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3 years ago

Its in the link belowwwww its 8th grade math.. tysvm

Mathematics

1 answer:

Alexandra [31]3 years ago

5 0

Answer:

Step-by-step explanation:

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3 years ago

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If GF is a midsegment of CDE, find CD. A. 3.4 B. 6.8 C. 13.6 D. 14

bogdanovich [222]

Answer:

Step-by-step explanation:

Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:

$\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}$

We can now cross multiply and solve for CD:

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

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

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3 years ago

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