✨[ALGEBRA]✨ A plumbing company charges $75 per hour with a $100 inspection fee. A sales tax of 8.25% is then calculated based on the charges (subtotal). Write a function for the charges c(h) for the number of hours worked, h. Then write a function for the sales tax, s(c) collected on the charges. Finally, write a function for the total, t(h), using c(h) and the composite of s(h) and c(h).
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Answers:

c(h) = 75h+100

s(c) = 0.0825c

t(h) = 1.0825*(75h+100)

Explanation:

h = number of hours worked

75h = total cost if we ignore the taxes and inspection fee

75h+100 = total cost if we include inspection fee, but ignore taxes

c(h) = 75h+100 is the cost function before tax. It tells us what c will be equal to for any given value of h.

The s(c) function tells us what the sales tax s will be for any given cost c

Sales tax in this case is 8.25% which converts to the decimal form 0.0825

So we can say

s(c) = 0.0825c

We can replace each 'c' with c(h) to get

s( c(h) ) = 0.0825*c(h)

The reasoning for this is because we can then plug in the c(h) function we found earlier to get

s( c(h) ) = 0.0825*c(h)

s( c(h) ) = 0.0825*(75h+100)

s(h) = 0.0825*(75h+100)

This is the composite function your teacher is talking about. It's combing the two ideas in a sort of chain.

The total is going to be the cost before tax, plus the amount of sales tax

total cost = (charge before tax) + (sales tax amount)

t(h) = c(h) + s(h)

t(h) = (75h+100) + 0.0825*(75h+100)

t(h) = 1*(75h+100) + 0.0825*(75h+100)

t(h) = (1+0.0825)*(75h+100)

t(h) = 1.0825*(75h+100)

Note how the total cost is 1.0825 times of the cost before tax.

So we could say

t(h) = 1.0825*c(h)

The 1.0825 multiplier indicates "increase the value by 8.25%"

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step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet