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3 years ago

5

Normally, a car wash costs $6. Today, Marie found a coupon so she only has to pay 60% of the normal amount. How much will Marie

have to pay?

1 answer:

Snezhnost [94]3 years ago

7 0

Marie will pay $3.60

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Step-by-step explanation:

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3 years ago

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and 3−

Neko [114]

Answer:

$P(x) = x^3 - 10x^2+ 34x-40$

Step-by-step explanation:

Given

$p =1$ -- Leading coefficient

$Zeros: 4\ and\ 3 - i$

Required

Determine the polynomial

Represent the zeros with a and b

Such that

$a = 4$

$b = 3 - i$

The polynomial is:

$P(x) = p * (x - a) * (x - b)$

$P(x) = 1 * (x - 4) * (x - (3 - i))$

However, to solve further: We need to symmetrise over 3-i and its conjugate

$P(x) = 1 * (x - 4) * (x - (3 - i))* (x - (3 + i))$

$P(x) = (x - 4) * (x - (3 - i))* (x - (3 + i))\\\\$

To define a suitable function, the expression becomes

$P(x) = (x - 4) * ((x - 3)^2+1)$

$P(x) = (x - 4) * ((x - 3)(x - 3)+1)$

$P(x) = (x - 4) * (x^2 - 6x + 9+1)$

$P(x) = (x - 4) * (x^2 - 6x +10)$

Open bracket

$P(x) = x^3 - 6x^2 +10x - 4x^2 + 24x-40$

$P(x) = x^3 - 6x^2 - 4x^2+10x + 24x-40$

$P(x) = x^3 - 10x^2+ 34x-40$

5 0

3 years ago