If DGH ~ DEF, find the value of x.

x = 25

Step-by-step explanation:

DGH is congruent with DEF

(meaning DG is congruent with DE, GH is congruent with EF, DH is congruent with DF)

DG = 52 & DE = 91

GH = x + 3 & EF = 2x-1

in this case we can disregard DH and DF since its providing no information

write the equation as:

52       x+3

  =  

91        2x-1

cross multiply 52 and 2x-1 then cross multiply 91 and x+3

this should give you:

52(2x-1) = 91(x+3)

distribute:

104x - 52 = 91x + 273

then solve using algebra

13x - 52 = 263

13 = 325

x = 25

Hope this helps!!

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

597

step-by-step explanation: