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ddd [48]
2 years ago
15

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

Mathematics
2 answers:
bogdanovich [222]2 years ago
6 0

Answer:

C


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}

<em>We can now cross multiply and solve for CD:</em>

\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

<em>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:</em>

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


<em>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:</em>

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

The correct answer is C

8090 [49]2 years ago
6 0

Answer:

C. 13.6

Step-by-step explanation:

We have been given that GF is a mid-segment of CDE.

Since we know that mid-segment of a triangle is half the length of its parallel side.

We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:

GF=\frac{1}{2}ED

Let us substitute given value of GF and ED to find our x.

2x+3=\frac{1}{2}(5x+4)

Multiply both sides of equation by 2.

2*(2x+3)=2*\frac{1}{2}(5x+4)

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

4x+6=5x+4

6=5x+4-4x

6=x+4

6-4=x

2=x

We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.

\frac{CF}{GF}=\frac{CD}{ED}

Substitute given values.

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

Upon substituting x=2 in our equation we will get,

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

Let us simplify our equation.

\frac{6+0.8}{4+3}=\frac{CD}{10+4}

\frac{6.8}{7}=\frac{CD}{14}

14*\frac{6.8}{7}=CD

2*6.8=CD

13.6=CD

Therefore, CD equals 13.6 and option C is the correct choice.

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in an examination ,80%examines passed in English ,70%in mathematics and 60% in both subject if 45 examines failed in both find t
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Answer:

135 and 135

Step-by-step explanation:

The computation is shown below:

The number of examiners who passed in only one subject is as follows

=  n(E) - n(E ∩M) + n(M) - n(E ∩M)

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Now the number of students who passed in minimum one subject is

n(E∪M) = n(E) + n(M) -  n(E ∩M)

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Now the number of students who failed in both subjects is

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Now the Number of students who failed in mathematics is

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Answer:

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Step-by-step explanation:

Well assuming that DM means diameter of a circle, then r should be the radius of the circle.

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