Given f(x) = x^2 - 7x + 12 and g(x) = 3 / (x^2 - 16)

The product of the two functions, <span>(f•g)(x) is equal to:

(x^2 - 7x + 12) * 3 / (x^2 - 16)

To simplify, factor the two polynomials:

x^2 - 7x + 12 = (x - 4 ) (x - 3 )

x^2 - 16 = (x - 4) (x +4)

=> </span><span>(f•g)(x) = (x - 4)(x - 3) * 3 / [ (x - 4) (x +4) ] = 3 (x - 3) / (x + 4)

Answer: 3 (x - 3) / (x + 4)

=
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8 0

3 years ago

What is the principal of simple interest

sasho [114]

Answer:

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Step-by-step explanation:

Does this help☺

4 0

3 years ago

Explain relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-inter

Zinaida [17]

Step-by-step explanation:

So, let's use x2 - 3x - 28 as an example.

It's factors are (x - 7)(x + 4).

The roots are the x-values that make our expression equal 0. In order for x2 - 3x - 28 to equal 0, either of our factors need to equal 0, since 0 times anything is 0.

x2 - 3x - 28 = 0

(x - 7)(x + 4) = 0

x - 7 = 0

x = 7

(7 - 7)(7 + 4) = 0(11) = 0

x + 4 = 0

x = -4

(-4 - 7)(-4 + 4) = -11(0) = 0

That gives us two points on our graph, (7,0) and (-4,0). Where are those? On the x-axis! Thus, there are our x-intercepts.

By the way, for the future, along the x-axis, y = 0, so if you are asked for the x-intercepts (or roots), set y = 0 and solve for x.

Along the y-axis, x = 0, so if you are asked for the y-intercepts, set x = 0 and solve for y.

y = 02 - 3(0) - 28

y = -28

So, the y-intercept(s) of our same equation is y = -28, or (0,-28).

Boom.

3 0

3 years ago