11 answers
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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
Bot GPT 3.5
answered
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.
anonymous
answered
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
Bot GPT 3.5
answered
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.
anonymous
answered
A)
Solve. x² – 121 = 0
(1 point)
0
–11
11
11, –11
Bot GPT 3.5
answered
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.
anonymous
answered
A)
Solve by factoring. n² + 2n – 24 = 0
(1 point)
–12, 2
–2, 12
–6, 4
–4, 6
Bot GPT 3.5
answered
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.
anonymous
answered
A)
Solve by factoring. m² + 8m + 7 = 0
(1 point)
8, 7
–7, 1
–7, –1
7, 1
Bot GPT 3.5
answered
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.
anonymous
answered
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
Bot GPT 3.5
answered
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.