In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

What is the difference? StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction Sta

katovenus [111]

Answer:

The option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct

That is $\frac{-2(x+6)}{(x+4)(x-4)}$

Therefore $\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}$

Step-by-step explanation:

Given problem is StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction

It can be written as below :

$\frac{x}{x^2-16}-\frac{3}{x-4}$

To solve the given expression

$\frac{x}{x^2-16}-\frac{3}{x-4}$

$=\frac{x}{x^2-4^2}-\frac{3}{x-4}$

$=\frac{x}{(x+4)(x-4)}-\frac{3}{x-4}$ ( using the property $a^2-b^2=(a+b)(a-b)$ )

$=\frac{x-3(x+4)}{(x+4)(x-4)}$

$=\frac{x-3x-12}{(x+4)(x-4)}$ ( by using distributive property )

$=\frac{-2x-12}{(x+4)(x-4)}$

$=\frac{-2(x+6)}{(x+4)(x-4)}$

$\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}$

Therefore $\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{-2(x+6)}{(x+4)(x-4)}$

Therefore the option "StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction" is correct

That is $\frac{-2(x+6)}{(x+4)(x-4)}$

5 0

3 years ago

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X − 3y if x = 3 and y = −2.

Korvikt [17]

Answer:

Step-by-step explanation:

x - 3y

3 - 3(-2) = 3 + 6 = 9

5 0

3 years ago

The following annual expenses for car insurance, vacation, and home repairs for the Clark family are $1130, $700, and $468, resp

eimsori [14]

Answer:

A) $192

Step-by-step explanation:

Given:

Yearly expense of Car insurance = $1130

Yearly expense of Vacation = $700

Yearly expense of home repairs = $468

we need to find the monthly allowance of Clark family.

First we find the total annual expense of Clark family.

Total Annual expense is equal to sum of Yearly expense of Car insurance and Yearly expense of Vacation and Yearly expense of home repairs.

Framing in equation form we get;

Total annual expense = $\$1130 + \$700+\$468 = \$2298$

Now we know that;

Number of months in a year = 12 months.

Total Monthly allowance will be equal to Total annual expense divided by Number of months in year.

Framing the equation we get;

Total Monthly allowance = $\frac{\$2298}{12}= \$191.5$

Rounding to nearest dollar we get;

Total Monthly allowance of Clark family is $192.

6 0

3 years ago

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-2x-4+5x=8 please help, I'm too stupid to do this.

nydimaria [60]

Answer: x=1 1/3

Step-by-step explanation:

5 0

3 years ago

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For the polynomial function ƒ(x) = −x6 + 3x4 + 4x2, find the zeros. Then determine the multiplicity at each zero and state wheth

murzikaleks [220]

There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.

You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.

-x^6 + 3x^4 + 4x^2

-x^2(x^4 - 3x^2 - 4)

Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.

-x^2(x^4 - 3x^2 - 4)

-x^2(x^2 - 4)(x^2 + 1)

Now we can use the factors of two perfect squares rule to factor the middle parenthesis.

-x^2(x^2 - 4)(x^2 + 1)

-x^2(x - 2)(x + 2)(x^2 + 1)

We would also want to split the term in the front.

-x^2(x - 2)(x + 2)(x^2 + 1)

(x)(-x)(x - 2)(x + 2)(x^2 + 1)

Now we would set each portion equal to 0 and solve.

First root

x = 0 ---> no work needed

Second root

-x = 0 ---> divide by -1

x = 0

Third root

x - 2 = 0

x = 2

Forth root

x + 2 = 0

x = -2

Fifth and Sixth roots

x^2 + 1 = 0

x^2 = -1

x = +/- $\sqrt{-1}$

x = +/- i

7 0

3 years ago