geometry help i have no clue what to do?

Question

If EF= 2x-12, FG= 3x-15, and EG = 23, find the values of x, EF, and FG.

x= ?
EF= ?
FG=?

Answer 1

EG=EF+FG

so, therefore you can set (2x-12)+(3x-15)=23 and solve for x

after solving for x, substitute that answer in for your x's in (2x-12) and (3x-15) to find your values for EF and FG

Answer 2

You also have given no diagram, so we have to assume;-{
EFG is a right-angled triangle, with EG the hypotenuse.
So (EF)^2 + (FG)^2 = (EG)^2
So substituting your information we have:
(2x-12)^2 + (3x-15)^2 = (23)^2
Expanding this we get:
(4x^2 - 24x + 144) + (9x^2 - 90x + 225) = 529
Gathering like terms we get:
13x^2 -114x + 369 = 529
Subtracting right-side from left-side gives:
13x^2 -114x - 160 = 0
Factoring into binomials:
(13x + 16)(x - 10) = 0
So either:
13x + 16 = 0, 13x = -16
Negative value makes no sense.
Or:
x - 10 = 0, x = 10
Substituting in original:
EF = 20 -12 is 8
FG = 30 - 15 is 15

Answer 3

a million. A 30-60-ninety triangle has the hypotenuse two times the scale of the shorter leg. it particularly is by way of fact sin 30 = 0.5. R lies on the line y = -3 by way of fact Q is a proper perspective. So R is at (x, -3). PR^2 = QR^2 + PQ^2. yet PQ = 9 contraptions (from given records). PR^2 = (x-a million)^2 + 80 one. additionally x-a million = PR/2. subsequently 4(x-a million)^2 = (x-a million)^2 + 80 one 3(x-a million)^2 = 80 one. (x-a million)^2 = 27 x = sqrt27 +a million or -sqrt27 + a million. a threat coordinates of R are (a million + sqrt27, -3) and (a million - sqrt27, -3) 2. you want a factor (x, y) this is equidistant from A, B, C. The circle passes by way of A, B, and C. for this reason you have 2 equations. (x-2)^2 + (y-2)^2 = (x-3)^2 + (y+a million)^2 = x^2 + (y-a million)^2. Simplify this and get: 8 - 4x - 4y = 10 - 6x + 2y = a million - 2y. those come to: 6x - 4y = 9 and x - 3y = a million. suggestions are: x = 23/14, y = 3/14. Circumcenter is at (23/14, 3/14).

Answer 4

2x-12+3x-15=23
x=10