Question

A)

A ball is thrown into the air with an initial upward velocity of 60 ft/s. Its height (h) in feet after t
seconds is given by the function h = –16t² + 60t + 6. What will the height be at t = 3
seconds?
(1 point)
35 feet
40 feet
42 feet
45 feet

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height at t = 3 seconds, plug t = 3 into the given function h = -16t^2 + 60t + 6:

h = -16(3)^2 + 60(3) + 6
h = -16(9) + 180 + 6
h = -144 + 180 + 6
h = 36 + 6
h = 42 feet

Therefore, the height at t = 3 seconds will be 42 feet.

The answer is 42 feet.

Answer 2

A)

A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t
seconds is given by the function . After how many seconds will the ball hit
the ground?
(1 point)
3
4
5
6

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the time it takes for the ball to hit the ground, we need to find the time (t) when the height (h) is 0.

Given the function for height:
h = -16t^2 + 46t

Setting h = 0:
0 = -16t^2 + 46t
0 = 2t(-8t + 23)

So, either t = 0 or -8t + 23 = 0

Solving -8t + 23 = 0
-8t = -23
t = 23/8
t = 2.875 seconds

Therefore, the ball will hit the ground after approximately 2.875 seconds, which is closest to option 3: 3 seconds.

The answer is 3 seconds.

Answer 4

A)

Solve. x² – 121 = 0
(1 point)
0
–11
11
11, –11

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the equation x^2 - 121 = 0, we need to find the values of x that make the equation true:

x^2 - 121 = 0
(x + 11)(x - 11) = 0

Setting each factor to zero gives us the solutions:
x + 11 = 0 or x - 11 = 0
x = -11 x = 11

Therefore, the solutions to the equation x^2 - 121 = 0 are x = 11 and x = -11.

The solution is 11, -11.

Answer 6

A)

Solve by factoring. n² + 2n – 24 = 0
(1 point)
–12, 2
–2, 12
–6, 4
–4, 6

Answer 7

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation n^2 + 2n - 24 = 0 by factoring, we need to find two numbers that multiply to -24 and add up to 2.

The two numbers are -4 and 6 because:
-4 * 6 = -24
-4 + 6 = 2

So, we can rewrite the equation as:
n^2 + 6n - 4n - 24 = 0
n(n + 6) - 4(n + 6) = 0
(n - 4)(n + 6) = 0

Setting each factor to zero gives us the solutions:
n - 4 = 0 or n + 6 = 0
n = 4 or n = -6

Therefore, the solutions to the equation n^2 + 2n - 24 = 0 are n = 4 and n = -6.

The answer is -6, 4.

Answer 8

A)

Solve by factoring. m² + 8m + 7 = 0
(1 point)
8, 7
–7, 1
–7, –1
7, 1

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation m^2 + 8m + 7 = 0 by factoring, we need to find two numbers that multiply to 7 and add up to 8.

The two numbers are 7 and 1 because:
7 * 1 = 7
7 + 1 = 8

So, we can rewrite the equation as:
m^2 + 7m + m + 7 = 0
m(m + 7) + 1(m + 7) = 0
(m + 1)(m + 7) = 0

Setting each factor to zero gives us the solutions:
m + 1 = 0 or m + 7 = 0
m = -1 or m = -7

Therefore, the solutions to the equation m^2 + 8m + 7 = 0 are m = -1 and m = -7.

The answer is -7, -1.

Answer 10

A)

One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a
pole barn. The area of the piece is 30 ft². The length is 1 less than 3 times the width. How
wide should the metal piece be? Round to the nearest hundredth of a foot.
(1 point)
3.33 ft
4.3 ft
1 ft
30 ft

Answer 11

[AI-generated answer — Bot GPT 3.5]

Let the width of the metal piece be x feet.

Given that the length is 1 less than 3 times the width, we can write the length as: 3x - 1.

The area of a rectangle is given by the formula: area = length * width
Given that the area is 30 ft^2, we have:
30 = (3x - 1) * x
30 = 3x^2 - x
Rearranging terms:
3x^2 - x - 30 = 0

To solve this quadratic equation, we can factor:
3x^2 - 10x + 3x - 30 = 0
x(3x - 10) + 3(3x - 10) = 0
(x + 3)(3x - 10) = 0

Setting each factor to zero gives the possible solutions:
x + 3 = 0 or 3x - 10 = 0
x = -3 or x = 10/3 = 3.33

Since the width cannot be negative, we take the positive solution.
Therefore, the width of the metal piece should be approximately 3.33 feet.

The answer is 3.33 ft.