Which statements are true check all that apply

The true statements are:

Statement 1: The equation |-x -4| = 8 will have two solutions

Statement 5: The equation | 0.5x  - 0.75 | + 4.6 = 0.25 will have no solutions.

Explanation:

These are six completely different and independent statements. Every one has one equation that needs to be solved.

Which statements are true?

A. Statement 1: The equation |-x -4| = 8 will have two solutions

true

Justification:

1. First step is to remove the bars of the absolute value function:

        ⇒ - x - 4 = 8 or - x - 4 = - 8

2. Solve first equation: - x - 4 = 8

3. Solve second equation: - x - 4 = - 8

Hence, the equation has two solutions x = - 12 and x = 4

B. Statement 2: The equation 3.4|0.5x - 42.1| = - 20.6 will have one solution.

false.

Justification:

C. Statement 3: The equation | (1/2)x - 3/4 | = 0 has no solutions

false

Justification:

Therefore, the equation has one solution.

D. Statement 4: |2x - 10 | = - 20 will have two solutions

false

Justification:

E. Statement 5: The equation | 0.5x  - 0.75 | + 4.6 = 0.25 will have no solutions.

true.

Justification:

F. Statement 6: the equation | (1/8)x - 1 | = 5 will have infinetely many solutions.

false:

Justification:

1. Remove the bars:

2. You do not need to solve the equations to see that you will obtain only two solutions. Hence, the statement is false.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2