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3 years ago

Simplify 18 - 2[x + (x - 5)].

1 answer:

7 0

First, distribute what's inside the parenthesis, and change all the subtractions to addition of negatives.

18 + -2 (x^2 + - 5x)

Next distribute the -2

18 + -2x^2 + 10x

Then I like to rearrange stuff to put it in standard form.

-2x^2 + 10x + 18

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Two problems here I need solved! I need every step, so please have that with your answers!!

Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}$

We multiply through by LCM of
$(x-4)(x - 2)$

$(x - 2) + x(x-4) = 2$

We expand to get,

$x - 2 + {x}^{2} - 4x= 2$

We group like terms and equate everything to zero,

${x}^{2} + x - 4x - 2 - 2 = 0$

We split the middle term,

${x}^{2} + - 3x - 4 = 0$

We factor to get,

${x}^{2} + x - 4x- 4 = 0$

$x(x + 1) - 4(x + 1) = 0$

$(x + 1)(x - 4) = 0$

$x + 1 = 0 \: or \: x - 4 = 0$

$x = - 1 \: or \: x = 4$

But
$x = 4$
is not in the domain of the given equation.

It is an extraneous solution.

$\therefore \: x = - 1$
is the only solution.

QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

This implies,

${x}^{2} - 3x - 10 = 0$

We solve this quadratic equation by factorization,

${x}^{2} - 5x + 2x - 10 = 0$

$x(x - 5) + 2(x - 5) = 0$

$(x + 2)(x - 5) = 0$

$x + 2 = 0 \: or \: x - 5 = 0$

$x = - 2 \: or \: x = 5$

But
$x = - 2$
is an extraneous solution

$\therefore \: x = 5$

7 0

4 years ago

PLEASE HELPPPPPP

boyakko [2]

Answer:

15 if b is supposed to the side length, √15 if b is the base which is a square.

Step-by-step explanation:

8 0

4 years ago

Rachael got a 550 on the analytical portion of the Graduate Record Exam (GRE). GRE scores are normally distributed and have mean

yawa3891 [41]

Answer:

0.0475

Step-by-step explanation:

Given that :

Area To the left :

P(Z < 550) = 0.0475 ; that is proportion who scored better than of 550 has a Zscore of 0.0475.

Hence, percentage of students who scored better than she did will be 0.0475

6 0

3 years ago

The wayside hotel charges guest $1

quester [9]

I think the answer to that is 1 guest because it said charges guest which means only 1 person is charged

4 0

3 years ago

What is the slope for the following:<br> 3x + 2y = 12

Cerrena [4.2K]

Answer:

slope = - $\frac{3}{2}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 2y = 12 ( subtract 3x from both sides )

2y = - 3x + 12 ( divide all terms by 2 )

y = - $\frac{3}{2}$ x + 6 ← in slope- intercept form

with slope m = - $\frac{3}{2}$

5 0

3 years ago