Act Algebra 2 Review

Michael is trying to solve a puzzle where he needs to find two numbers. The first number is twice the second number, and their sum is -15. What are the numbers?

Let the first number be y and the second number be x.

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Answer explanation

Substituting x = 3y into 2y + x = -15 gives 2y + 3y = -15. This simplifies to 5y = -15, so y = -3. Then, x = 3(-3) = -9. The solution is (-9, -3).

Isla is trying to solve an equation where the number of apples she has plus 5, divided by 10, equals the number of apples she has minus 12, divided by 9. How many apples does Isla have?

• 165

• 17

• 1/17

• 1/165

Answer explanation

To solve the problem, we find that the correct answer is 165. This choice is derived from the calculations or context provided in the question, confirming that 165 is the valid solution.

Isla has 5x + 3 apples, and she gives (2x - 5) apples to Sophia. How many apples does Isla have left?

• 3x + 8

• 3x - 2

• 7x + 8

• 7x - 2

Answer explanation

To simplify (5x + 3) - (2x - 5), distribute the negative: 5x + 3 - 2x + 5. Combine like terms: (5x - 2x) + (3 + 5) = 3x + 8. Thus, the correct answer is 3x + 8.

Emma is designing a rectangular garden. The length of the garden is represented by (2x + 3) meters and the width is represented by (2x − 3) meters. What is the area of the garden?

• 4x² − 9

• 4x² + 9

• 4x² − 12x − 9

• 4x² + 12x − 9

Answer explanation

To find the product of (2x + 3)(2x - 3), use the difference of squares formula: a^2 - b^2. Here, a = 2x and b = 3. Thus, (2x)^2 - (3)^2 = 4x^2 - 9. The correct answer is 4x² - 9.

Michael is planning to plant a rectangular garden and wants to calculate the area. The area of the garden can be represented by the expression n² + 16n + 63. Help Michael factor this expression to find the possible dimensions of the garden.

• (n-7)(n+4)

• (n+7)(n-9)

• (n-3)(n-10)

• (n+7)(n+9)

Answer explanation

To factor n² + 16n + 63, we look for two numbers that multiply to 63 and add to 16. The numbers 7 and 9 fit this, leading to the factors (n+7)(n+9). Thus, the correct answer is (n+7)(n+9).

Kai is designing a parabolic arch for a bridge. What is the domain and range of the quadratic function that models the arch?

• D: ℝ R: y ≤ 4

• D: -5 ≤ x ≤ 2 R: -6≤ y ≤ 4

• D: ℝ R: ℝ

• D: -3 ≤ x ≤ 1 R: 0≤ y ≤ 4

Answer explanation

The correct choice is D: ℝ for domain, indicating all real numbers, and R: y ≤ 4 for range, which shows the maximum value of the quadratic function is 4, consistent with its vertex being at or below this point.

Ava is designing a garden and wants to create a rectangular flower bed. The area of the flower bed is represented by the equation 5x^2 - 2x = 1, where x is the width in meters. Solve for x using the quadratic formula and round your answers to the nearest tenth.

• x = -2.9; x = 6.9

• x = 3.4; x = -1.4

• x = 0.7; x = -0.3

• x = 0.5; x = -0.1

Answer explanation

Using the quadratic formula, we find the roots of the equation. The calculations yield x = 0.7 and x = -0.3, which match the correct answer choice. Thus, the correct answers are x = 0.7; x = -0.3.

Evaluate 10 to the 0 power

• 1

• 10

• 0

• 100

Answer explanation

10⁰ is equivalent to 1 because any non-zero number raised to the power of 0 equals 1. Therefore, the correct answer is 1.

Aria is trying to find out between which two whole numbers the square root of 277 lies. Can you help her?

• 15 and 16

• 16 and 17

• 18 and 19

• 14 and 15

Answer explanation

The square root of 277 is approximately 16.64. Since 16^2 = 256 and 17^2 = 289, the square root lies between 16 and 17. Thus, the correct answer is 16 and 17.

Simplify.

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