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sesenic [268]
3 years ago
15

Ray is purchasing a laptop that is on sale for 25% off. He knows the function that represents the sale price of his laptop is c(

p) = 0.75p, where p is the original price of the laptop. He also knows he has to pay 8% sale's tax on the laptop. The price of the laptop with tax is f(c) = 1.08c, where c is the sale price of the laptop. Determine the composite function that can be used to calculate the final price of Ray's laptop by solving for f[c(p)]. f[c(p)] = 1.83p f[c(p)] = 1.83cp f[c(p)] = 0.81p f[c(p)] = 0.81cp
Mathematics
1 answer:
Lelu [443]3 years ago
3 0
F[c(p)]=  f ( 0.75p ) = 1.08*0.75p = .81p
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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai
nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}

\frac{1}{4} = \frac{15 + x + x}{x(15+x)}

\frac{1}{4} = \frac{15 + 2x}{x(15+x)}

Applying cross multiplication.

x^2 + 15x = 4(15 + 2x)

x^2 + 15x = 60 + 8x

x^2 + 7x - 60 = 0

Quadratic equation with a = 1, b = 7, c = -60. So

\Delta = 7^{2} - 4*1*60 = 289

x_{1} = \frac{-7 + \sqrt{289}}{2} = 5

x_{2} = \frac{-7 - \sqrt{289}}{2} = -12

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0
2 years ago
Solve for x, angle A, and Angle B<br> A x+50 B x+80 c72
jolli1 [7]
I’m assuming you man degrees? Are these angles of a triangle?

This doesn’t really make sense because the angles in a triangle add up to 180° so your equation would be x+50+x+80+72=180

Combine like terms to get
2x+202=180

Then subtract 202 from both sides
2x=-22

So x would be -11 which doesn’t seem right lol
7 0
3 years ago
Read 2 more answers
Math help please I promise to give brainliest
AlekseyPX

Answer:

y = 0.5

x = 4 - y (0.5)

3.5 = 4 - 0.5

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3x - 10 = y

3(3.5) - 10 = y

10.5 - 10 = y

0.5 = y

5 0
2 years ago
Read 2 more answers
Elizabeth is going to invest $480 and leave it in an account for 8 years. Assuming the interest is compounded continuously, what
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Answer:

4.2

Step-by-step explanation:

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5 0
2 years ago
The cost of renting ice skates is $4 plus $3.50 for each hour that the ice skates are
Elis [28]

Answer: D)3.5h+4

Step-by-step explanation:

Let h denotes the number of hours that the ice skates are  rented.

Since, The cost of renting ice skates is $4 plus $3.50 for each hour that the ice skates are  rented.

So , the total cost for ice-skating = $4 + $3.50 x (number of hours that the ice skates are  rented.)

= 4+3.50 x ( h) [as expression]

Hence, the expression can be used to find the cost in dollars of renting ice skates for h hours :-

3.5h+4

5 0
3 years ago
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