also a base verb). To maintain a parallel grammatical structure, the third function must also be a base verb. Words such as 'maximize', 'increase', 'boost', or 'improve' maintain this parallel base verb form.

Adım Adım Çözüm

1

Identify the parallel elements in the sentence.

The sentence presents a list of three actions following the helping verb phrase 'are designed to'. The first two elements are the base verbs 'conserve' and 'reduce'.

Parallel structure requires that all items in a list or series share the same grammatical form.

2

Determine the grammatical form required for the blank.

To match the base verbs 'conserve' and 'reduce', the third element in the series must also be a base verb.

Using a non-base verb form would create faulty parallelism.

3

Select a base verb that logically fits the context of crop yields.

Verbs like 'maximize', 'increase', 'boost', 'improve', 'optimize', or 'enhance' fit both the grammatical constraint and the semantic context of agricultural productivity.

The correct word must be grammatically parallel and contextually logical.

Anahtar Kavram

Parallel Structure

Tahmini Süre:45s

Soru 1064Soru →

Although the behavior of an individual slime mold cell is relatively simple, a dispersed colony of these single-celled organisms, when searching for nutrient sources in dense forest undergrowth, displays a highly sophisticated collective intelligence that effectively allows _______ to navigate complex spatial obstacles and find the shortest path to food without any central leader.

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

them

they

it

their

Cevabı ve açıklamayı göster

Cevap: it

Cevap

The pronoun 'it' is correct because it agrees in number with the singular collective noun antecedent 'colony' and fits the objective case requirement.

The pronoun refers to the singular collective noun 'colony,' which is the antecedent. Although the plural noun 'organisms' is closer to the blank, it is part of the prepositional phrase 'of these single-celled organisms' modifying the main subject. Therefore, the singular pronoun 'it' is required to agree in number with the singular antecedent 'colony.' Additionally, 'it' is in the objective case, which correctly functions as the object of the verb 'allows.'

Adım Adım Çözüm

1

Identify the antecedent of the pronoun that needs to fill the blank.

The antecedent is the singular collective noun 'colony' (specifically 'a dispersed colony of these single-celled organisms').

Identifying the antecedent determines the required grammatical number (singular or plural) of the pronoun.

2

Identify and ignore intervening phrases that might distract from the true antecedent.

The prepositional phrase 'of these single-celled organisms' contains a plural noun, and the adverbial clause 'when searching for nutrient sources in dense forest undergrowth' is also intervening, but the main subject and true antecedent remains the singular noun 'colony.'

Intervening elements often contain plural nouns that can trick the reader into using a plural pronoun.

3

Determine the required grammatical case of the pronoun based on its role in the sentence.

The pronoun acts as the object of the verb 'allows,' which requires an objective case pronoun.

The pronoun must function correctly within the sentence structure (subject vs. object).

4

Evaluate the choices to find the singular objective pronoun.

Only 'it' is singular and in the objective case. The other options are either plural or possessive.

Selecting 'it' ensures grammatical correctness under Standard English conventions.

Anahtar Kavram

Pronoun-antecedent agreement in number requires a pronoun to match its antecedent's grammatical number, even when separated by intervening modifying phrases or clauses.

Soru 1065Soru →

A scientist is measuring the temperature of a sample that is being heated at a constant rate. At a starting time of $0$ minutes, the temperature of the sample is $12^\circ\text{C}$ . After $8$ minutes of heating, the temperature of the sample is $44^\circ\text{C}$ . If the temperature of the sample increases linearly with time, what is the temperature of the sample, in degrees Celsius, after $15$ minutes of heating?

Cevabı ve açıklamayı göster

Cevap: 72

Cevap

72

The rate of temperature change is

\frac{44 - 12}{8 - 0} = 4^\circ\text{C}

per minute. Using the slope-intercept form, the temperature

T

after

t

minutes can be represented by the function

T(t) = 4t + 12

. Substituting

15

for

t

yields

T(15) = 4(15) + 12 = 60 + 12 = 72

.

Adım Adım Çözüm

1

Calculate the constant rate of temperature change (slope).

4 degrees Celsius per minute

To find how much the temperature increases each minute, divide the total change in temperature by the total change in time:

\frac{44 - 12}{8 - 0} = \frac{32}{8} = 4

.

2

Set up the linear function for temperature

T(t)

over time

t

.

T(t) = 4t + 12

The initial temperature at

t = 0

is

12^\circ\text{C}

, which represents the vertical intercept. The constant rate of change is

4^\circ\text{C}

per minute.

3

Find the temperature at

t = 15

minutes.

72

Substitute

15

for

t

in the equation:

T(15) = 4(15) + 12 = 60 + 12 = 72

.

Anahtar Kavram

Linear Functions and Rates of Change

Tahmini Süre:1m 0s

Soru 1066Soru →

A line in the $xy$ -plane has a slope of $-3$ . The line passes through the point $(2, k)$ and has an $x$ -intercept of $(r, 0)$ , where $k$ and $r$ are constants. If $r + k = 10$ , what is the $y$ -intercept of the line?

(0, 4)

(0, 6)

(0, 10)

(0, 12)

Cevabı ve açıklamayı göster

Cevap: $(0, 12)$

Cevap

The y-intercept of the line is

(0, 12)

.

The correct answer is

(0, 12)

. By using the formula for slope

m = \frac{y_2 - y_1}{x_2 - x_1}

with the points

(2, k)

and

(r, 0)

, we obtain

-3 = \frac{k - 0}{2 - r}

. Multiplying both sides by

2 - r

gives

k = -3(2 - r)

, which simplifies to

k = -6 + 3r

, or

3r - k = 6

. We can solve this alongside the given equation

r + k = 10

by adding the two equations:

(3r - k) + (r + k) = 6 + 10 \implies 4r = 16

, which yields

r = 4

. Substituting

r = 4

back into the sum equation gives

k = 6

. Now, using the x-intercept point

(4, 0)

and the slope of

-3

, the equation of the line in point-slope form is

y - 0 = -3(x - 4)

, which simplifies to

y = -3x + 12

. The y-intercept of this line is found by setting

x = 0

, yielding

(0, 12)

.

Adım Adım Çözüm

1

Express the slope of the line using the coordinates of the two given points,

(2, k)

and the x-intercept

(r, 0)

.

Using the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

, we set up the equation:

-3 = \frac{k - 0}{2 - r}

.

This connects the geometric concept of slope to the algebraic coordinates of the points on the line.

2

Simplify the slope equation to relate

k

and

r

.

Multiplying both sides by

2 - r

gives

k = -3(2 - r) \implies k = -6 + 3r

, which can be rewritten as

3r - k = 6

.

Simplifying the equation makes it easier to solve as part of a system of linear equations.

3

Solve the system of equations consisting of

3r - k = 6

and the given equation

r + k = 10

.

Adding the two equations together:

(3r - k) + (r + k) = 6 + 10 \implies 4r = 16 \implies r = 4

. Substituting

r = 4

into

r + k = 10

gives

4 + k = 10 \implies k = 6

.

Solving the system of equations determines the numerical values of the constants

r

and

k

.

4

Find the equation of the line using the slope

m = -3

and the x-intercept

(4, 0)

, then determine the y-intercept.

Using point-slope form:

y - 0 = -3(x - 4) \implies y = -3x + 12

. The y-intercept occurs when

x = 0

, giving

y = 12

, which corresponds to the point

(0, 12)

.

Writing the full linear equation allows us to find the y-intercept by evaluating the function at

x = 0

.

Anahtar Kavram

Writing linear equations from given points and slope, and solving a system of linear equations to identify intercepts.

Tahmini Süre:2m 0s

Soru 1067Soru →

If $2x + 7 = 15$ , what is the value of $4x - 3$ ?

Cevabı ve açıklamayı göster

Cevap: 13

Cevap

13

To find the value of the expression, first solve the linear equation for the variable. Subtracting 7 from both sides of the equation yields

2x = 8

. Dividing both sides of the equation by 2 yields

x = 4

. Substituting this value back into the expression yields

4(4) - 3 = 16 - 3 = 13

. Alternatively, since

2x = 8

, multiplying both sides by 2 gives

4x = 16

. Subtracting 3 from both sides of this relation yields

4x - 3 = 16 - 3 = 13

.

Adım Adım Çözüm

1

Subtract 7 from both sides of the equation

2x = 8

To isolate the variable term on one side of the equation

2

Divide both sides by 2

x = 4

To solve for the variable

3

Substitute the value of the variable into the target expression

13

To find the final evaluated value requested by the question

Anahtar Kavram

Solving a linear equation in one variable and evaluating an expression

Soru 1068Soru →

Although neither of the newly discovered deep-sea hydrothermal vents in the Mariana Trench has been fully mapped by marine geologists, ______ unique chemical composition has already provided researchers with invaluable insights into the ecological limits of microbial life on Earth. These findings could help astrobiologists understand potential habitability on icy moons.

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

its

their

they're

it's

Cevabı ve açıklamayı göster

Cevap: its

Cevap

its

The correct pronoun is 'its' because it is a singular possessive pronoun that agrees in number with the singular indefinite pronoun 'neither', which acts as the antecedent. The plural noun 'vents' is part of an intervening prepositional phrase and does not determine the number of the pronoun.

Adım Adım Çözüm

1

Identify the antecedent of the pronoun to be placed in the blank.

The antecedent is the singular indefinite pronoun 'neither'.

The pronoun must agree in number with its true grammatical antecedent.

2

Identify and eliminate intervening words or phrases.

The plural prepositional phrase 'of the newly discovered deep-sea hydrothermal vents in the Mariana Trench' is an intervening element that does not affect the number of the antecedent.

This prevents the common error of matching the pronoun to a nearby plural noun instead of the subject.

3

Select the grammatically correct pronoun.

The singular possessive pronoun 'its' matches the singular antecedent 'neither' and correctly functions as a determiner for 'unique chemical composition'.

This satisfies both pronoun-antecedent agreement and case requirements.

Anahtar Kavram

Pronoun-Antecedent Agreement and Case

Tahmini Süre:1m 0s

Soru 1069Soru →

Although modern astronomers utilize advanced digital imaging to map the Martian surface, nineteenth-century researchers relied entirely on direct optical observations. By the time the Mariner 4 spacecraft returned the first close-up images of Mars in 1965, astronomers _______ hundreds of maps detailing what they mistakenly believed were artificial canals, sparking decades of scientific speculation.

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

have published

had published

published

will publish

Cevabı ve açıklamayı göster

Cevap: had published

Cevap

The correct verb form is 'had published', which uses the past perfect tense to indicate that the maps were created and completed before the 1965 Mariner 4 mission.

The correct answer is the past perfect verb form 'had published'. The sentence introduces a sequence of events where one action (the publishing of the maps) was completed prior to another past action (the return of the spacecraft's photos in 1965). According to the rules of Standard English conventions, the past perfect tense is required to show this relationship when introduced by phrases like 'By the time'.

Adım Adım Çözüm

1

Identify the overall temporal framework of the sentence.

The text describes historical events, utilizing past-tense verbs like 'relied' and 'returned' along with the time marker '1965'.

This establishes that the target verb must exist within a past temporal framework.

2

Determine the relationship between the two events in the second sentence.

The subordinating conjunction phrase 'By the time' indicates that the action in the blank was completed before the main action ('returned') occurred.

When describing an action that was completed prior to another past action, the past perfect tense (had + past participle) must be used.

3

Identify the past perfect form among the choices.

The past perfect form of the verb 'publish' is 'had published'.

This form correctly conveys the proper temporal sequence and adheres to Standard English conventions.

Anahtar Kavram

Verb Tense, Aspect, and Mood

Tahmini Süre:1m 0s

Soru 1070Soru →

A chemist mixes two saline solutions. Solution A is $12\%$ salt by mass, and Solution B is $30\%$ salt by mass. The mass of Solution B used in the mixture is 20 grams more than $\frac{1}{3}$ of the mass of Solution A used. If the resulting mixture is $18\%$ salt by mass, what is the mass, in grams, of Solution A used?

Cevabı ve açıklamayı göster

Cevap: 120

Cevap

The mass of Solution A used is 120 grams.

The correct answer is 120. By setting the mass of Solution A to

x

, the mass of Solution B is

\frac{1}{3}x + 20

. Equating the total salt content from both individual solutions to the total salt content of the final mixture gives the linear equation

0.12x + 0.30\left(\frac{1}{3}x + 20\right) = 0.18\left(x + \frac{1}{3}x + 20\right)

. Simplifying both sides yields

0.22x + 6 = 0.24x + 3.6

. Solving this equation gives

0.02x = 2.4

, which simplifies to

x = 120

.

Adım Adım Çözüm

1

Define the variable

x

as the mass, in grams, of Solution A used in the mixture, and express the mass of Solution B in terms of

x

.

Mass of Solution A =

x

grams; Mass of Solution B =

\frac{1}{3}x + 20

grams.

To set up expressions representing the mass of each solution in the mixture.

2

Calculate the mass of salt contributed by each solution and write an expression for the total mass of salt.

Salt from Solution A =

0.12x

grams; Salt from Solution B =

0.30\left(\frac{1}{3}x + 20\right) = 0.10x + 6

grams; Total salt =

0.22x + 6

grams.

To find the total amount of salt before mixing.

3

Express the total mass of the mixture and the total salt content using the final mixture's percentage.

Total mass of mixture =

\frac{4}{3}x + 20

grams; Total salt in final mixture =

0.18\left(\frac{4}{3}x + 20\right) = 0.24x + 3.6

grams.

To write the total salt content in terms of the final mixture's concentration.

4

Equate the two expressions for the total mass of salt and solve the linear equation for

x

.

0.22x + 6 = 0.24x + 3.6 \implies 2.4 = 0.02x \implies x = 120

.

To find the mass of Solution A that satisfies the mixture conditions.

Anahtar Kavram

Setting up and solving a linear equation in one variable from a mixture word problem.

Soru 1071Soru →

In 1901, sponge divers recovering artifacts from a shipwreck near the Greek island of Antikythera salvaged a heavily corroded bronze device containing dozens of interlocking gearwheels. Modern historians believe the mechanism was a sophisticated astronomical calculator. The device_______could predict the positions of the sun, moon, and planets decades into the future.

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

—which was capable of tracking complex celestial cycles,

, which was capable of tracking complex celestial cycles—

—which was capable of tracking complex celestial cycles—

which was capable of tracking complex celestial cycles,

Cevabı ve açıklamayı göster

Cevap: —which was capable of tracking complex celestial cycles—

Cevap

The option containing '—which was capable of tracking complex celestial cycles—' is correct because it sets off the nonessential relative clause with matching em dashes.

The correct answer correctly uses matching em dashes to enclose the nonessential relative clause. Nonessential relative clauses must be separated from the main clause by matching punctuation marks, such as a pair of commas or a pair of em dashes.

Adım Adım Çözüm

1

Identify the nonessential relative clause in the sentence.

The clause 'which was capable of tracking complex celestial cycles' is nonessential because the main clause remains grammatically complete and retains its core meaning without it.

Nonessential elements must be set off from the rest of the sentence with punctuation.

2

Check for punctuation consistency around the nonessential clause.

Standard English conventions require that punctuation setting off a nonessential element must be symmetrical (two commas, two parentheses, or two em dashes). Only one option uses matching em dashes to open and close the clause.

Mixing punctuation marks, such as a comma and an em dash, violates grammatical conventions.

Anahtar Kavram

Punctuation of Nonessential Elements

Tahmini Süre:1m 0s

Soru 1072Soru →

The passage below contains a blank. Based on the rules of Standard English conventions, which punctuation mark should fill the blank to correctly set off the nonessential element?

Aşağıdaki boşlukları doldurun

In the 1940s, geneticist Barbara McClintock studied maize plants to understand inheritance patterns. Her research on transposons, which are genetic elements that can change positions within a genome ultimately challenged the prevailing scientific belief that genes were fixed in place on chromosomes.

Cevabı ve açıklamayı göster

Cevap

A comma (,) must be placed in the blank to complete the punctuation pair setting off the nonessential element.

The sentence contains the nonessential relative clause 'which are genetic elements that can change positions within a genome,' which modifies the noun 'transposons.' Standard English conventions require nonessential elements to be set off by matching pairs of punctuation. Because the clause is introduced with a comma after 'transposons,' it must close with a matching comma after 'genome' before the sentence continues with the main verb 'ultimately.'

Adım Adım Çözüm

1

Identify the nonessential element in the sentence.

The clause 'which are genetic elements that can change positions within a genome' is a nonessential relative clause modifying the noun 'transposons'.

This clause provides descriptive details about transposons but is not grammatically necessary for the main clause of the sentence.

2

Examine the punctuation currently used to introduce the nonessential element.

The nonessential clause begins with a comma after the word 'transposons'.

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

3

Determine the punctuation required to close the nonessential element.

A comma is required in the blank to match the opening comma.

Using any other punctuation mark, such as an em dash or parenthesis, would create asymmetrical punctuation, violating Standard English conventions.

Anahtar Kavram

Punctuation of Nonessential Elements

Soru 1073Soru →

Many species of bamboo grow at an astonishingly rapid rate_______ others take years to reach their full height.

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

rate; others

rate, others

rate: others

rate; although others

Cevabı ve açıklamayı göster

Cevap: rate; others

Cevap

rate; others

The correct option uses a semicolon to join two independent clauses ('Many species of bamboo grow at an astonishingly rapid rate' and 'others take years to reach their full height') without a coordinating conjunction. This conforms to Standard English punctuation rules.

Adım Adım Çözüm

1

Identify the clause boundaries around the blank.

The sentence contains two clauses: 'Many species of bamboo grow at an astonishingly rapid rate' and 'others take years to reach their full height.' Both are independent clauses because they can stand alone as complete sentences.

Determining the grammatical status of the clauses helps identify the correct punctuation rule.

2

Evaluate the punctuation options to connect these two independent clauses.

A semicolon is the correct punctuation to join two closely related independent clauses. A comma alone creates a comma splice, a colon is incorrect because the second clause does not explain or expand on the first, and a semicolon cannot be used if the second clause becomes dependent due to a subordinating conjunction.

Applying the rules of punctuation ensures the sentence conforms to Standard English conventions.

Anahtar Kavram

Using semicolons to connect independent clauses

Tahmini Süre:45s

Soru 1074Soru →

For the linear function $f$ , the table below displays selected values of $x$ and their corresponding function values $f(x)$ .

$x$	$f(x)$
$-2$	$1$
$2$	$9$
$4$	$13$

What is the value of $f(10)$ ?

Cevabı ve açıklamayı göster

Cevap: 25

Cevap

The value of

f(10)

is 25.

The correct answer is 25. By using the points

(-2, 1)

and

(2, 9)

, the slope of the linear function is calculated as

m = \frac{9 - 1}{2 - (-2)} = 2

. Substituting this slope and the point

(2, 9)

into the slope-intercept form,

f(x) = 2x + b

, gives

9 = 2(2) + b

, which resolves to

b = 5

. Thus, the linear function is defined by

f(x) = 2x + 5

. Evaluating the function at

x = 10

yields

f(10) = 2(10) + 5 = 25

.

Adım Adım Çözüm

1

Calculate the slope of the linear function using two coordinate pairs.

Slope

m = 2

The slope of a linear function can be determined by the formula

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

. Substituting

(-2, 1)

and

(2, 9)

yields

m = \frac{9 - 1}{2 - (-2)} = \frac{8}{4} = 2

.

2

Find the y-intercept of the function to write its equation.

f(x) = 2x + 5

Substituting the slope

m = 2

and the point

(2, 9)

into the slope-intercept form

f(x) = mx + b

gives

9 = 2(2) + b

, which simplifies to

b = 5

.

3

Evaluate the function for the input value 10.

f(10) = 25

Substituting

x = 10

into the linear function equation

f(x) = 2x + 5

yields

f(10) = 2(10) + 5 = 25

.

Anahtar Kavram

Determining a linear function from a table of values and using it to find specific outputs.

Tahmini Süre:1m 30s

Soru 1075Soru →

The following passage is from an academic text about animal behavior. Which pronoun or noun correctly completes the sentence to establish proper subject-modifier agreement? Fill in the blank with the correct word or phrase.

Aşağıdaki boşlukları doldurun

French biologist Karl von Frisch spent decades studying the communication patterns of honeybees. By translating their complex 'waggle dance' into spatial coordinates, demonstrated that insects possess a sophisticated form of symbolic communication.

Cevabı ve açıklamayı göster

Cevap

The correct answer is the pronoun 'he' or the proper noun 'Karl von Frisch' (or 'the biologist' / 'the scientist').

The introductory modifying phrase 'By translating their complex "waggle dance" into spatial coordinates' describes an action that must be performed by a logical agent. The only logical agent in the context is the biologist Karl von Frisch. Therefore, the subject of the main clause must be a pronoun or noun referring to him (such as 'he', 'Karl von Frisch', or 'the biologist').

Adım Adım Çözüm

1

Identify the introductory modifying phrase and determine its logical subject.

The modifying phrase 'By translating their complex "waggle dance" into spatial coordinates' describes an action.

The subject immediately following the modifier must be the entity performing the action of translating.

2

Select the correct noun or pronoun based on the context.

Since Karl von Frisch is the biologist who performed the research, the subject must refer to him, resulting in the pronoun 'he' or the noun 'Karl von Frisch'.

This establishes correct subject-modifier agreement and avoids a dangling modifier.

Anahtar Kavram

Subject-Modifier Agreement

Soru 1076Soru →

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

Aşağıdaki boşlukları doldurun

In his influential treatise on modern urban development, architectural theorist Marcus Giamatti argues that creating a truly sustainable skyscraper requires focusing less on installing complex, high-tech energy-monitoring systems than on passive design strategies. By prioritizing simple architectural solutions like solar orientation and natural cross-ventilation over mechanical ones, architects can drastically lower a building’s operational footprint while maintaining occupant comfort.

Cevabı ve açıklamayı göster

Cevap

A gerund (such as 'implementing', 'utilizing', or 'employing') to maintain parallel structure with the gerund 'installing' following the preposition 'on'.

The sentence uses the comparative structure 'focusing less on [X] than on [Y]'. The first element (X) is 'installing complex, high-tech energy-monitoring systems', where 'installing' is a gerund. To maintain parallel structure, the second element (Y) must also begin with a gerund that takes 'passive design strategies' as its direct object. A gerund like 'implementing' or 'utilizing' perfectly fits this grammatical pattern.

Adım Adım Çözüm

1

Identify the comparative structure in the sentence.

The sentence uses the comparative structure 'focusing less on [X] than on [Y]'.

This structure requires the elements X and Y to be grammatically parallel.

2

Analyze the grammatical form of the first element (X).

The phrase following the first 'on' begins with the gerund 'installing' ('installing complex, high-tech energy-monitoring systems').

Understanding the part of speech of the first element establishes the pattern for the second.

3

Determine the required grammatical form for the second element (Y) in the blank.

The phrase following the second 'on' must also begin with a gerund (an -ing verb acting as a noun) to remain parallel.

Using any other form (such as an infinitive or a noun phrase) would violate parallel structure rules.

Anahtar Kavram

Parallel Structure

Tahmini Süre:1m 30s

Soru 1077Soru →

Discovered in the late twentieth century, deep-sea hydrothermal vents support complex ecosystems that thrive in complete darkness, far beyond the reach of solar radiation. Rather than utilizing photosynthesis to produce food, the diverse organisms inhabiting these extreme environments rely on a process known as chemosynthesis ______ specialized bacteria oxidize toxic hydrogen sulfide dissolved in the geothermal fluids, thereby generating the organic carbon that sustains the entire local food web.

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

chemosynthesis, specialized

chemosynthesis specialized

chemosynthesis: specialized

chemosynthesis, but specialized

Cevabı ve açıklamayı göster

Cevap: chemosynthesis: specialized

Cevap

The correct choice is the option that uses a colon to separate the two independent clauses, as the second clause explains the process of chemosynthesis introduced in the first clause.

The correct choice is the option that uses a colon to separate the two independent clauses. The clause before the blank and the clause after the blank are both independent. A colon is grammatically correct here because the second clause directly explains and details the concept of chemosynthesis mentioned in the first clause.

Adım Adım Çözüm

1

Identify the clause boundaries and determine if the clauses on either side of the blank are independent.

The clause before the blank contains a subject ('organisms') and a verb ('rely') and constitutes a complete thought. The clause after the blank also contains a subject ('bacteria') and a verb ('oxidize') and constitutes a complete thought. Both are independent clauses.

Determining the grammatical independence of the clauses dictates the types of punctuation or conjunctions allowed to join them.

2

Analyze the logical relationship between the first and second independent clauses.

The second clause explains the chemical process that defines 'chemosynthesis' mentioned at the end of the first clause.

Understanding how the two ideas connect determines which transitional punctuation mark or coordinating conjunction is appropriate.

3

Evaluate the grammar of the choices to select the one that correctly links the clauses.

Using a colon is correct because a colon can link two independent clauses when the second explains, illustrates, or expands on the first. Other choices result in a comma splice, a run-on, or a logical contradiction.

Only one choice successfully links the clauses grammatically and logically without violating Standard English conventions.

Anahtar Kavram

Connecting independent clauses using a colon when the second clause explains or illustrates the first.

Tahmini Süre:1m 15s

Soru 1078Soru →

If $\frac{5}{6}(y - 2) - \frac{1}{3}(2y - 5) = \frac{3}{2}$ , what is the value of $4y$ ?

Cevabı ve açıklamayı göster

Cevap: 36

Cevap

The correct answer is 36.

To solve the equation

\frac{5}{6}(y - 2) - \frac{1}{3}(2y - 5) = \frac{3}{2}

, we first clear the fractions by multiplying the entire equation by the least common denominator, 6, which yields

5(y - 2) - 2(2y - 5) = 9

. Distributing the terms on the left side gives

5y - 10 - 4y + 10 = 9

. Combining like terms simplifies this to

y = 9

. The question asks for the value of

4y

, so we multiply

9

by

4

to get the final answer of

36

.

Adım Adım Çözüm

1

Multiply both sides of the equation by the least common denominator, which is 6.

5(y - 2) - 2(2y - 5) = 9

Multiplying by 6 eliminates the fractions, simplifying the equation.

2

Distribute the coefficients across the parentheses.

5y - 10 - 4y + 10 = 9

Expanding the terms allows like terms to be combined in the next step.

3

Combine the variable terms and constant terms on the left side of the equation.

y = 9

Combining

5y - 4y

yields

y

, and combining

-10 + 10

yields

0

, isolating the variable.

4

Multiply the value of

y

by 4.

4y = 36

The question asks for the value of

4y

rather than just

y

.

Anahtar Kavram

Solving a linear equation in one variable by clearing fractions and combining like terms.

Soru 1079Soru →

To reduce environmental waste and reliance on fossil fuels, chemical engineers are developing bioplastics made from plant starches like corn and sugarcane. In recent laboratory tests, these bio-based alternatives have shown great promise because they are designed to decompose quickly under compost conditions, release fewer greenhouse gases during their production, and _______

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

leave no toxic residue in the surrounding soil

leaving no toxic residue in the surrounding soil

they leave no toxic residue in the surrounding soil

the avoidance of leaving toxic residue in the surrounding soil

Cevabı ve açıklamayı göster

Cevap: leave no toxic residue in the surrounding soil

Cevap

leave no toxic residue in the surrounding soil

The correct option is 'leave no toxic residue in the surrounding soil' because it uses the base verb 'leave,' which maintains the parallel structure established by the other verbs in the series, 'decompose' and 'release.' All three verbs function as infinitives controlled by the helper phrase 'are designed to' ('are designed to decompose... [to] release... and [to] leave...').

Adım Adım Çözüm

1

Identify the grammatical structure of the listed items preceding the conjunction 'and'.

The sentence lists three characteristics: 'decompose quickly under compost conditions' and 'release fewer greenhouse gases during their production.' Both are base verbs controlled by the phrase 'are designed to'.

To maintain parallel structure, the final item in the list must also be a base verb phrase.

2

Evaluate the choices to find the one that begins with a base verb matching 'decompose' and 'release'.

The phrase beginning with 'leave' is the only choice that matches this grammatical pattern.

Selecting this option ensures the sentence conforms to parallel structure.

Anahtar Kavram

Parallel structure requires that items in a list or comparison maintain a consistent grammatical form.

Tahmini Süre:1m 0s

Soru 1080Soru →

A line in the $xy$ -plane is defined by the equation $5y - 2x = 15$ . What is the slope of the line?

\frac{5}{2}

-\frac{2}{5}

\frac{2}{5}

3

Cevabı ve açıklamayı göster

Cevap: $\frac{2}{5}$

Cevap

The slope of the line is

\frac{2}{5}

.

To find the slope of the line, convert the equation

5y - 2x = 15

into slope-intercept form,

y = mx + b

, where

m

represents the slope. First, add

2x

to both sides to get

5y = 2x + 15

. Next, divide both sides by

5

to isolate

y

, yielding

y = \frac{2}{5}x + 3

. In this form, the coefficient of

x

is the slope, which is

\frac{2}{5}

.

Adım Adım Çözüm

1

Write the given equation of the line.

5y - 2x = 15

To identify the slope, we need to manipulate the given equation.

2

Isolate the

y

term on one side by adding

2x

to both sides.

5y = 2x + 15

This is the first step in converting the equation to slope-intercept form (

y = mx + b

).

3

Divide both sides of the equation by

5

to solve for

y

.

y = \frac{2}{5}x + 3

Dividing isolates

y

completely, putting the equation in the form

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

4

Identify the slope

m

from the equation.

The slope

m

is

\frac{2}{5}

.

In the equation

y = \frac{2}{5}x + 3

, the coefficient of

x

represents the slope of the line.

Anahtar Kavram

Slope of a line from its equation

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