What is the rational exponent expression of 6 square root of f

Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

rusak2 [61]

Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form $ax^2+bx+c$ . To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
$x^2+2x-8=(x+4)(x-2)$
In the denominator we have a difference of squares:
$x^2-9=x^2-3^2=(x+3)(x-3)$

Now we can rewrite our function:
$y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}$

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at $x=3$ and $x-3$

We can conclude that the graphic of our rational function is:

7 0

3 years ago

Jim takes out a mortgage for 30 years at an interest rate of 2.49% and his monthly repayments are $986.50. What is the principal

Svetllana [295]

The principal loan amount will be 250000. P is denoted by the principal loan amount

<h3> What is the amount?</h3>

The complete repayment of money at the end of the period for which it was borrowed is referred to as the amount.

The given data in the problem is;

P is the principal loan amount

r is the rate of interest = 2.49%

n is the time period= of 30 years

The formula for the principal loan amount is found as;

$\rm P=M(1-(1+\frac{r}{12} )^{\frac{12}{n}$

$\rm P=986.50(1-(1+\frac{0.249}{12} )^{\frac{12}{30} }\\\\ P= 250000$

Hence the principal loan amount will be 250000.

To learn more about the amount, refer to the link;

brainly.com/question/12184047

#SPJ1

6 0

2 years ago

The ratio of boys to girls in a class is 4:5 what fraction of the class is boys and what fraction of the class is girls

ale4655 [162]

First, let's start off with the information we already have. Since the ratio is 4 boys to 5 girls, there has to be a minimum of 9 students (4 being boys and 5 being girls).

9 will be the denominator of both of our fractions since the boys and girls are in the same class.

The fraction of boys in the class is 4/9 (since there are 4 boys to 5 girls in a class of 9, we would write 4 over 9) and the fraction of girls in the class is 5/9.

This is a simplified version of the fractions. If this is a multiple-answer question and 4/9 and 5/9 are not up there, try multiplying the fractions with different numbers and see what fractions will be correct.

But either way, 4/9 and 5/9 are correct :)

7 0

3 years ago

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Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of f(x)=x^2+2 for 0≤x≤5 about x

Irina18 [472]

For each x in the interval 0 ≤ x ≤ 5, the shell at that point has

• radius = 5 - x, which is the distance from x to x = 5

• height = x ² + 2

• thickness = dx

and hence contributes a volume of 2π (5 - x) (x ² + 2) dx.

Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

$\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}$