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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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Put the following equation in standard form and determine the quadratic, linear, and constant coefficients. -3x2 - 8 = 5x - 7
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Answer:

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  • -3 (quadratic)
  • -5 (linear)
  • -1 (constant)

Step-by-step explanation:

The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.

<h3>Standard form</h3>

We can subtract the right-side expression from both sides to get standard form.

  -3x² -8 -(5x -7) = 5x -7 -(5x -7)

  -3x² -8 -5x +7 = 0 . . . . . . . simplify a bit

  -3x² -5x -1 = 0 . . . . . . . . . collect terms

The standard form equation can be written ...

  -3x² -5x -1 = 0

<h3>Coefficients</h3>

The quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.

The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.

The constant coefficient is the coefficient of the term with no variables. The constant is -1.

__

<em>Additional comment</em>

We can make the leading coefficient positive by multiplying the equation by -1. This gives ...

  3x² +5x +1 = 0

with quadratic, linear, and constant coefficients 3, 5, 1.

This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.

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