A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, (h), in feet after t seconds is given by the function h(t) = –16t² + 184t +20. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.

I know the seconds: 5.75
Height?: 11.6 or 549

Please help! Thanks!

seconds: 5.75

Height?: 549

549:)

Use the graph of f (x) to find the solutions to the equation f (x) = 0.

A coordinate plane with parabola opening up. The y-intercept is negative 12 and the x-intercepts are 2 and negative 6.
A. two solutions: x = 6, negative 2
B. two solutions: x = negative 6, 2
C. one solution: x = negative 12
D. no solutions

B. two solutions: x = negative 6, 2

What are the solutions of the equation 2 x squared equals 2? Use a graph of a related function whose roots answer the question.

A. An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 1
B. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
C. An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
There are no solutions.
D. An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root

B. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. There are two solutions: x equals plus or minus 2.

Solve the equation using the Zero Product Property.

The quantity 2x plus 6 times the quantity 3x minus 6 equals 0.
A. 3 and 2
B. negative 3 comma negative 2
C. negative 3 and 2
D. 3 and negative 2
What are the solutions of the equation?

z squared minus 6z minus 27 equals 0.
A. 3, 9
B. 3, negative 9
C. negative 3, 9
D. negative 3, negative 9
A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden.
A. 15 m
B. 3 m
C. 12 m
D. Start Root 12 End Root m
What is the value of c so that x2 + 9x + c is a perfect square trinomial?
A. 18
B. nine-halves
C. nine-fourths
D. 81-fourths

The answers are:

- C. negative 3 and 2
- A. 3, 9
- C. 12 m
- D. nine-fourths

Explanation:

1. To solve the equation using the Zero Product Property, we need to set each factor equal to zero and solve for x:

2x + 6 = 0 or 3x - 6 = 0

Solving for x, we get:

x = -3 or x = 2

Therefore, the solutions are negative 3 and 2.

2. To solve the equation z^2 - 6z - 27 = 0 using factoring, we need to find two numbers whose product is -27 and whose sum is -6. These numbers are -9 and 3.

Therefore, we can write:

z^2 - 6z - 27 = (z - 9)(z + 3)

Setting each factor equal to zero and solving for z, we get:

z - 9 = 0 or z + 3 = 0

z = 9 or z = -3

Therefore, the solutions are 3 and 9.

3. Let s be the length of each side of the original garden. The area of the original garden is s^2. The area of the new garden is (s + 3)^2 = s^2 + 6s + 9.

We are given that the new total area is 225:

s^2 + 6s + 9 = 225

Simplifying the equation, we get:

s^2 + 6s - 216 = 0

Factoring out a 3, we get:

(s + 18)(s - 12) = 0

Setting each factor equal to zero and solving for s, we get:

s + 18 = 0 or s - 12 = 0

s = -18 or s = 12

We reject the negative solution, so the length of each side of the original garden is 12 meters.

4. To make x^2 + 9x + c a perfect square trinomial, we need to add and subtract the square of half the coefficient of x:

x^2 + 9x + (9/2)^2 - (9/2)^2 + c

Simplifying the expression, we get:

(x + 9/2)^2 - 81/4 + c

For this to be a perfect square trinomial, we need to have:

c - 81/4 = 0

c = 81/4

Therefore, the value of c is nine-fourths.

Solve the equation by completing the square. Round to the nearest hundredth.

x squared plus 6 x equals negative 7
A. 4.41, 1.59
B. negative 4.41, 1.59
C. negative 4.41, negative 1.59
D. 4.41, negative 1.59
Solve the equation by completing the square.

x squared plus 9 x minus 14 equals 0
A. 10.35, 1.35
B. 10.35, negative 1 point 35
C. negative 10.35, negative 1.35
D. negative 10.35, 1.35
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

x squared plus 3 equals negative 4 x
A. 1, 3
B. negative 1, negative 3
C. 1, negative 3
D. negative 1, 3
Which kind of function best models the data in the table? Use differences or ratios.

x
y
0
0.6
1 4.2
2 29.4
3 205.8
4 1440.6
A. exponential
B. quadratic
C. linear

The answers are:

1. D. 4.41, negative 1.59
2. A. 10.35, 1.35
3. B. negative 1, negative 3
4. A. exponential

Explanations:

1. To solve the equation x^2 + 6x = -7 by completing the square, we need to add and subtract (6/2)^2 = 9 from both sides:

x^2 + 6x + 9 = -7 + 9

(x + 3)^2 = 2

Taking the square root of both sides, we get:

x + 3 = ±√2

Solving for x, we get:

x = -3 ± √2

Therefore, the solutions are 4.41 and -1.59 (rounded to the nearest hundredth).

2. To solve the equation x^2 + 9x - 14 = 0 by completing the square, we need to add and subtract (9/2)^2 = 40.5 from both sides:

x^2 + 9x - 14 + 40.5 = 40.5

(x + 4.5)^2 = 54.5

Taking the square root of both sides, we get:

x + 4.5 = ±√54.5

Solving for x, we get:

x = -4.5 ± √54.5

Therefore, the solutions are 10.35 and -1.35 (rounded to the nearest hundredth).

3. To solve the equation x^2 + 3 = -4x using the quadratic formula, we first need to rearrange it in standard form:

x^2 + 4x + 3 = 0

Using the quadratic formula, we get:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in a = 1, b = 4, and c = 3, we get:

x = (-4 ± √(4^2 - 4(1)(3))) / 2(1)

Simplifying the expression, we get:

x = (-4 ± √4) / 2

x = -2 ± 1

Therefore, the solutions are -1 and -3.

4. To determine which kind of function best models the data in the table, we calculate the ratios of consecutive y-values:

y(1)/y(0) = 7

y(2)/y(1) = 7

y(3)/y(2) = 7

y(4)/y(3) = 7

The ratios are all equal to 7, so the data follows an exponential function of the form y = ab^x, where b = 7. Plugging in the values of x and y(0), we get:

y = 0.6 * 7^x

Therefore, the best model is an exponential function.