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