Question

PLEASE HELP I NEED THIS RN

Answer 1

x = 415.

Explanation:

1. Identify the information provided in the statement.

Check attached image 1.

2. Find a value to solve the equation.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

3. Write the equation.

We know that the sum of angles DBE and CBE equal 90°. Hence:

`DBE+CBE=90`

In terms of variable "x", this is:

`(0.1x-22)+(0.3x-54)=90`

4. Solve the parenthesis.

`0.1x-22+0.3x-54=90`

5. Operate with like terms.

`0.1x+0.3x-54-22=90\\ \\0.4x-76=90`

6. Add "76" on both sides of the equation.

`0.4x-76+76=90+76\\ \\0.4x=166`

7. Divide by "0.4" on both sides of the equation.

`(0.4x)/(0.4) =(166)/(0.4) \\ \\x=415`

8. Verify.

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

`(0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90`

9. Conclude.

x = 415.