Mathematics Flashcard

Front

What will be the total distance fallen by a rock after 5 seconds if it falls 16 feet after 1 second, 48 feet after 2 seconds, and 80 feet after 3 seconds?

Back

160 feet

Answer explanation

The distance fallen follows a pattern: after 1 second 16 ft, after 2 seconds 48 ft, and after 3 seconds 80 ft. The increments are 16 ft, 32 ft, and 48 ft respectively. Continuing this pattern, after 5 seconds, it falls 160 ft.

Front

What is the time when the container will be empty if the function f(t) = 128 - 8t represents the amount of tea in the container over time?

Back

16 minutes

Answer explanation

To find when the container is empty, set f(t) = 0: 128 - 8t = 0. Solving gives t = 16 minutes. Thus, the container will be empty at 16 minutes.

Front

Ava is planning to renovate her living room, which is 2 feet wider than its length and has an area of 120 square feet. What is the width of the room?

Back

12 feet

Answer explanation

Let the length be x feet. Then, the width is x + 2 feet. The area is x(x + 2) = 120. Solving the equation x^2 + 2x - 120 = 0 gives x = 10. Thus, the width is 10 + 2 = 12 feet.

Front

Mia is planning a party and needs to decide on the number of sodas and hamburgers to buy. Which combination of sodas and hamburgers would exceed her budget limit? Options: 7 sodas and 4 hamburgers, 4 sodas and 5 hamburgers, 2 sodas and 3 hamburgers, 9 sodas and 3 hamburgers

Back

7 sodas and 4 hamburgers

Answer explanation

Mia's budget is exceeded by 7 sodas and 4 hamburgers due to their combined cost being higher than her limit, making this the only option that surpasses her budget.

Front

What is the average rate of change in the plant's height over the interval 1 ≤ t ≤ 3 for the function h(t) = t² - 2t + 4?

Back

2

Answer explanation

To find the average rate of change from t=1 to t=3, calculate h(3) - h(1) / (3 - 1). h(3) = 7, h(1) = 3, so (7 - 3) / 2 = 2. Thus, the average rate of change is 2.

Front

William is designing a square garden and wants the area to be 49 square meters. What should be the length of each side of the garden?

Back

Length = ±7 meters

Answer explanation

The area of a square is calculated as side length squared. To find the side length for an area of 49 square meters, we take the square root: √49 = ±7 meters. However, only the positive length is practical for a garden.

Front

Elijah is planning a dance party and the cost function is $ y = 0.50x + 5.00 $. What represents the initial cost?

Back

5.00

Answer explanation

The cost function is in the form y = mx + b, where b represents the initial cost. Here, the initial cost is 5.00, which is the fixed cost before any additional expenses based on x.

Front

Zoe is trying to balance her budget. She knows that $13 plus 3 times the square of her savings equals $16. What is the first step she should take to find out her savings?

Back

Subtract 13 from both sides

Answer explanation

To isolate the term with savings, Zoe should first eliminate the constant on the left side. Subtracting 13 from both sides simplifies the equation to 3 times the square of her savings equals 3, making it easier to solve.

Front

Charlotte is designing a garden in the shape of a parabola, and the equation for the garden's boundary is $ y = 3x^2 - 13x - 10 $. Which is the correct factored form of this equation?

Back

(2x + 2)(x - 5)

Answer explanation

To factor the equation y = 3x^2 - 13x - 10, we look for two numbers that multiply to -30 (3 * -10) and add to -13. The correct factors are (2x + 2)(x - 5), which simplifies to the original equation.

Front

Rohan is tracking the growth of a plant over time. For what interval of time is the plant's height increasing? Options: (-∞, -1), (1, ∞), (2, ∞), (0, ∞)

Back

(2, ∞)

Answer explanation

The plant's height is increasing for the interval (2, ∞), indicating that after time 2, the growth continues indefinitely. The other intervals do not include this growth phase.