Tüm alıştırma soruları

2789 soru

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Complete the passage by writing the appropriate punctuation mark(s) in the blank to set off the nonessential element.

Aşağıdaki boşlukları doldurun

To evaluate the long-term efficacy of the urban revitalization project, researchers conducted a multi-year analysis of local economic indicators. Though the group’s initial reports focused on the fiscal impact of the policy, the committee’s final report—which synthesized data from three separate pilot programs, including the controversial municipal transit initiativeoffered a far more comprehensive analysis of the social outcomes.

Cevabı ve açıklamayı göster

Cevap

An em dash (—)

The correct punctuation is an em dash (—) because the nonessential relative clause beginning with 'which synthesized data' is introduced by an em dash after 'report'. To maintain grammatical symmetry, the clause must also be closed with an em dash before the main verb 'offered'.

Adım Adım Çözüm

Identify the subject and main verb of the principal clause in the second sentence.

The subject is 'the committee’s final report' and the main verb is 'offered'.

Understanding the core sentence structure helps isolate any intervening nonessential elements.

Examine the grammatical nature of the intervening clause starting with 'which synthesized data'.

The clause 'which synthesized data... municipal transit initiative' is a nonessential relative clause modifying 'the committee’s final report'.

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

Locate the punctuation mark used to introduce the nonessential relative clause.

An em dash (—) immediately follows the subject 'report'.

Punctuation setting off nonessential elements must be symmetrical.

Select the punctuation mark that matches the opening em dash to close the nonessential clause before the main verb.

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

A matching em dash is required to maintain punctuation symmetry, closing the parenthetical information without causing grammatical asymmetry.

Anahtar Kavram

Punctuation of Nonessential Elements

Soru 882Soru →

In 2021, geologist Dr. Elena Vance led an expedition to retrieve mineral samples from the remote floor of the Mariana Trench. Using a high-resolution scanning electron microscope to examine the specimen, _______

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

unusual crystalline structures were identified by Dr. Vance that suggest past hydrothermal activity.

the identification of unusual crystalline structures suggesting past hydrothermal activity was made by Dr. Vance.

Dr. Vance identified unusual crystalline structures that suggest past hydrothermal activity.

unusual crystalline structures suggesting past hydrothermal activity revealed themselves to Dr. Vance.

Cevabı ve açıklamayı göster

Cevap: Dr. Vance identified unusual crystalline structures that suggest past hydrothermal activity.

Cevap

Dr. Vance identified unusual crystalline structures that suggest past hydrothermal activity.

The introductory modifying phrase 'Using a high-resolution scanning electron microscope to examine the specimen' describes an action that must be performed by a person. The option beginning with 'Dr. Vance' correctly places the logical subject immediately after the comma, ensuring clear and conventional sentence structure.

Adım Adım Çözüm

Analyze the introductory modifying phrase to determine its logical subject.

The phrase is 'Using a high-resolution scanning electron microscope to examine the specimen.' The logical agent performing this action must be a person, specifically Dr. Vance.

An introductory modifier must describe the subject of the main clause that follows it.

Select the option that places the logical subject immediately after the modifying phrase.

The correct option starts with 'Dr. Vance,' making her the grammatical subject of the sentence.

This positioning satisfies the rule of subject-modifier agreement and prevents a dangling modifier.

Anahtar Kavram

Subject-Modifier Agreement

Soru 883Soru →

Having analyzed the chemical composition of the glaze on the earthenware fragments excavated at the ancient Roman site, _______

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

archaeologists determined that the clay had been sourced from a local volcanic deposit.

the pottery fragments revealed to researchers that the clay had been sourced from a local volcanic deposit.

it was determined by archaeologists that the clay had been sourced from a local volcanic deposit.

the analysis conducted by archaeologists suggested that the clay had been sourced from a local volcanic deposit.

Cevabı ve açıklamayı göster

Cevap: archaeologists determined that the clay had been sourced from a local volcanic deposit.

Cevap

archaeologists determined that the clay had been sourced from a local volcanic deposit.

The introductory modifying phrase 'Having analyzed the chemical composition of the glaze...' describes an action. The noun immediately following the comma must be the entity that performed this action. Since archaeologists are the ones who conducted the analysis, the clause must begin with 'archaeologists.' This structure ensures correct subject-modifier agreement.

Adım Adım Çözüm

Identify the introductory modifying phrase and determine the entity performing the action.

The phrase is 'Having analyzed the chemical composition of the glaze...', which represents an action that requires a conscious agent (the analyzer).

Understanding the function of the modifier allows us to identify the logical subject.

Evaluate the choices to find which one puts the logical subject immediately after the modifier.

Only the option starting with 'archaeologists' correctly places the logical agent directly after the comma.

This positioning avoids a dangling or misplaced modifier error.

Anahtar Kavram

Subject-Modifier Agreement

Soru 884Soru →

In 1915, amateur astronomer George Willis Ritchey designed a new type of reflecting telescope that utilized a hyperbolic primary mirror. This innovative configuration ______ eliminated the optical aberration known as coma, which had long plagued traditional Newtonian reflectors and limited the clarity of deep-sky astrophotography. Today, nearly all major research installations, including the Hubble Space Telescope, rely on this design to capture high-resolution images of distant galaxies.

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

—a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope,

—a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope—

, a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope—

, a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope

Cevabı ve açıklamayı göster

Cevap: —a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope—

Cevap

The correct choice is the option that sets off the nonessential appositive phrase with a matching pair of em dashes.

The correct choice uses matching em dashes at both the beginning and the end of the nonessential appositive phrase. This maintains punctuation symmetry and grammatically isolates the descriptive details from the main independent clause.

Adım Adım Çözüm

Identify the core grammatical structure of the sentence.

The core sentence is 'This innovative configuration eliminated the optical aberration...', with a modifying phrase inserting information about the configuration's design history.

Determining what is essential to the sentence's grammatical structure helps identify if the intervening phrase is nonessential.

Determine if the modifying phrase is essential or nonessential.

The phrase 'a design later refined by French astronomer Henri Chrétien and known as the Ritchey-Chrétien telescope' is parenthetical and can be removed without changing the core meaning or syntax of the main clause; it is therefore nonessential.

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

Evaluate the options for punctuation symmetry.

Only the option using matching em dashes on both sides of the nonessential phrase maintains grammatical symmetry and correctly isolates the appositive.

Standard English conventions require consistent opening and closing punctuation marks to isolate nonessential parenthetical elements.

Anahtar Kavram

Nonessential elements (such as appositives, parenthetical phrases, or nonrestrictive clauses) must be set off from the rest of the sentence using matching punctuation marks on both sides. Mixing punctuation marks (e.g., starting with a comma and ending with a dash) is grammatically incorrect.

Tahmini Süre:1m 0s

Soru 885Soru →

If $2(3x - 4) - 5(x - 1) = 3(x + 2) - 1$ , what is the value of $2x + 3$ ?

-15

-5

Cevabı ve açıklamayı göster

Cevap: -5

Cevap

The correct answer is

-5

Solving the given equation step-by-step yields

x = -4

. Substituting

x = -4

into the expression

2x + 3

results in

2(-4) + 3 = -5

Adım Adım Çözüm

Distribute the values outside the parentheses on both sides of the equation.

6x - 8 - 5x + 5 = 3x + 6 - 1

This step removes parentheses so that like terms can be combined.

Combine like terms on each side of the equation.

x - 3 = 3x + 5

Simplifying both sides makes it easier to isolate the variable.

Isolate the variable

x

by subtracting

x

and

5

from both sides.

x = -4

This determines the value of

x

which is required to evaluate the final expression.

Substitute the value of

x

into the expression

2x + 3

2(-4) + 3 = -5

This calculates the final value requested by the question.

Anahtar Kavram

Solving linear equations in one variable involving parentheses and distributing terms.

Soru 886Soru →

In 2006, the International Astronomical Union officially reclassified Pluto as a dwarf planet. This decision ______ sparked widespread debate among scientists and the public alike, many of whom had grown fond of the distant icy world. Ultimately, the reclassification helped astronomers establish a clearer definition for what constitutes a true planet in our solar system.

Which choice completes the text with the most logical and grammatically correct punctuation?

, which altered our understanding of the solar system—

—which altered our understanding of the solar system—

—which altered our understanding of the solar system,

which altered our understanding of the solar system—

Cevabı ve açıklamayı göster

Cevap: —which altered our understanding of the solar system—

Cevap

The phrase starting with an em dash and ending with an em dash correctly punctuates the nonessential relative clause.

The correct answer correctly uses matching em dashes to set off the nonessential relative clause, which is necessary to maintain punctuation symmetry in the sentence.

Adım Adım Çözüm

Identify the nonessential element in the target sentence.

The clause 'which altered our understanding of the solar system' is nonessential because removing it leaves the main sentence grammatically complete and coherent.

Nonessential elements must be set off from the rest of the sentence using matching punctuation marks.

Evaluate the punctuation surrounding the nonessential element in the options.

To correctly set off the clause, the punctuation marks at the start and the end must match (e.g., two commas, two em dashes, or parentheses).

Mixing different punctuation marks (such as a comma and an em dash) creates grammatically incorrect asymmetry.

Select the option that uses a matching pair of punctuation marks.

The option that begins and ends the clause with an em dash is the only choice that maintains punctuation symmetry.

This correctly integrates the nonessential clause into the sentence without creating structural asymmetry.

Anahtar Kavram

Punctuation of Nonessential Elements

Soru 887Soru →

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

Aşağıdaki boşlukları doldurun

Albert Einstein is widely known for his theory of relativity, but his contributions to quantum mechanics were also monumental. Having explained the photoelectric effect in 1905, was awarded the Nobel Prize in Physics in 1921.

Cevabı ve açıklamayı göster

Cevap

he (or Einstein / Albert Einstein / the physicist / the scientist)

The correct answer provides a subject (such as 'he' or 'Einstein') that directly performs the action of the introductory modifier 'Having explained the photoelectric effect in 1905.' This alignment maintains grammatical coherence and avoids a dangling modifier.

Adım Adım Çözüm

Identify the introductory modifying phrase in the sentence.

The modifying phrase is 'Having explained the photoelectric effect in 1905,' which is a participial phrase.

To ensure correct modifier agreement, the noun or pronoun immediately following the comma must be the logical subject performing the action in the modifying phrase.

Determine the logical subject of the modifying phrase.

The person who explained the photoelectric effect in 1905 is Albert Einstein.

Since Einstein is the one who performed the action, the main clause must start with a subject that refers to him (such as 'he' or 'Einstein') rather than an inanimate object or a different person.

Fill in the blank with the appropriate subject pronoun or name.

Using 'he' or 'Einstein' establishes a clear and grammatically correct connection, avoiding a dangling modifier.

This aligns the modifier directly with its logical subject, satisfying standard English conventions.

Anahtar Kavram

Subject-Modifier Agreement

Tahmini Süre:1m 0s

Soru 888Soru →

Consider the system of equations below.

y = 3x - 4

x + y = 8

What is the value of $x$ ?

3

5

1

2

Cevabı ve açıklamayı göster

Cevap: $3$

Cevap

The value of

x

3

To solve the system, substitute the value of

y

from the first equation into the second equation:

x + (3x - 4) = 8

. Combining the

x

terms gives

4x - 4 = 8

. Adding

4

to both sides of the equation results in

4x = 12

. Dividing both sides by

4

isolates the variable, giving

x = 3

Adım Adım Çözüm

Substitute the expression for

y

from the first equation into the second equation.

x + (3x - 4) = 8

This eliminates the variable

y

to create a single equation in terms of

x

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

4x - 4 = 8

Grouping the

x

variables simplifies the expression.

Add

4

to both sides of the equation to isolate the term with

x

4x = 12

Performing the inverse operation of subtraction isolates the variable term.

Divide both sides of the equation by

4

to solve for

x

x = 3

Performing the inverse operation of multiplication isolates the variable

x

Anahtar Kavram

Solving a system of linear equations using the substitution method.

Soru 889Soru →

If $(x, y)$ is the solution to the system of equations below, what is the value of $x$ ?

y = 2x + 1

3x + 2y = 16

Cevabı ve açıklamayı göster

Cevap: 2

Cevap

The correct answer is 2.

Substituting

y = 2x + 1

into the second equation yields

3x + 2(2x + 1) = 16

. Expanding this expression gives

3x + 4x + 2 = 16

, which simplifies to

7x + 2 = 16

. Subtracting 2 from both sides gives

7x = 14

, and dividing by 7 yields

x = 2

Adım Adım Çözüm

Substitute the expression for

y

from the first equation into the second equation.

3x + 2(2x + 1) = 16

This reduces the system of two variables to a single equation in terms of

x

Expand and simplify the equation by distributing and combining like terms.

7x + 2 = 16

Simplifying the equation makes it easier to isolate the variable

x

Isolate the variable

x

by performing inverse operations.

x = 2

Subtracting 2 and then dividing by 7 isolates

x

to find its value.

Anahtar Kavram

Solving a system of linear equations using the substitution method.

Alternatif Yöntem

Alternatively, you can multiply the first equation by 2 to get

-4x + 2y = 2

and subtract it from

3x + 2y = 16

to eliminate

y

, which also yields

7x = 14

and thus

x = 2

Tahmini Süre:1m 0s

Soru 890Soru →

In 1977, oceanographers first discovered hydrothermal vents on the deep ocean floor, revealing complex ecosystems that thrive in complete darkness. Because these communities depend on chemosynthesis rather than photosynthesis, researchers ______ numerous expeditions since the initial discovery to study how these specialized organisms survive on chemical energy alone.

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

conducted

conduct

have conducted

will conduct

Cevabı ve açıklamayı göster

Cevap: have conducted

Cevap

The correct answer is 'have conducted'.

The correct answer uses the present perfect tense 'have conducted' to correctly match the temporal framework established by the prepositional phrase 'since the initial discovery.' This phrase indicates an action that began in the past and continues to have relevance or occur up to the present moment, which is the primary function of the present perfect aspect.

Adım Adım Çözüm

Identify the subject and temporal clues in the sentence.

The plural subject is 'researchers'. The key temporal clue is 'since the initial discovery', which points to a time period starting in the past (1977) and continuing to the present.

Establishing the timeframe of the sentence is necessary to choose the correct verb tense and aspect.

Select the verb form that corresponds to this timeframe.

The present perfect tense ('have conducted') is used for actions that began in the past and continue to the present or have occurred repeatedly during a timeframe that includes the present.

This aligns with the grammatical function of 'since', which requires a perfect aspect verb.

Anahtar Kavram

Using the present perfect tense to express an action that began in the past and continues to the present, especially when cued by the word 'since'.

Tahmini Süre:1m 0s

Soru 891Soru →

The giant squid (*Architeuthis dux*) has long captivated researchers, but its deep-sea habitat makes direct observation extremely difficult. In 2004, Japanese marine biologists captured the first active images of a live giant squid in its natural environment. This historic achievement ______ helped scientists understand the predatory behaviors of this elusive creature.

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

, which occurred off the coast of the Ogasawara Islands—

—which occurred off the coast of the Ogasawara Islands,

—which occurred off the coast of the Ogasawara Islands—

which occurred off the coast of the Ogasawara Islands

Cevabı ve açıklamayı göster

Cevap: —which occurred off the coast of the Ogasawara Islands—

Cevap

The correct answer is the choice that uses matching em dashes to set off the nonessential relative clause.

The correct choice uses a matching pair of em dashes to set off the nonessential relative clause 'which occurred off the coast of the Ogasawara Islands' from the rest of the sentence. Nonessential elements must be set off from the main clause by matching punctuation marks: either two commas, two em dashes, or two parentheses.

Adım Adım Çözüm

Identify the nonessential element in the sentence.

The relative clause 'which occurred off the coast of the Ogasawara Islands' adds descriptive detail but is not essential to the main grammatical structure of the sentence.

This helps determine that the clause must be punctuated as a nonessential element.

Apply the punctuation rules for nonessential elements.

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

This establishes the criteria for evaluating the punctuation in each option.

Evaluate the choices for punctuation symmetry.

Only the option using matching em dashes correctly isolates the clause, whereas other options use mismatched punctuation or no punctuation.

This identifies the grammatically correct option.

Anahtar Kavram

Punctuation of nonessential elements

Soru 892Soru →

Prior to the landmark discovery of the fossilized cranium of *Sahelanthropus tchadensis* in Chad in 2001, researchers lacked physical evidence of hominids older than six million years. If a team of paleontologists had not recovered this crucial specimen, evolutionary biologists ________ the precise timeline of early hominid divergence from the chimpanzee lineage, as it provided the earliest known anatomical indicators of bipedalism.

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

still debated

would still be debating

would have still debated

will still debate

Cevabı ve açıklamayı göster

Cevap: would still be debating

Cevap

The correct answer is the phrase 'would still be debating'.

The sentence describes a counterfactual scenario where a past event (the recovery of the fossil in 2001) did not occur, resulting in an ongoing hypothetical state in the present (biologists still debating the timeline). This requires a mixed conditional construction. The phrase 'would still be debating' correctly pairs the past counterfactual condition ('had not recovered') with a present continuous counterfactual result.

Adım Adım Çözüm

Analyze the temporal and conditional structure of the sentence.

The sentence begins with a past counterfactual condition ('If a team of paleontologists had not recovered... in 2001'), which sets up a hypothetical scenario contrary to historical facts.

This establishes that the sentence requires a conditional mood to express a hypothetical outcome.

Determine the timeframe of the hypothetical result.

The result clause refers to an ongoing state of debate among evolutionary biologists in the present day.

Because the debate regarding the human evolutionary timeline continues to this day, a present continuous counterfactual result is required.

Select the correct mixed conditional verb form.

The mixed conditional structure combining a past condition with a present result requires 'would' followed by the present continuous infinitive 'still be debating'.

Using 'would still be debating' correctly conveys the present-day hypothetical consequence of the past event.

Anahtar Kavram

Mixed Conditional Mood and Tense Consistency

Soru 893Soru →

In the system of linear equations shown below, what value of $x$ satisfies both equations?

y = 2x - 5

3x - 2y = 12

-22

-2

2

-9

Cevabı ve açıklamayı göster

Cevap: $-2$

Cevap

-2

To find the value of

x

, substitute the expression for

y

from the first equation,

y = 2x - 5

, into the second equation,

3x - 2y = 12

. This yields

3x - 2(2x - 5) = 12

. Distributing the

-2

across the terms in the parentheses results in

3x - 4x + 10 = 12

. Simplifying the left side of the equation by combining like terms gives

-x + 10 = 12

. Subtracting

10

from both sides results in

-x = 2

. Finally, multiplying or dividing both sides by

-1

yields

x = -2

Adım Adım Çözüm

Substitute the expression for

y

from the first equation into the second equation

3x - 2(2x - 5) = 12

To eliminate

y

and obtain an equation containing only

x

Distribute

-2

to the terms inside the parentheses

3x - 4x + 10 = 12

To remove parentheses and prepare the equation for simplifying.

Combine like terms and solve for

x

-x + 10 = 12

, which gives

-x = 2

, and thus

x = -2

To isolate and find the value of

x

Anahtar Kavram

Solving systems of linear equations using substitution

Soru 894Soru →

Although previous models of Martian geologic history suggested the planet's core cooled rapidly, recent research presents a different timeline. Using a newly developed numerical simulation to model the thermal evolution of early Martian crustal reservoirs, _______

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

the simulation enabled planetary scientists to identify a surprisingly prolonged period of volcanic activity, thereby providing an explanation for the planet's asymmetric topography.

planetary scientists have identified a surprisingly prolonged period of volcanic activity, thereby providing an explanation for the planet's asymmetric topography.

a surprisingly prolonged period of volcanic activity was identified by planetary scientists, thereby providing an explanation for the planet's asymmetric topography.

the identification of a surprisingly prolonged period of volcanic activity by planetary scientists provided an explanation for the planet's asymmetric topography.

Cevabı ve açıklamayı göster

Cevap: planetary scientists have identified a surprisingly prolonged period of volcanic activity, thereby providing an explanation for the planet's asymmetric topography.

Cevap

planetary scientists have identified a surprisingly prolonged period of volcanic activity, thereby providing an explanation for the planet's asymmetric topography.

The introductory modifying phrase 'Using a newly developed numerical simulation to model the thermal evolution of early Martian crustal reservoirs' describes an action. The noun immediately following the comma must be the logical actor performing this action. Since planetary scientists are the ones using the simulation, the main clause must begin with 'planetary scientists'. The correct option properly establishes this relationship, ensuring subject-modifier agreement.

Adım Adım Çözüm

Identify the introductory modifying phrase and its logical subject.

The modifying phrase is 'Using a newly developed numerical simulation...', and the logical actor performing this action must be 'planetary scientists'.

An introductory participial phrase must modify the subject of the main clause.

Evaluate the subject of the main clause in each choice.

Only the option beginning with 'planetary scientists' provides the correct logical subject immediately following the comma.

Placing any other noun (like 'the simulation', 'a surprisingly prolonged period', or 'the identification') as the subject creates a dangling or misplaced modifier error.

Anahtar Kavram

Subject-Modifier Agreement

Soru 895Soru →

A line representing the linear function $f$ is graphed in the $xy$ -plane. The line intersects the $y$ -axis at $(0, 3)$ and also passes through the point $(2, 11)$ . What is the slope of this line?

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

The slope of the line is 4.

The slope

m

of a line passing through two points

(x_1, y_1)

and

(x_2, y_2)

is given by the formula

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

. Substituting the given points

(0, 3)

and

(2, 11)

into the formula gives

m = \frac{11 - 3}{2 - 0} = \frac{8}{2} = 4

Adım Adım Çözüm

Identify two coordinates on the line from the given information.

The points are

(0, 3)

and

(2, 11)

To find the slope of a line, we need at least two points on that line.

Apply the slope formula

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

m = \frac{11 - 3}{2 - 0}

The slope formula calculates the ratio of the vertical change (rise) to the horizontal change (run).

Perform the subtraction and division to find the slope value.

m = \frac{8}{2} = 4

Simplifying the fraction gives the final numerical slope.

Anahtar Kavram

Calculating the slope of a linear function given two points

Soru 896Soru →

Complete the text by filling in the blank with the phrase that conforms to the conventions of Standard English (specifically, subject-modifier agreement). Enter either 'reactive oxygen species (ROS) are now known' or 'scientists now know that reactive oxygen species (ROS) are'. Do not include a period at the end of your entry.

Aşağıdaki boşlukları doldurun

Long considered a mere byproduct of cellular respiration, to play a critical signaling role in pathways regulating cell survival.

Cevabı ve açıklamayı göster

Cevap

reactive oxygen species (ROS) are now known

The introductory modifier 'Long considered a mere byproduct of cellular respiration' describes a substance or entity that is produced during respiration. Logically, this describes 'reactive oxygen species (ROS)'. To avoid a dangling modifier, the noun phrase 'reactive oxygen species (ROS)' must serve as the subject of the main clause and immediately follow the comma. The phrase 'reactive oxygen species (ROS) are now known' satisfies this requirement.

Adım Adım Çözüm

Identify the introductory modifying phrase and determine its logical target.

The phrase is 'Long considered a mere byproduct of cellular respiration'. The entity that was historically considered a byproduct of respiration is 'reactive oxygen species (ROS)'.

An introductory modifying phrase must logically describe the subject of the main clause that immediately follows it.

Evaluate the proposed options to identify which one places the logical target as the subject of the main clause.

The phrase 'reactive oxygen species (ROS) are now known' begins with the logical target, whereas 'scientists now know...' begins with 'scientists' as the subject.

Placing 'scientists' immediately after the comma incorrectly implies that the scientists themselves were considered a byproduct of cellular respiration, creating a dangling modifier.

Anahtar Kavram

Subject-Modifier Agreement

Soru 897Soru →

If $3(k + 4) = 5k - 8$ , what is the value of $k$ ?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

Distributing the

3

on the left side yields

3k + 12 = 5k - 8

. Subtracting

3k

from both sides yields

12 = 2k - 8

. Adding

8

to both sides yields

20 = 2k

. Dividing by

2

gives the solution

k = 10

Adım Adım Çözüm

Distribute

3

to the terms inside the parentheses

3k + 12 = 5k - 8

To simplify the left side of the equation

Subtract

3k

from both sides of the equation

12 = 2k - 8

To group the variable terms on one side

Add

8

to both sides of the equation

20 = 2k

To isolate the variable term

Divide both sides by

2

k = 10

To solve for

k

Anahtar Kavram

Solving linear equations with variables on both sides using distributive property

Soru 898Soru →

In the equation below,

k

is a constant.

5x - 2(3 - k)x = 9x - 1

If the equation has no solution, what is the value of

k

-5

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

To find the value of

k

for which the equation has no solution, we simplify the left side of the equation:

5x - 2(3 - k)x = 5x - 6x + 2kx = -x + 2kx = (2k - 1)x

. This yields the simplified equation

(2k - 1)x = 9x - 1

. A linear equation in one variable has no solution when the variable terms on both sides cancel each other out (meaning the coefficients of

x

are equal) but the constant terms are different. Setting the coefficients of

x

equal to each other gives

2k - 1 = 9

. Adding

1

to both sides gives

2k = 10

, and dividing by

2

yields

k = 5

. Since the constant term on the left side is

0

and the constant term on the right side is

-1

, the constants are different, confirming that the equation has no solution when

k

equals

5

Adım Adım Çözüm

Distribute the term

-2

to the expressions inside the parentheses on the left side of the equation.

5x - 6x + 2kx = 9x - 1

To eliminate the parentheses so that all like terms can be grouped.

Combine the

x

terms on the left side of the equation.

-x + 2kx = 9x - 1

, which can be factored as

(2k - 1)x = 9x - 1

Grouping the coefficients of the variable

x

allows direct comparison of both sides of the linear equation.

Set the coefficient of

x

on the left side equal to the coefficient of

x

on the right side.

2k - 1 = 9

For a linear equation in one variable to have no solution, the variable terms on both sides must cancel out (meaning their coefficients must be equal), while the constant terms must remain unequal.

Solve the resulting equation for

k

2k = 10 \implies k = 5

Isolating

k

by adding

1

to both sides and then dividing by

2

determines the specific constant value.

Verify that the constant terms are different when

k = 5

Substitute

k = 5

back into the original equation to get

9x = 9x - 1

, which simplifies to

0 = -1

Since

0 = -1

is a false statement, the equation has no solution, confirming that

k = 5

is correct.

Anahtar Kavram

Linear Equations in One Variable

Alternatif Yöntem

Instead of algebraic simplification, the value of

k

can be found by substituting the answer choices into the equation to see which value eliminates the variable

x

while leaving an untrue statement. Plugging in

5

for

k

gives

5x - 2(3 - 5)x = 9x - 1 \implies 5x - 2(-2)x = 9x - 1 \implies 9x = 9x - 1 \implies 0 = -1

. Because this statement is false, the equation has no solution, verifying that

5

is the correct answer.

Tahmini Süre:2m 0s

Soru 899Soru →

Complete the passage with the noun or pronoun that is logically described by the introductory modifying phrase.

Aşağıdaki boşlukları doldurun

Manatees are large, slow-moving aquatic mammals that inhabit warm coastal waters. Using its powerful tail to propel itself through the water, grazes on seagrass and other marine plants.

Cevabı ve açıklamayı göster

Cevap

The correct answer is a noun or pronoun representing the manatee (such as 'the manatee' or 'it') because the introductory modifier 'Using its powerful tail to propel itself through the water' must describe the subject immediately following it.

The introductory phrase 'Using its powerful tail to propel itself through the water' describes the entity that is actively swimming and using its tail. The correct subject to fill the blank must be 'the manatee' (or a pronoun referring to it) to ensure that the modifying phrase logically describes the subject of the main clause, avoiding a dangling modifier.

Adım Adım Çözüm

Identify the introductory modifying phrase and determine what it describes.

The modifying phrase is 'Using its powerful tail to propel itself through the water'. It describes an entity that has a tail and uses it to swim.

An introductory modifier must logically describe the subject of the clause that immediately follows it.

Determine the logical subject from the context of the sentence.

The preceding sentence establishes that manatees are large aquatic mammals. A manatee is the entity that uses its tail to swim.

Ensuring subject-modifier agreement requires placing the noun being modified directly after the modifier.

Fill in the blank with a noun or pronoun that correctly identifies this subject.

The blank should be filled with 'the manatee' (or a pronoun like 'it') to serve as the subject of the verb 'grazes'.

This completes the main clause while maintaining correct subject-modifier agreement.

Anahtar Kavram

Subject-Modifier Agreement

Soru 900Soru →

Complete the academic passage by filling in the blank with a noun or pronoun that correctly completes the sentence according to the conventions of Standard English.

Aşağıdaki boşlukları doldurun

In her 2023 monograph on the ancient Maya, historian Dr. Beatriz Gomez scrutinized the agricultural terraces of the Copán Valley. Having meticulously mapped the distribution of these stone-walled fields, argued that Maya farming practices were far more sustainable than previously assumed.

Cevabı ve açıklamayı göster

Cevap

The blank must be filled with a subject that can logically perform the action of mapping the fields, such as 'Dr. Gomez', 'Gomez', 'she', or 'the historian'.

The sentence begins with the introductory participial phrase 'Having meticulously mapped the distribution of these stone-walled fields'. For the sentence to be grammatically correct, the subject of the main clause must be the entity that performed the mapping. Since Dr. Beatriz Gomez is the historian who conducted this research, a noun or pronoun referring directly to her must occupy the subject position.

Adım Adım Çözüm

Identify the introductory modifying phrase.

The modifying phrase is 'Having meticulously mapped the distribution of these stone-walled fields'.

This phrase describes an action that must be performed by the subject of the main clause.

Identify the logical agent of the action.

The person performing the mapping is the historian, Dr. Beatriz Gomez.

Only a person (the historian) can map agricultural fields; objects like the monograph or the fields themselves cannot.

Select a noun or pronoun representing the agent to place immediately after the modifier.

Placing 'Dr. Gomez', 'Gomez', 'she', or 'the historian' immediately after the comma resolves the dangling modifier.

This alignment ensures subject-modifier agreement in accordance with Standard English conventions.

Anahtar Kavram

Subject-Modifier Agreement

Tahmini Süre:1m 30s

ÖncekiSayfa 45 / 140Sonraki

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