Solve the absolute value equation. |5m + 2| + 5 = 8

Begin the solution of |5m + 2| + 5 = 8 by subtracting 5 from both sides:

|5m + 2| = 3

Divide all 3 terms by 5 to isolate m: |m + 2/5| = 3/5

Case 1: m + 2/5 is already positive. The absolute value operator has no bearing. We have m + 2/5 = 3/5, or m = 1/5.

Case 2: (m + 2/5) is negative. Then we have -(m + 2/5) = 3/5, or

-m - 2/5 = 3/5, or

-m = 1, or m=-1

The solution set is {-1, 1/5}. Check both results via substitution.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).