$\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}$

Since GF is a midsegment of CDE, CD is double of CF. So we can write:

$CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0$

By using quadratic formula $\frac{-b+-\sqrt{b^2-4ac} }{2a}$ and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:

$\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2$

Since the expression for CD is $\frac{15x^2+16x+3.2}{2x+3}$ , we plug in $x=2$ into this expression to find value of CD:

$\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6$

The correct answer is C

6 0

3 years ago

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X3 + 2x2 - 48x Help please

lutik1710 [3]

Answer:

Step-by-step explanation:

4 0

3 years ago

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What is the solution to the equation? (-9x+5)^1/2=(3+4x)1/2

Phoenix [80]

x in (-oo:+oo)

((5-9*x)^1)/2 = ((4*x+3)^1)/2 // - ((4*x+3)^1)/2

((5-9*x)^1)/2-(((4*x+3)^1)/2) = 0

(5-9*x)/2-((4*x+3)/2) = 0

(5-9*x)/2+(-1*(4*x+3))/2 = 0

5-1*(4*x+3)-9*x = 0

2-13*x = 0

(2-13*x)/2 = 0

(2-13*x)/2 = 0 // * 2

2-13*x = 0

2-13*x = 0 // - 2

-13*x = -2 // : -13

x = -2/(-13)

x = 2/13

x = 2/13

4 0

4 years ago