Tüm alıştırma soruları

Soru 4721Soru →

Modern high-bypass turbofan engines utilize cascade-type thrust reversers to decelerate aircraft upon landing. When deployed, mechanical actuator rings slide the translating cowls aft, exposing stationary cascade vanes while simultaneously positioning blocker doors across the bypass air duct. These blocker doors redirect cold fan bypass airflow forward and outward through the angled cascades to generate reverse thrust. Because the core engine flow remains uninterrupted and continues traveling straight aft, the reverser operates safely without stalling the internal compressor stages. Thrust reversers automatically stow before ground taxi speed drops below sixty knots to prevent airborne ingestion of foreign debris.

According to the passage, all of the following are true regarding cascade thrust reversers EXCEPT:

Translating cowls slide aft to uncover the stationary cascade structures.

Blocker doors deploy across the bypass duct to redirect cold fan air forward.

Core engine exhaust is redirected forward through the cascade vanes to provide stopping force.

The mechanism stows before taxi speed decreases below sixty knots to prevent debris ingestion.

Cevabı ve açıklamayı göster

Cevap: Core engine exhaust is redirected forward through the cascade vanes to provide stopping force.

Cevap

Core engine exhaust is redirected forward through the cascade vanes to provide stopping force.

The passage explicitly notes that core engine flow remains uninterrupted and continues traveling straight aft. Only the cold bypass airflow is redirected forward through the cascades, making the claim that core exhaust is redirected forward factually contradicted by the text.

Adım Adım Çözüm

1

Identify the negative qualifier in the question stem.

The word 'EXCEPT' indicates that the correct answer is the statement contradicted by or absent from the text.

Recognizing the negative requirement prevents accidentally selecting verified facts.

2

Cross-reference each option against the facts provided in the passage.

The passage confirms that cowls slide aft, blocker doors redirect bypass air, and the system stows below sixty knots.

Systematic verification isolates supported details from unsupported or false assertions.

3

Locate the false or contradicted claim.

The text explicitly specifies that core engine flow continues traveling straight aft rather than being redirected forward.

The contradicted statement fulfills the criteria for the correct answer to an EXCEPT question.

Anahtar Kavram

Negative Detail Identification

Tahmini Süre:1m 0s

Soru 4722Soru →

Before clearing a pathway for underground communication lines, field engineers must assess the soil composition. In arid test zones, excavation teams often encounter friable soil—material that is easily crumbled and fragile—which poses a significant cave-in hazard. When working with such unstable ground, crews must immediately brace the trench walls with modular shoring boxes to maintain stability and prevent structural collapse.

As used in the passage, what is the meaning of the word friable?

Reinforced with modular shoring

Easily crumbled or broken

Compact and densely packed

Inherently resistant to moisture

Cevabı ve açıklamayı göster

Cevap: Easily crumbled or broken

Cevap

Easily crumbled or broken

The passage provides an explicit synonymous context clue offset by dashes directly after the target word: 'material that is easily crumbled and fragile'. The option stating 'Easily crumbled or broken' accurately restates this definition.

Adım Adım Çözüm

1

Locate the target word 'friable' within the passage.

Identified in the second sentence: '...excavation teams often encounter friable soil—material that is easily crumbled and fragile—which poses...'

Finding the immediate sentence context is necessary to identify surrounding grammatical markers and clues.

2

Identify the structural context clue defining the word.

The dashes offset the appositive phrase 'material that is easily crumbled and fragile', directly explaining 'friable'.

Appositives set off by dashes serve as explicit restatements or definitions of technical vocabulary.

3

Match the definition to the corresponding answer choice.

The phrase 'easily crumbled and fragile' directly corresponds to the option 'Easily crumbled or broken'.

The correct answer in synonymous context clue questions must directly reflect the definition given in the text.

Anahtar Kavram

Identifying synonymous context clues via appositive restatement

Tahmini Süre:45s

Soru 4723Soru →

Read the following technical passage:

"An aircraft's pitot-static system utilizes air pressure differentials to operate three essential flight instruments: the airspeed indicator, the altimeter, and the vertical speed indicator. Ram air pressure entering the forward-facing pitot tube drives the airspeed indicator alone. Ambient atmospheric pressure enters through flush-mounted static ports on the fuselage and is routed to all three instruments. When pitot tube drain holes become clogged in icing conditions, electrical heating elements prevent ice accumulation. If the static port freezes shut, the altimeter freezes at its current altitude and the vertical speed indicator drops to zero, but the system does not utilize engine bleed air to clear the blockage."

Based on the passage, match each operational statement with its corresponding factual status according to the text.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Engine bleed air is channeled to clear frozen static ports matches Explicitly identified as a method NOT used by the system to remove ice blockages; Electrical heating elements are used to prevent ice accumulation matches Directly confirmed as the safeguard mechanism against ice buildup on the pitot tube; Ambient air pressure from static ports is routed exclusively to the vertical speed indicator matches Directly contradicted by the passage, which states static pressure is routed to all three instruments; Ram air pressure captured by the forward-facing pitot tube drives only the airspeed indicator matches Directly confirmed as supplying pressure exclusively to a single flight instrument.

Each statement aligns precisely with its textual verification status: the use of engine bleed air is explicitly negated by the phrase 'does not utilize engine bleed air'; electrical heating is explicitly affirmed for pitot ice prevention; the routing of static air exclusively to one instrument is directly contradicted by the text stating it feeds all three instruments; and ram air driving only the airspeed indicator is directly confirmed by the word 'alone'.

Adım Adım Çözüm

1

Analyze the passage for negative assertions and explicit operational exclusions.

Identified the explicit negative detail: the passage clarifies that the system does not use engine bleed air for de-icing.

Negative detail identification requires isolating qualifying words like 'not', 'never', or explicit exclusions in the stimulus.

2

Verify positive and contradictory factual statements against the passage text.

Confirmed that electrical heating is directly stated, ram air powering only the airspeed indicator is directly stated, and routing static pressure to only one instrument directly contradicts the passage.

Cross-referencing each claim against textual evidence determines whether each item is stated, contradicted, or negatively excluded.

3

Map each statement to its matching textual status.

Formed all four unambiguous matching pairs.

Ensures complete alignment between statements and their textual status.

Anahtar Kavram

Negative Detail Identification in Technical Texts

Tahmini Süre:1m 15s

Soru 4724Soru →

Read the passage below and complete the statement that follows. Based on the synonymous context clue provided in the text, which word or phrase directly defines the target term?

Aşağıdaki boşlukları doldurun

During deep-water salvage operations inside the sunken vessel's flooded cargo hold, specialized divers encountered turbid water—that is, cloudy and sediment-laden liquid—which drastically reduced visibility. Because standard floodlights were rendered useless by the suspended silt, the dive supervisor instructed the team to rely exclusively on tactile acoustic beacons to navigate the compartment safely.

Based on the text, the word "turbid" most nearly means .

Cevabı ve açıklamayı göster

Cevap

cloudy (or sediment-laden)

The author provides a direct synonymous context clue set off by em dashes immediately following the target word ('—that is, cloudy and sediment-laden liquid—'). The transitional phrase 'that is' explicitly signals a clarifying restatement, confirming that 'turbid' means cloudy or filled with sediment.

Adım Adım Çözüm

1

Locate the target word 'turbid' within the first sentence of the passage.

The target word appears in the phrase: 'encountered turbid water—that is, cloudy and sediment-laden liquid—which drastically reduced visibility.'

Identifying the target word's immediate syntactic context is the necessary first step to finding any adjacent structural clues.

2

Identify the structural context clue punctuation and indicator phrase surrounding the target word.

The author uses em dashes containing the restatement signal 'that is' followed immediately by 'cloudy and sediment-laden liquid.'

Phrases set off by dashes and introduced by 'that is' function as appositive definitions or synonymous restatements of the preceding noun or adjective.

3

Extract the synonym to complete the definition statement.

'Cloudy' or 'sediment-laden' accurately defines 'turbid' according to the passage.

The direct restatement provides the exact textual meaning required without relying on external assumptions.

Anahtar Kavram

Identifying Synonymous Context Clues

Tahmini Süre:1m 0s

Soru 4725Soru →

What is the simplified form of the algebraic expression below?

2(4x + 3) - x

13x

7x + 6

7x + 3

9x + 6

Cevabı ve açıklamayı göster

Cevap: $7x + 6$

Cevap

The correctly simplified expression is

7x + 6

.

To simplify the expression, first apply the distributive property by multiplying 2 by both terms inside the parentheses:

2(4x) + 2(3) = 8x + 6

. Then, bring down the rest of the expression:

8x + 6 - x

. Finally, combine the like terms involving

x

:

8x - x = 7x

. The simplified result is

7x + 6

.

Adım Adım Çözüm

1

Distribute the 2 to both terms inside the parentheses.

8x + 6 - x

The distributive property requires multiplying the outside term by every term inside the parentheses.

2

Combine the like terms (

8x

and

-x

).

7x + 6

Only terms with the same variable and exponent can be combined.

Anahtar Kavram

Simplifying Algebraic Expressions (Distributive Property and Combining Like Terms)

Soru 4726Soru →

Read the following technical passage:

Modern forward-looking infrared (FLIR) targeting pods rely on closed-cycle Stirling cryocoolers to chill mercury-cadmium-telluride sensors down to operating temperatures of approximately 77 Kelvin. At this extreme temperature, ambient thermal noise is suppressed, enabling clear detection of distant heat signatures. Technicians servicing the hermetic cooling unit must purge the compressor manifold with ultra-high-purity helium gas rather than nitrogen to avoid internal icing. During operational checkout, the system must reach thermal stabilization within eight minutes before technicians initiate optical sensor calibration.

Based on the passage, complete the statement with the exact details directly stated in the text.

Aşağıdaki boşlukları doldurun

Technicians servicing the unit must purge the manifold with gas, and the system must achieve thermal stabilization within prior to calibration.

Cevabı ve açıklamayı göster

Cevap

The compressor manifold must be purged with ultra-high-purity helium (or helium), and thermal stabilization must occur within eight minutes (or 8 minutes).

The passage directly and explicitly identifies 'ultra-high-purity helium' (or 'helium') as the gas used to purge the manifold and establishes 'eight minutes' (or '8 minutes') as the mandatory timeframe for the system to reach thermal stabilization before calibration.

Adım Adım Çözüm

1

Scan the passage for the specific purging procedure and the required gas type.

The text explicitly states that technicians must 'purge the compressor manifold with ultra-high-purity helium gas rather than nitrogen.'

Locates the explicit factual requirement for the first blank while distinguishing the correct gas from the prohibited one.

2

Locate the explicit operational checkout timeframe for thermal stabilization.

The text specifies that 'the system must reach thermal stabilization within eight minutes before technicians initiate optical sensor calibration.'

Extracts the exact numerical duration designated for stabilization prior to calibration.

Anahtar Kavram

Direct Fact Retrieval

Tahmini Süre:1m 0s

Soru 4727Soru →

Read the following passage:

Marine vessels operating in saltwater environments face severe galvanic corrosion when dissimilar metals contact electrolyte solutions. To protect submerged steel hulls, naval engineers install cathodic protection systems utilizing sacrificial zinc or aluminum anodes. These sacrificial metals possess a lower electrochemical potential, ensuring they corrode preferentially while preserving the critical steel structure. However, vessel operators must regularly inspect these anodes; once consumed beyond fifty percent of their original volume, their protective current drops significantly, leaving the hull vulnerable. While impressed-current systems offer an adjustable alternative, sacrificial anodes remain the most reliable, cost-effective safeguard for routine harbor craft operations.

Match each excerpted statement from the passage to the author's primary communicative intent in including it.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Match the opening statement on galvanic corrosion to establishing the underlying operational threat; match the warning regarding the fifty percent consumption threshold to emphasizing a critical maintenance threshold and cautioning against neglect; match the comparison between impressed-current and sacrificial systems to justifying the practical preference for one engineering solution over an alternative.

Each statement serves a distinct rhetorical function within the passage structure: establishing the baseline hazard, specifying operational precautions to maintain system efficacy, and providing a reasoned defense of the chosen technical approach against alternatives.

Adım Adım Çözüm

1

Analyze the rhetorical role of the first excerpt concerning galvanic corrosion in saltwater.

The author opens with this fact to establish the core problem and context for the entire discussion.

Identifying introductory context helps distinguish problem-setting statements from technical solutions.

2

Examine the function of the second excerpt regarding anode inspection and the fifty percent depletion limit.

The word 'However' and the focus on vulnerability indicate a warning about maintenance discipline.

Recognizing transitional markers and cautionary phrasing clarifies the intent to mandate action and warn of hazards.

3

Determine the purpose of the final sentence comparing sacrificial anodes to impressed-current systems.

The author evaluates competing methods and defends the selection of sacrificial anodes based on reliability and cost.

Comparative language concluding a passage typically serves to defend or justify a specific practical choice.

Anahtar Kavram

Inferring Author Purpose and Intent

Tahmini Süre:1m 0s

Soru 4728Soru →

Read the passage about underground mine ventilation systems. Complete the concluding statement with the word that reflects the only logically supported outcome.

Aşağıdaki boşlukları doldurun

Deep-mine ventilation systems use dual-fan bulkheads to maintain positive air pressure in active drift headings, preventing explosive methane gas from seeping out of abandoned shafts. If one fan trips offline, an automatic counterbalanced louver closes over its exhaust port to prevent the remaining active fan from pulling air backward through the disabled housing. If this louver jams open during a single-fan failure, the running fan will circulate air in a closed loop within the fan house rather than drawing air through the mine. Under these specific conditions, the air pressure in the active drift headings will .

Cevabı ve açıklamayı göster

Cevap

decrease (or drop / fall / decline)

The passage establishes that positive air pressure in the headings requires active airflow through the mine. When one fan fails and the isolation louver jams open, the operating fan circulates air only in a localized loop within the fan house. Because fresh air is no longer drawn through the mine, positive pressure cannot be sustained, meaning heading pressure will decrease or drop.

Adım Adım Çözüm

1

Identify the primary operational requirement for maintaining pressure in active drift headings.

Positive air pressure depends on the fans actively drawing and moving air through the mine network.

The passage states positive pressure is maintained by the bulkhead fan system moving air through the mine.

2

Analyze the mechanical consequence of the jammed louver during a single-fan failure.

The operational fan circulates air in a localized short-circuit loop inside the fan house instead of drawing air from the mine drifts.

The passage states that an open louver allows backward flow, resulting in an internal closed loop.

3

Synthesize the cause and effect to deduce the resulting pressure change in the drift headings.

Because air is no longer being drawn through the mine to maintain positive pressure, the pressure must drop or decrease.

A loss of positive airflow directly leads to a reduction in heading pressure.

Anahtar Kavram

Synthesizing Systemic Mechanical Failures to Deduce Environmental Effects

Tahmini Süre:1m 0s

Soru 4729Soru →

An aviation squadron reduces its weekly flight hours by $15\%$ to conserve fuel. If the new weekly flight schedule is $340$ hours, what was the original number of weekly flight hours before the reduction?

400

391

289

40

Cevabı ve açıklamayı göster

Cevap: 400

Cevap

The original number of weekly flight hours was 400.

The problem describes a reverse percentage scenario. Because the hours were reduced by 15%, the current 340 hours represent 85% (100% - 15%) of the original schedule. To find the original amount, you divide the current amount by the decimal form of the remaining percentage: 340 / 0.85 = 400.

Adım Adım Çözüm

1

Determine what percentage the new hours represent compared to the original.

The new hours represent

100\% - 15\% = 85\%

of the original hours.

A reduction of 15% means 85% of the original amount remains.

2

Set up an equation where the original hours are represented by the variable

x

.

0.85x = 340

This translates the relationship into an algebraic equation to solve for the unknown original base.

3

Solve for

x

by dividing both sides by

0.85

.

x = \frac{340}{0.85} = 400

Isolating

x

provides the original number of flight hours.

Anahtar Kavram

Reverse Percentage Calculations

Alternatif Yöntem

You can set this up as a proportion:

\frac{85}{100} = \frac{340}{x}

. Cross-multiply to get

85x = 34000

, and divide by 85 to find

x = 400

.

Tahmini Süre:1m 0s

Soru 4730Soru →

Multiplying both sides of the inequality $-\frac{x}{3} < 5$ by $-3$ results in the equivalent inequality $x > -15$ .

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True

The statement correctly applies the algebraic rule that multiplying an inequality by a negative number reverses the direction of the inequality sign, properly yielding

x > -15

.

Adım Adım Çözüm

1

Identify the operation needed to isolate the variable

x

.

Multiply both sides of the inequality

-\frac{x}{3} < 5

by

-3

.

The variable

x

is being divided by

-3

, so multiplying by

-3

is the inverse operation.

2

Perform the multiplication and apply the inequality division/multiplication rule.

-3 \times (-\frac{x}{3}) > -3 \times 5

, which simplifies to

x > -15

.

When multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed to maintain a true mathematical statement.

Anahtar Kavram

When solving inequalities, multiplying or dividing both sides by a negative number requires flipping the inequality sign.

Soru 4731Soru →

Solve the following linear equation for $x$ :

\frac{2}{3}(6x - 9) - \frac{1}{2}(4x + 10) = -\frac{1}{4}(8 - 12x) + 3

Aşağıdaki boşlukları doldurun

The value of

x

that satisfies the equation is .

Cevabı ve açıklamayı göster

Cevap

The correct value for

x

is -12.

The correct answer is derived by methodically applying the distributive property to all grouped terms on both sides of the equation. By taking special care with negative signs during the multiplication of

-\frac{1}{2}

and

-\frac{1}{4}

, the equation simplifies cleanly to

2x - 11 = 3x + 1

. From there, standard algebraic isolation steps lead directly to

x = -12

.

Adım Adım Çözüm

1

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

4x - 6 - 2x - 5

Applying the distributive property multiplies

\frac{2}{3}

by both

6x

and

-9

, and

-\frac{1}{2}

by both

4x

and

10

. Careful attention must be given to the negative sign.

2

Combine like terms on the left side.

2x - 11

Grouping the variable terms (

4x - 2x

) and constant terms (

-6 - 5

) simplifies the expression.

3

Distribute the fractional coefficient on the right side of the equation.

-2 + 3x + 3

Multiplying

-\frac{1}{4}

by

8

gives

-2

, and

-\frac{1}{4}

by

-12x

gives

+3x

. The negative times negative results in a positive term.

4

Combine like terms on the right side.

3x + 1

Adding the constant terms (

-2 + 3

) simplifies the right side.

5

Set the simplified left side equal to the simplified right side and isolate the variable

x

.

x = -12

Starting with

2x - 11 = 3x + 1

, subtract

2x

from both sides to get

-11 = x + 1

. Then, subtract

1

from both sides to solve for

x

.

Anahtar Kavram

Solving complex one-variable linear equations requiring careful fractional distribution and negative sign rules.

Soru 4732Soru →

Which of the following describes the correct solution set for the inequality $-2x - 3 \leq 9$ ?

x \geq -6

x \leq -6

x \geq 6

x \leq 6

Cevabı ve açıklamayı göster

Cevap: $x \geq -6$

Cevap

The correct solution is

x \geq -6

.

To solve the inequality, first isolate the variable term by adding 3 to both sides, which simplifies to

-2x \leq 12

. Next, divide both sides by -2. A critical rule of inequalities is that dividing or multiplying by a negative number requires reversing the inequality symbol. Therefore,

\leq

becomes

\geq

, and

12 \div -2 = -6

, resulting in the final answer of

x \geq -6

.

Adım Adım Çözüm

1

Isolate the variable term by adding 3 to both sides of the inequality.

-2x \leq 12

This removes the constant term from the side with the variable, leaving only the term with x.

2

Divide both sides by -2 and reverse the inequality symbol.

x \geq -6

When multiplying or dividing an inequality by a negative number, the direction of the inequality must flip to keep the mathematical statement true.

Anahtar Kavram

Solving one-variable inequalities and applying the inequality flip rule.

Tahmini Süre:45s

Soru 4733Soru →

If $x = -3$ , $y = -5$ , and $z = 2$ , what is the value of the expression $-2|x^2 - |y - 3z|| + 4x$ ?

-26

-16

-52

-8

Cevabı ve açıklamayı göster

Cevap: -16

Cevap

-16

The correct answer is found by strictly adhering to the order of operations and properties of absolute values. First, the inner absolute value |-5 - 3(2)| evaluates to |-11|, which is 11. The expression then simplifies to -2|(-3)² - 11| + 4(-3). Squaring -3 gives 9, so the expression inside the outer absolute value becomes 9 - 11, which is -2. The absolute value of -2 is 2. Multiplying this by the leading coefficient of -2 gives -4, and adding 4(-3), which is -12, results in -16.

Adım Adım Çözüm

1

Substitute the given variable values into the expression.

-2|(-3)² - |-5 - 3(2)|| + 4(-3)

To prepare the expression for evaluation by replacing variables with their known numeric values.

2

Evaluate the innermost operations following the order of operations, starting with the inner absolute value.

-5 - 3(2) = -5 - 6 = -11, so |-11| = 11

The order of operations (PEMDAS) requires evaluating multiplication before subtraction, and operations inside the innermost grouping symbols first.

3

Evaluate the exponent and substitute the result of the inner absolute value back into the expression.

-2|9 - 11| - 12

Exponents must be evaluated before subtraction within the remaining absolute value.

4

Evaluate the subtraction inside the remaining absolute value and apply the absolute value function.

|9 - 11| = |-2| = 2

The absolute value of any non-zero integer is its positive counterpart.

5

Multiply by the leading coefficient and add the final term.

-2(2) - 12 = -4 - 12 = -16

Multiplication must be performed before subtraction to find the final value.

Anahtar Kavram

Evaluating multi-step algebraic expressions with nested absolute values

Soru 4734Soru →

A student needs to solve the following algebraic inequality:

7 - 2(x - 3) \geq 4x - 5

What is the correct solution for $x$ ?

x \geq 3

x \geq 10

x \leq 3

x \leq -3

Cevabı ve açıklamayı göster

Cevap: $x \leq 3$

Cevap

The correct solution is

x \leq 3

.

The correct answer is derived by carefully distributing the

-2

, combining the constants, grouping the variables on one side, and dividing by

-6

. Crucially, dividing by a negative coefficient triggers the rule to flip the

\geq

sign to

\leq

, resulting in

x \leq 3

.

Adım Adım Çözüm

1

Distribute the

-2

into the parentheses on the left side of the inequality.

7 - 2x + 6 \geq 4x - 5

To eliminate the parentheses and allow like terms to be combined.

2

Combine the constant terms on the left side.

13 - 2x \geq 4x - 5

Adding

7

and

6

simplifies the left side of the algebraic expression.

3

Subtract

4x

from both sides of the inequality.

13 - 6x \geq -5

To group all terms containing the variable

x

onto the left side.

4

Subtract

13

from both sides.

-6x \geq -18

To isolate the variable term on one side and the constant values on the other.

5

Divide both sides by

-6

and reverse the inequality symbol.

x \leq 3

Whenever an inequality is multiplied or divided by a negative number, the direction of the inequality sign must be flipped.

Anahtar Kavram

Solving multi-step inequalities, including the distributive property and the inequality flip rule for negative coefficients.

Soru 4735Soru →

Determine the exact value of the expression below by applying the correct sequence of mathematical operations:

20 - 2 \times (3 - 5)^3 + \frac{-16}{4}

Which of the following represents the correct numerical result?

0

-148

32

80

Cevabı ve açıklamayı göster

Cevap: 32

Cevap

32

Following the proper order of operations, we first simplify the parentheses to get -2. Next, we apply the exponent:

(-2)^3

equals -8. Then we perform multiplication and division:

-2 \times -8

gives a positive 16, and dividing -16 by 4 gives -4. Finally, substituting these values back into the expression leaves

20 + 16 - 4

, which evaluates to 32.

Adım Adım Çözüm

1

Evaluate the expression inside the parentheses:

(3 - 5)

-2

According to the order of operations, operations inside parentheses must be resolved first.

2

Apply the exponent to the result of the parentheses:

(-2)^3

-8

Exponents must be evaluated before multiplication or division.

3

Perform the multiplication:

-2 \times (-8)

16

Multiplication is performed left-to-right before any addition or subtraction. Note that multiplying two negative numbers yields a positive result.

4

Perform the division:

\frac{-16}{4}

-4

Division is also resolved before addition and subtraction. A negative divided by a positive yields a negative result.

5

Complete the final addition and subtraction left-to-right:

20 + 16 - 4

32

Once all higher-order operations are complete, add and subtract from left to right.

Anahtar Kavram

Order of Operations with Signed Numbers and Exponents

Soru 4736Soru →

Consider the algebraic expression:

$3a(2a - 5b) - 2b(a + 4b) + 7ab$

When completely simplified, what is the resulting polynomial?

6a^2 - 10ab - 8b^2

6a^2 - 10ab + 8b^2

6a^2 - 6ab - 8b^2

-12ab

Cevabı ve açıklamayı göster

Cevap: $6a^2 - 10ab - 8b^2$

Cevap

The simplified polynomial is

6a^2 - 10ab - 8b^2

.

The correct answer is found by first distributing the outer terms to eliminate parentheses, carefully observing negative signs. Distributing

3a

gives

6a^2 - 15ab

. Distributing

-2b

gives

-2ab - 8b^2

. Adding the

+7ab

at the end produces the expanded expression

6a^2 - 15ab - 2ab - 8b^2 + 7ab

. Combining the like terms (

-15ab - 2ab + 7ab

) yields

-10ab

, resulting in the final expression

6a^2 - 10ab - 8b^2

.

Adım Adım Çözüm

1

Distribute

3a

to the terms inside the first set of parentheses.

3a(2a) - 3a(5b) = 6a^2 - 15ab

Applying the distributive property to eliminate the first set of parentheses.

2

Distribute

-2b

to the terms inside the second set of parentheses.

-2b(a) - 2b(4b) = -2ab - 8b^2

Applying the distributive property, ensuring the negative sign is multiplied into both terms.

3

Rewrite the full expression with the expanded terms.

6a^2 - 15ab - 2ab - 8b^2 + 7ab

Putting all terms together to prepare for combining like terms.

4

Identify and combine the like terms (the

ab

terms).

-15ab - 2ab + 7ab = -10ab

Only terms with the exact same variable combinations can be added or subtracted.

5

Construct the final polynomial.

6a^2 - 10ab - 8b^2

The

a^2

and

b^2

terms cannot be combined with anything else.

Anahtar Kavram

Simplifying algebraic expressions using the distributive property and combining like terms.

Soru 4737Soru →

Before chemical treatment systems became widespread, municipal water utilities relied primarily on slow sand filtration to purify drinking water. Unlike rapid filters that depend on chemical flocculants to trap suspended debris mechanically, slow sand filters cultivate a dense biological layer known as the schmutzdecke on the sand's surface. This living matrix of algae, protozoa, and harmless bacteria actively digests pathogenic microorganisms as water percolates downward. Although slow sand filters require substantial land area and periodic manual scraping of the top layer, their ability to deliver high-grade biological purification without complex electrical or chemical infrastructure makes them invaluable in rural and decentralized settings.

Based on the passage, the author's primary purpose is to:

criticize rural communities for relying on outdated water purification infrastructure

explain the biological mechanism of slow sand filtration and highlight its enduring value

describe the physical maintenance process of manually scraping the schmutzdecke layer

advocate for replacing modern chemical flocculants in large municipal facilities

Cevabı ve açıklamayı göster

Cevap: explain the biological mechanism of slow sand filtration and highlight its enduring value

Cevap

The author wrote the passage primarily to explain the biological mechanism of slow sand filtration and highlight its enduring value.

The passage dedicates most of its discussion to explaining how the biological schmutzdecke layer purifies water and concludes by emphasizing why this low-infrastructure method remains valuable for rural areas.

Adım Adım Çözüm

1

Analyze the scope and progression of the paragraph

The text begins by contrasting slow sand filters with chemical rapid filters, explains how the biological layer (schmutzdecke) works, and concludes by underscoring why this method remains valuable for rural areas.

Determining the overall rhetorical flow helps separate the core message from individual supporting details.

2

Evaluate the author's tone and primary communicative goal

The tone is informative and appreciative of the technology's advantages in decentralized settings, not critical or overly argumentative.

Author intent depends on the attitude conveyed toward the subject matter.

3

Match the synthesized intent to the most comprehensive and accurate statement

The statement explaining the biological working principle while affirming its ongoing usefulness matches both the content and purpose.

The correct answer must encompass the whole passage rather than an isolated detail or an exaggerated claim.

Anahtar Kavram

Inferring the author's primary purpose requires identifying the central concept the writer wants the reader to understand and distinguishing it from minor supporting facts or unsupported assumptions.

Tahmini Süre:1m 0s

Soru 4738Soru →

Which of the following algebraic expressions correctly represents the statement: 'Five less than the quotient of twice a number $p$ and three is subtracted from the product of four and the sum of the number and six'?

4(p + 6) - \left(\frac{2p}{3} - 5\right)

\left(\frac{2p}{3} - 5\right) - 4(p + 6)

4(p + 6) - \left(5 - \frac{2p}{3}\right)

4p + 6 - \left(\frac{2p}{3} - 5\right)

Cevabı ve açıklamayı göster

Cevap: $4(p + 6) - \left(\frac{2p}{3} - 5\right)$

Cevap

The expression

4(p + 6) - \left(\frac{2p}{3} - 5\right)

correctly translates the word phrase into algebra.

The phrase requires breaking down into two parts. 'Five less than the quotient of twice a number

p

and three' translates to

(\frac{2p}{3} - 5)

because 'less than' reverses the order. 'The product of four and the sum of the number and six' translates to

4(p + 6)

because parentheses are needed to multiply the entire sum. Finally, 'is subtracted from' is a turnaround phrase meaning the first part is taken away from the second part, resulting in

4(p + 6) - \left(\frac{2p}{3} - 5\right)

.

Adım Adım Çözüm

1

Translate the first phrase: 'Five less than the quotient of twice a number

p

and three'.

\frac{2p}{3} - 5

'Twice a number' is

2p

. The 'quotient... and three' means divide by

3

, giving

\frac{2p}{3}

. 'Five less than' indicates subtracting

5

from that quantity.

2

Translate the second phrase: 'the product of four and the sum of the number and six'.

4(p + 6)

'The sum of the number and six' requires grouping symbols:

(p + 6)

. 'The product of four and...' means multiplying

4

by the entire grouped sum.

3

Combine the two expressions using the operation 'is subtracted from'.

4(p + 6) - \left(\frac{2p}{3} - 5\right)

The phrase 'A is subtracted from B' translates to

B - A

. Therefore, the first expression must be subtracted from the second expression, requiring parentheses around the first expression.

Anahtar Kavram

Translating complex word phrases into algebraic expressions using correct order and grouping symbols.

Soru 4739Soru →

High-voltage electrical substations utilize sulfur hexafluoride circuit breakers to isolate transmission faults. Inside the breaker's expansion chamber, technicians install molecular sieve desiccant packets to absorb residual moisture, which would otherwise react with arc byproducts to generate corrosive hydrofluoric acid. During scheduled five-year maintenance, technicians replace the desiccant and recharge the sealed tank until the pressure reaches 0.65 megapascals before energizing the bus bar. If an internal density monitor registers a drop below 0.58 megapascals, an automated interlock halts breaker operation to prevent catastrophic contact failure.

According to the passage, what occurs when the circuit breaker's internal pressure falls below 0.58 megapascals?

The five-year maintenance cycle is automatically reset.

An automated interlock halts breaker operation.

Corrosive hydrofluoric acid is released to seal the chamber.

Technicians immediately energize the main bus bar.

Cevabı ve açıklamayı göster

Cevap: An automated interlock halts breaker operation.

Cevap

An automated interlock halts breaker operation.

The passage explicitly states in the concluding sentence that if the density monitor registers a pressure drop below 0.58 megapascals, an automated interlock halts breaker operation.

Adım Adım Çözüm

1

Locate the targeted numerical condition in the passage.

Identified the condition describing an internal pressure drop below 0.58 megapascals in the final sentence.

Direct fact retrieval requires locating the specific keyword or parameter in the text.

2

Extract the explicit factual outcome associated with this condition.

The text states that an automated interlock halts breaker operation.

Matching the explicit statement eliminates incorrect alternatives and confirms the direct fact.

Anahtar Kavram

Direct Fact Retrieval

Tahmini Süre:1m 0s

Soru 4740Soru →

A tool kit originally costs $\$40$ . Its price is increased to $\$50$ . What is the percentage increase in the price of the tool kit?

20\%

125\%

25\%

250\%

Cevabı ve açıklamayı göster

Cevap: $25\%$

Cevap

25\%

The correct percentage increase is found by determining the difference between the new price and the old price (

\$10

), and then dividing that difference by the original price (

\$40

). The fraction

10/40

reduces to

1/4

, which equals

0.25

or

25\%

.

Adım Adım Çözüm

1

Calculate the absolute increase in price.

\$50 - \$40 = \$10

The percentage increase is always based on the amount of change in value.

2

Divide the price increase by the original price to find the decimal rate.

10 \div 40 = 0.25

Percentage change must be calculated relative to the starting amount, not the final amount.

3

Convert the decimal rate to a percentage.

0.25 \times 100 = 25\%

Multiplying a decimal by 100 formats it as a standard percentage.

Anahtar Kavram

Percentage Increase

Tahmini Süre:45s

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