if you have a rectangle with width 5 inches and length 10 inches and scale it by a factor of 2 what will the new perimeter be
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ATI TEAS 7

TEAS Math Questions

1. If you have a rectangle with a width of 5 inches and a length of 10 inches and scale it by a factor of 2, what will the new perimeter be?

Correct answer: C

Rationale: When a rectangle is scaled by a factor of 2, both the length and width are multiplied by 2. The new dimensions become width = 5 * 2 = 10 inches and length = 10 * 2 = 20 inches. Therefore, the new perimeter is calculated as 2 * (10 + 20) = 60 inches. Choice A, B, and D are incorrect as they do not reflect the correct calculation based on scaling the dimensions of the rectangle.

2. Simplify the expression: 2x + 3x - 5.

Correct answer: A

Rationale: To simplify the expression 2π‘₯ + 3π‘₯ - 5, follow these steps: Identify and combine like terms. The terms 2π‘₯ and 3π‘₯ are both 'like terms' because they both contain the variable π‘₯. Add the coefficients of the like terms: 2π‘₯ + 3π‘₯ = 5π‘₯. Simplify the expression. After combining the like terms, the expression becomes 5π‘₯ - 5, which includes the simplified term 5π‘₯ and the constant -5. Thus, the fully simplified expression is 5π‘₯ - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

3. Which of the following is not a negative value?

Correct answer: B

Rationale: To identify the negative value, simplify each expression. A) simplifies to 6 which is positive. B) simplifies to 0 which is neither positive nor negative. C) simplifies to -11 which is negative. D) simplifies to -30 which is negative. Therefore, only choice B results in a non-negative value, making it the correct answer.

4. Divide 4/3 by 9/13 and reduce the fraction.

Correct answer: A

Rationale: To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, (4/3) Γ· (9/13) = (4/3) * (13/9) = 52/27. This fraction is already in its reduced form, making choice A the correct answer. Choices B, C, and D are incorrect as they do not represent the correct result of dividing the fractions 4/3 by 9/13.

5. x Γ· 7 = x βˆ’ 36. Solve the equation. Which of the following is correct?

Correct answer: B

Rationale: To solve the equation x Γ· 7 = x βˆ’ 36, start by multiplying both sides by 7 to get 7(x Γ· 7) = 7(x βˆ’ 36), which simplifies to x = 7x βˆ’ 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.

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