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 = -16t^2 + 60t + 6. What will the height be at t = 3 seconds?
(1 point)
A. 35 feet
B. 40 feet
C. 42 feet
D. 45 feet
To find the height of the ball at t = 3 seconds, we can substitute t = 3 into the equation h = -16t^2 + 60t + 6.
h = -16(3)^2 + 60(3) + 6
= -16(9) + 180 + 6
= -144 + 180 + 6
= 42
Therefore, the height of the ball at t = 3 seconds is 42 feet.
The answer is C. 42 feet.
Solve. x^2 - 121 = 0
A. 0
C. -11
B. 11
D. 11, -11
To solve the equation x^2 - 121 = 0, we can set the equation equal to zero and solve for x.
x^2 - 121 = 0
To solve this quadratic equation, we can use the square root property. Taking the square root of both sides, we get:
x = ± √121
Since √121 = 11, we have:
x = 11 or x = -11
Therefore, the solution to the equation x^2 - 121 = 0 is x = 11, -11.
The answer is D. 11, -11.
Solve by factoring. m^2 + 8m + 7 = 0
(1 point)
A. 8, 7
B. -7, 1
C. -7, -7
D. 7,1
To solve the equation m^2 + 8m + 7 = 0 by factoring, we need to find two numbers whose product is 7 and whose sum is 8.
The numbers that satisfy these conditions are 1 and 7, because 1 * 7 = 7 and 1 + 7 = 8.
Therefore, we can rewrite the equation as:
(m + 1)(m + 7) = 0
Now, we can set each factor equal to zero and solve for m:
m + 1 = 0 or m + 7 = 0
m = -1 or m = -7
Therefore, the solution to the equation m^2 + 8m + 7 = 0 by factoring is m = -1, -7.
The answer is B. -7, 1.
Solve by factoring. n^2 + 2n - 24 = 0
A. -12, 2
B. -2, 12
C. -6, 4
D. -4, 6
To solve the equation n^2 + 2n - 24 = 0 by factoring, we need to find two numbers whose product is -24 and whose sum is 2.
The numbers that satisfy these conditions are 6 and -4, because 6 * -4 = -24 and 6 + (-4) = 2.
Therefore, we can rewrite the equation as:
(n + 6)(n - 4) = 0
Now, we can set each factor equal to zero and solve for n:
n + 6 = 0 or n - 4 = 0
n = -6 or n = 4
Therefore, the solution to the equation n^2 + 2n - 24 = 0 by factoring is n = -6, 4.
The answer is C. -6, 4.
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 ft^2. 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)
A. 3.33 ft
B. 4.3 ft
C. 1 ft
D. 30 ft
Let's assume the width of the metal piece is represented by w (in feet).
According to the problem, the length is 1 less than 3 times the width. So, the length is given by 3w - 1 (in feet).
The area of the piece is given as 30 ft^2. We can set up an equation to represent this:
w * (3w - 1) = 30
Expanding the equation:
3w^2 - w = 30
Rearranging the equation:
3w^2 - w - 30 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.
In this case, let's use factoring. The quadratic equation can be factored as:
(3w + 10)(w - 3) = 0
Setting each factor equal to zero:
3w + 10 = 0 or w - 3 = 0
Solving for w:
3w = -10 or w = 3
w = -10/3 or w = 3
Since width cannot be negative in this context, we discard the negative solution.
Therefore, the width of the metal piece should be 3 feet.
The answer is C. 3 ft.