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Solve for the equation, show all your work. This is an absolute value equation. You need to show both equations and the work for

VMariaS [17]

Answer:

$x=-1$ or $7$

Step-by-step explanation:

We use casework on when $3x-9=12$ and when $3x-9=-12$ .

For the first case, $3x-9=12$ , we add 9 to both sides to get

$3x=21$ .

Dividing both sides by 3 gives

$x=7.$

For the second case, $3x-9=-12$ , we add 9 to both sides to get

$3x=-3$ .

Dividing both sides by 3 gives

$x=-1$ .

Checking both cases, we plug in $x=7$ and $x=-1$ .

For the first case, we have $|3(7)-9|=|21-9|=|12|=12$ , which satisfies the equation.

For the second case, we have $|3(-1)-9|=|-3-9|=|-12|=12$ , which also satisfies the equation.

This gives us two solutions to the equation; $x=7$ and $x=-1$ .

4 0

2 years ago

A walkway forms one diagonal of a square playground. The walkway is 14 m long. How long is a side of the playground?

Vilka [71]

Answer: The side of the playground is around 10 meters long

Step-by-step explanation:

use the diagonal as the hypotenuse of a right triangle, where the sides of the square form the legs of said triangle.

Usually

$a^{2} +b^{2} =c^{2}$

since we know a and b are the same length (sides of a square are congruent) we would have

$a^{2} +a^{2} =c^{2} \\2a^{2} =c^{2}$

We know that c is 14 so

$2a^{2} =14^{2} \\2a^{2} =196\\a^{2} =98\\a=\sqrt{98} \\a= 9.999$

5 0

3 years ago

A van can travel 18 miles on each gallon of gasoline. at that rate how many miles can the van travel on 15 gallons of gasoline

tensa zangetsu [6.8K]

18 / 1 = x / 15......18 miles to 1 gallon = x miles to 15 gallon
cross multiply
(1)(x) = (18)(15)
x = 270 miles

7 0

3 years ago

Read 2 more answers

You need to count all the loaves of bread in the front area. There are 22 loaves of white bread , 17 loaves of wheat bread , and

pickupchik [31]

This is easy first do 22+17=39
next do 39+19=58

3 0

3 years ago

Read 2 more answers

9*10^7 is how many times as large as 3*10^3 Please help

sesenic [268]

Answer:

30000 times larger.

Step-by-step explanation:

10^7 * 9/10^3*3

Law of exponents cancel some of the tens.

10^4 * 9/3

Cancel out the three.

10^4 *3

Compute

30000 times larger.

4 0

3 years ago