Question

1. find the length of pr

p q + q r = p r
pr = 25

1. if eg = 71, find the value of x.

ef + fg = eg
8x - 17 + 5x - 3 = 71
which equation will correctly solve for x?
a. 8x - 17 = 5x - 3
b. 5x - 3 + 71 = 8x - 17
c. 8x - 17 + 5x - 3 = 180
d. 8x - 17 + 5x - 3 = 71

1. if tv = 14x - 8, find tu.

tu + uv = tv
9x + 2 + 10 = 14x - 8
x =
tu =
tv =

1. if t is the mid - point of su, find x.

st + tu = su
8x + 11 + 12x - 5 = x
20x + 6 = x
x =
st =
su =

Explanation:

Step1: Solve for x in problem 3

Given $TU + UV=TV$, so $9x + 2+10 = 14x-8$.
First, simplify the left - hand side: $9x+12 = 14x - 8$.
Then, move the terms with x to one side and constants to the other side: $14x-9x=12 + 8$.
$5x=20$.
Solve for x: $x = 4$.

Step2: Find TU in problem 3

Substitute $x = 4$ into the expression for TU, $TU=9x + 2$.
$TU=9\times4+2=36 + 2=38$.

Step3: Find TV in problem 3

Substitute $x = 4$ into the expression for TV, $TV=14x-8$.
$TV=14\times4-8=56 - 8=48$.

Step4: Solve for x in problem 4

Since T is the mid - point of SU, $ST = TU$.
So $8x+11=12x - 5$.
Move the terms with x to one side and constants to the other side: $12x-8x=11 + 5$.
$4x=16$.
Solve for x: $x = 4$.

Step5: Find ST in problem 4

Substitute $x = 4$ into the expression for ST, $ST=8x + 11$.
$ST=8\times4+11=32 + 11=43$.

Step6: Find SU in problem 4

$SU=ST+TU$, and since $ST = TU = 43$, $SU=43+43 = 86$.

Answer:

3.
$x = 4$
$TU = 38$
$TV=48$
4.
$x = 4$
$ST = 43$
$SU=86$