All categories

3 years ago

Solve for x: 4|2x − 2| 10 = 34. (5 points) x = −4, x = 2 x = 4, x = −4 x = 2, x = −2 x = 4, x = −2

1 answer:

7 0

4|2x − 2| + 10 = 34
4|2x − 2| + 10 - 10 = 34 - 10
4|2x − 2| = 24
|2x − 2| = 24/4 = 6
2x - 2 = 6 or 2x - 2 = -6
2x = 6 + 2 or 2x = -6 + 2
2x = 8 or 2x = -4
x = 8/2 or x = -4/2
x = 4 or x = -2

To check for extraneous solutions:
For x = 4: 
4|2(4) − 2| + 10 = 34
4|8 − 2| = 34 - 10 = 24
6 = 24/4 = 6 (solution is valid)

For x = -2: 
4|2(-2) − 2| + 10 = 34
4|-4 − 2| = 34 - 10 = 24
|-6| = 6 = 24/4 = 6 (solution is valid) 

Therefore, solutions are x = 4 , x = -2

You might be interested in

Find dy/dx for y - xy + 1 = x-1

zimovet [89]

Answer:

dx/dy = 1 -x / y + 1

5 0

3 years ago

A changes saved Set up a proportion and use it to solve for x. 2 10 х 3

V125BC [204]

Answer:

C. 15

Step-by-step explanation:

The following proportional can be set-up for the figure given:

$\frac{x + 3}{x} = \frac{10 + 2}{10}$

Solve for x

$\frac{x + 3}{x} = \frac{12}{10}$

$\frac{x + 3}{x} = \frac{6}{5}$

Cross multiply

$5(x + 3) = x(6)$

$5x + 15 = 6x$

15 = 6x - 5x

15 = x

x = 15

3 0

3 years ago

-0.2(-67+22)=2(7n 3)-8n =?

dangina [55]

70.6 what i got was 70.6753275399

4 0

4 years ago

Does anyone know how to solve this? It’s really starting to stress me out.

bekas [8.4K]

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

3 0

3 years ago

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y

posledela

*the figure is shown in the attachment

Answer/Step-by-step explanation:

Since <XYZ and <YZX are said to be congruent, therefore, the side opposite to each of the angle are also equal. Therefore, ∆XYZ is an isosceles ∆.

Find the value of n by creating an equation to solve for n:

XY = (9n + 12) ft

XZ = (15n - 6) ft

XY = XZ (2 equal lengths of isosceles ∆)

9n + 12 = 15n - 6 (substitution)

Combine like terms

9n - 15n = - 12 - 6

-6n = -18

Divide both sides by -6

-6n/-6 = -18/-6

n = 3

Find the length of leg XY by substituting n = 3 into XY = (9n + 12) ft.

XY = (9(3) + 12) ft

XY = (27 + 12) ft

XY = 39 ft

Find the length of leg XZ by substituting n = 3 into XZ = (15n - 6) ft.

XZ = (15(3) - 6) ft

XZ = (45 - 6) ft

XZ = 39 ft

7 0

3 years ago