Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x − 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.

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Step-by-step explanation:

OpenStudy (amorfide):

s(x)=85 piggy bank

a(x)=10(x-1) allowance

he currently has the money in his piggy bank which is 85

then he gains 10(x-1) for every week that x is,

so you know that on the first week he is doing laundry he has the allowance a(1)=0

but you already have 85 in your piggy bank so your new function will give you 0+85

meaning 85 is your starting case so you always have 85 from the start

therefore you get a new function s(x)+a(X) which we will label f(x)

so f(x)=s(x)+a(x)

f(x)=85+ 10(x-1)

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answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)