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3 years ago

Apply the distribution to solve

Mathematics

1 answer:

Viefleur [7K]3 years ago

8 0

Answer:

4(5+k)

Step-by-step explanation:

20+4k

20 = 2*10 = 2* 2*5

4k = 2*2*k

The common factors are 2*2 = 4

We can factor out a 4

What is left over is inside the parentheses

4(5+k)

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Consider the equation 5/3v +4 + 1/3v = 8. What is the resulting equation after the first step in the equation?

Fed [463]

I hope this helps you

5+1/3v=8-4

6/3v=4

2/v=4

v=2/4

v=1/2

4 0

3 years ago

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

3 years ago

Write a equation for the line parallel to

Llana [10]

Paralell has same slope
y=mx+b
m=slope
b=yint

same slope so other equation is
y=4x+b

input given point
(2,0)
x=2
y=0
0=4(2)+b
0=8+b
minus 8 both sides
-8=b

the equation is y=4x-8

8 0

3 years ago

I need help with this question it’s urgentttt

Andreas93 [3]

Answer:

EF is equal to 6.

Step-by-step explanation:

Those triangles are similar so put them in proportion , as in 8/16=EF/12 then cross multiply and solve

4 0

3 years ago

Given interest of $10,510 at 12 percent for 30 days one can calculate the principal as:

gtnhenbr [62]

Answer:

$1,065,597.22

Step-by-step explanation:

Simple interest = Principal * Rate * Time/100

10,510 = P * 12 * 30/365*100

10,510*365*100 = 360P

383,615,000 = 360P

Note that the time was converted to years by dividing by 365

P = 383,615,000/360

P = $1,065,597.22

Hence the principal is $1,065,597.22

7 0

2 years ago