The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground

Answers

Answer 1

Answer: f(t) = 4t² - 8t + 7

f(t) = 4(t² - 2t) + 7
f(t) - 7 = 4(t² - 2t - __)

t² ⇒ t * t
2t ⇒ 2 * 1t
1² ⇒ 1 * 1

f(t) - 7 + 4(1) = 4(t² - 2t + 1)

(t-1)(t-1) = t(t-1) -1(t-1) = t² - t - t + 1 = t² - 2t + 1

f(t) = 4(t-1)² + 3

Answer 2

Answer:

Answer:

A f(1) =4(1)^2 – 8(1) +7 min height 3

Step-by-step explanation:

The function is a parabola, and the problem asks to transform the equation into f(t)=a(x-h)2 + k

Given f(t) = 4t2 -8t +7

= (4t2 - 8t + 4) + 7 - 4

=4 (t2 - 2t + 1) + 3

= 4 (t-1) 2 +3

This removes C and D from the viable choices.

Differentiating the f(t),

f’(t) = 8t – 8, the maximum/minimum value occurs at f’(t) = 0

0 = 8t – 8

t = 1

determining if maximum or minimum, f”(t) > 0 if minimum, f”(t) < 0 maximum

f”(t) = 8 > 0, therefore minimum

f(1) =4(1)^2 – 8(1) +7

= 3

Therefore, minimum height is 3.

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Must show your work and will make brainliest

Answers

Answer:

7/3x + 2/3 = 7/9x - 5/6

7/3x - 7/3x + 2/3 = 7/9x - 7/3x - 5/6 (7/9x-7/3x--->7/9x-21/9x---> -14/9x)

2/3= -14/9x - 5/6

2/3+5/6 = -14/9x - 5/6 + 5/6 - (2/3 + 5/6---> 4/6 + 5/6---> 9/6 ----> 3/2)

3/2 = -14/9x

3/2 / -14/9 = -14/9x / -14/9 - (3/2 / -14/9 ------> 3/2 x -9/14 ----->

- 27/28)

-27/28 = x

Step-by-step explanation:

a) The average height of sunflowers in a field is 64 inches with a standard deviation of 3.5 inches. Describe a normal curve for the distribution, including the values on the horizontal axis at one, two, and three standard deviations from the mean. b) If there are 3,000 plants in the field, approximately how many will be taller than 71 inches?

Answers

The values on the horizontal axis are:
at 0 = 64
at one standard deviation (lower, upper) = (60.5 , 67.5)
at two standard deviation (lower, upper) = (57 , 71)
at three standard deviation (lower, upper) = (53.5 , 74,5)

B. P(x > 71) = 1 - P(x < 71) = 1 - P[z < (71 - 64)/3.5] = 1 - P(z < 2) = 1 - 0.97725 = 0.02275
Therefore the no of plants taller than 71 inches will be approximately 0.02275 * 3000 = 68

y=-3x+5

5x - 4y= -3

solvining systems of equations by substitution

Answers

$\left\{\begin{array}{ccc}y=-3x+5\n5x-4y=-3\end{array}\right\n\n\nsubstitute\n\n5x-4(-3x+5)=-3\n5x+12x-20=-3\n17x-20=-3\n17x=-3+20\n17x=17\ \ \ \ /:17\nx=1\n\ny=-3\cdot1+5=-3+5=2\n\n \left\{\begin{array}{ccc}x=1\ny=2\end{array}\right$

Sheila had a piece of rope that was 62.41 centimeters long. She cut pieces 8.95, 3.17, and39.77 centimeters long from the rope. How many centimeters of the rope did Sheila have left?