Equivalent Expressions MCQ Quiz - Objective Question with Answer for Equivalent Expressions - Download Free PDF

To find , we start by factoring . The GCF is , so we can write the expression as .

We want this to be equivalent to .

Setting these expressions equal gives:

-

By comparing the coefficients, we get:

-

Thus, the value of is .

To find the area of a rectangle, multiply the length and width: .

1. Multiply the coefficients: .

2. For : , so .

3. For : , so .

The area is . Thus, Option 4 is correct. Other options fail to properly apply exponent rules or miscalculate the coefficients.

The area of the garden is calculated by multiplying the height and width: .

1. Multiply the coefficients: .

2. For : , hence .

3. For : , hence .

Therefore, the area is , which can be expressed as in terms of positive exponents. Option 1 is correct. Other options either incorrectly add exponents or incorrectly multiply coefficients.

To simplify  , apply the rule . This gives  . Simplifying the exponents, we get  . Thus,   and  . Therefore,  . The correct answer is 7 .

To solve , we first apply the power of a power rule to . This gives us:

.

Next, multiply this result by :

.

Using the product of powers rule, we add the exponents for each base:

- For : .

- For : , and since any number to the power of zero is 1, simplifies to 1.

- For : .

Thus, the simplified expression is . Therefore, the correct answer is option 3.

Choice C is correct. The first expression (1.5x - 2.4)² can be rewritten as (1.5x - 2.4)(1.5x - 2.4). Applying the distributive property to this product yields (2.25x² - 3.6x - 3.6x + 5.76)-(5.2x² - 6.4). This difference can be rewritten as (2.25x² - 3.6x - 3.6x + 5.76) + (-1)(5.2x² - 6.4). Distributing the factor of -1 through the second expression yields 2.25x² - 3.6x - 3.6x + 5.76 - 5.2x² + 6.4. Regrouping like terms, the expression becomes (2.25x² - 5.2x²) + (-3.6x - 3.6x) + (5.76 + 6.4). Combining like terms yields -2.95x² - 7.2x + 12.16.

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

The correct answer is . It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 14 teaspoons is equivalent to teaspoons. Note that 14/3, 4.666, and 4.667 are examples of ways to enter a correct answer.

The correct answer is 73,920. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 112 furlongs is equivalent to , or 73,920 feet.

The correct answer is 40,260. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 61 furlongs is equivalent to . or 40,260 feet.

Choice A is correct. Since 1 kilometer is equal to 1,000 meters, it follows that 90 kilometers is equal to 90(1,000)=90,000  meters. Since 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds, it follows that 1 hour is equal to 60(60) = 3,600 seconds. Now is equal to , which reduces to  or 25 meters per second. 
Choices B, C, and D are incorrect and may result from conceptual or calculation errors. 

Choice C is correct. It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 44 tablespoons is equivalent to , or 132 teaspoons.
Choice A is incorrect. This is equivalent to approximately 15.66 tablespoons, not 44 tablespoons.
Choice B is incorrect. This is equivalent to approximately 29.33 tablespoons, not 44 tablespoons.
Choice D is incorrect. This is equivalent to approximately 58.66 tablespoons, not 44 tablespoons.

Choice A is correct. It's given that t = 4u. Multiplying both sides of this equation by 2 yields 2t = 2(4u), or 2t = 8u.
Choice B is incorrect and may result from dividing, instead of multiplying, the right-hand side of the equation by 2. Choices C and D are incorrect and may result from calculation errors.

The correct answer is 102. It's given that 1 yard is equivalent to 3 feet. Therefore, 34 yards is equivalent to . or 102 feet.

Choice B is correct. It's given that 1 yard = 36 inches. Therefore, 612 inches is equivalent to  which can be rewritten as or 17 yards. 36
Choice A is incorrect. This is the number of yards that are equivalent to 2.124 inches.
Choice C is incorrect. This is the number of yards that are equivalent to 20,736 inches.
Choice D is incorrect. This is the number of yards that are equivalent to 793,152 inches.

Choice A is correct. It's given that . Solving this formula for H expresses the relative humidity in terms of the temperature and the dew point. Subtracting T from both sides of this equation yields . Multiplying both sides by  yields . Subtracting 100 from both sides yields . Multiplying both sides by -1 results in the formula .

Choices B, C, and D are incorrect and may result from errors made when rewriting the given formula.