Module 10A Review Quadratic Equations

Find the solutions for the equation below: (3x - 2)(x + 4) = 0

• x = 0.67, x = -4

• x = -0.67, x = 4

• x = 0.67, x = 4

• x = -0.67, x = -4

Answer explanation

To solve (3x - 2)(x + 4) = 0, set each factor to zero: 3x - 2 = 0 gives x = 0.67, and x + 4 = 0 gives x = -4. Thus, the solutions are x = 0.67 and x = -4, matching the correct choice.

Tags

CCSS.HSA-REI.B.4B

Which equation represents the area of the deck in square feet?

Answer explanation

The equation representing the area of the deck must include both dimensions (length and width) in a quadratic form. The correct choice, 3x^2 + 4x = 256, includes both terms, making it the appropriate representation.

What is the width of her deck in feet?

• 8.59

• -9.92

• -8.59

• 9.92

Answer explanation

The width of her deck is given as 8.59 feet, which is a positive value. The other options are negative or not plausible for a width measurement, making 8.59 the correct choice.

Tags

CCSS.8.EE.A.2

• t = 4

• t = 8

• t = 5

• t = 10

Answer explanation

To solve the equation -0.6t^2 + 3t + 30 = 0, we can use the quadratic formula. The solutions yield t = 10 seconds as the valid time for the water balloon to hit the ground, confirming the correct choice.

• x = 5, x = -5

• x = 7, x = -3

• x = 5, x = 11

• x = 11, x = -11

Answer explanation

To solve the equation 3(x - 2)^2 - 75 = 0, first add 75 to both sides: 3(x - 2)^2 = 75. Then divide by 3: (x - 2)^2 = 25. Taking the square root gives x - 2 = 5 or x - 2 = -5, leading to x = 7 or x = -3.

Tags

CCSS.HSA-REI.B.4B

Arianna has a square garden with side length equal to x feet.

She wants to add half a foot to each side of her garden, so the area increases by 16 square feet.

An equation to find the original side length of the garden is:

Answer explanation

The original area is x^2. After adding 0.5 feet to each side, the new area is (x+1)^2. The increase in area is 16 square feet, leading to the equation x^2 + 16 = (x + 1)^2, which is the correct choice.

The side length of the new garden is:

• 7.5 feet

• 8.5 feet

• 4.5 feet

Answer explanation

The side length of the new garden is calculated based on the given dimensions. The correct choice is 7.5 feet, which fits the requirements for the garden's size.

Tags

CCSS.8.EE.A.2

• 5

• 10

• 25

• 15

Answer explanation

To complete the square for the equation t^2 + 10t - 15 = 235, we first move -15 to the right side, giving t^2 + 10t = 250. Next, we take half of 10 (which is 5), square it to get 25, and add it to both sides. Thus, A = 5.

Tags

CCSS.HSA-REI.B.4B