MATHEMATICS HIGH SCHOOL

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).(A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
(B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
(C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
(D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground

Answers

Answer 1

Answer:

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.

Answer 2

Answer:

Answer:

T= 4 s (second option).

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An electronics company is planning to introduce a new line of computers. For the 1st year, the fixed costs for setting up the production line are $200,000. The variable costs for producing each computer are $40. the revenue from each computer is $65. find the total profit P(x) from the production and sale of x computers and break-even point.
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Let f(x) = 7x - 13. Find f-1(x).

janelle practices basketball every afternoon in driveway.Each day,her goal is to make 4 more baskets than she made the day before. if she makes 10 baskets the first day and meets her goal for 2 weeks,howmany baskets will janelle make on the 14th day?

Answers

In the given question, there are several information's worth noting. Based on these given information's the actual answer to the question can be found. She makes 10 baskets on the first day and then increases the number of baskets by 4 on every consecutive days. So the thing that needs to be found is the number of baskets he makes on the 14th day. This is an arithmetic progression problem.
Now if we consider the 14th day as the Nth term, then we can write the equation as
A(N) = 4(N - 1) + 10
A(14) = 4(14 - 1) + 10
A(14) = (4 * 13) + 10
= 52 + 10
= 62
So Janelle will make 62 baskets on the 14th day.

At the beginning of each year, Bill Ross invests $1,400 semi-annually at 8 percent for 9 years. The cash value of the annuity due at the end of the ninth year is: ...?

Answers

The correct answer would be D. $37,339.68.

To solve this,
$1,400 x 27.6712 = $38,739.68 - 1,400.00 = $37,339.18

This is what the cash value of the annuity due at the end of the ninth year is if Bill Ross invests $1,400 semi-annually at 8 percent for 9 years.

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help.

What is the approximate volume of the cone with a height of 9 cm and a radius of 15 cm.

Answers

V = (1/3) pi r^2 h where r is the radius of the circular base and h is the height of the cone.

V = (1/3) pi (15)^2 * 9

V = 675 pi
V = 2120,575 square cm (approx)

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?See attachment below for picture/answer choices

Answers

Answer:

$-1.5x-3.5y=-31.5$

Step-by-step explanation:

we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

$m1*m2=-1$

In this problem line AB and line PQ are perpendicular

Step 1

Find the slope of the line AB

The equation of the line AB is

$-7x+3y=-21.5$

isolate the variable y

$3y=7x-21.5$ ------> $y=(7/3)x-21.5/3$

The slope of the line AB is equal to

$m1=7/3$

Step 2

Find the slope of the line PQ

remember that

$m1*m2=-1$

we have

$m1=7/3$ ----> slope line AB

substitute and solve for m2

$(7/3)*m2=-1$

$m2=-3/7$

Step 3

Find the equation of the line PQ

The equation of the line into point-slope form is equal to

$y-y1=m(x-x1)$

we have

$m=-3/7$

$P(7,6)$

substitute

$y-6=(-3/7)(x-7)$

$y=(-3/7)x+3+6$

$y=(-3/7)x+9$ -----> multiply by $7$ both sides

$7y=-3x+63$

$7y+3x=63$ -----> divide by $2$ both sides

$1.5x+3.5y=31.5$ -----> multiply by $-1$ both sides

$-1.5x-3.5y=-31.5$

its B -1.5x − 3.5y = -31.5

In order for two triangles to be similar, all corresponding pairs of angles must be __________.adjacent
congruent
proportional
supplementary

Answers

Supplementary idk if it’s this cuz I just started learning this and the teacher said all triangles equal 180 degrees so I hope this helped

Please help with this Pythagoras' theorem
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Answers

Omg that's easy, a^2 + b^2=c^2. The longest side is your hypotenuse. The shortest side is your A. Basically just plugging it in. After you set it up you unsquare it. Then find the square root of the missing side. This is from my knowledge, so if you're still confused, ask your teacher for clarification, because it took me the second day to get it. Or just watch a video on it.

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