∠e and ∠f are vertical angles with m∠e=9x+12 and m∠f=3x+24 .

what is the value of x?

vertical angles are always congruent so the E & F have to have the same end result

therefore we have to find a single x value that makes E & F equal each other

okay so we can set the equations to equal each other and solve for x

so:

9x + 12 = 3x + 24

we need to get all the x terms to one side so let's subtract 12 from both sides

now we have

9x = 3x + 12

now let's subtract 3x from both sides to get

6x = 12

we can solve for x like normal now

x = 2

now to check this and see if it is accurate we plug in 2 for x in both equations

E = 9(2) + 12

E = 30

F = 3(2) + 24

F = 30

because they both got the same answer, we know that x = 2 is the right answer

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !