1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
A red die, a blue die, and a yellow die (all six sided) are rolled. we are interested in the probability that the number appeari
NISA [10]

5/54 or approximately 0.092592593  
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
 r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
 r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
 r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
 r = 4, y = 2, b = 1, so n = 3 + 1 = 4
 r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
 r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
 r = 5, y = 2, b = 1, so n = 9 + 1 = 10
 
 And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
 r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
 r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
 r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
 r = 6, y = 2, b = 1, so n = 19 + 1 = 20 
 And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
6 0
2 years ago
Translate the sentence into an equation
Veseljchak [2.6K]
7(y+2)=3
seven times the sum of a number (y) and 2
means y+2 multiplying by 7
4 0
3 years ago
Read 2 more answers
Find the distance between the points (-3, 11) and (5, 5).<br><br> 10<br><br> 2<br><br> 2
Masja [62]
The correct answer is 10
7 0
3 years ago
Read 2 more answers
What is the height of this relation: <br> h= -0.3d² + 1.2d + 1.5
marshall27 [118]

Answer:

h = -0.3d^2 + 1.2d + 1.5

Step-by-step explanation:

3 0
3 years ago
Please help STRUGGLING with math few math questions! Ty
-BARSIC- [3]

Question 1:


F(x) and g(x) are like variables, just plug into the equation.


f(x) + g(x) = (x + 6) + (12x - 7)


x+6+12x-7 = 13x-1


Question 2: f(3) + g(-1)


You plug in the x-values into the equation, and then take the answer and add them together.


f(3) = 3+4

g(-1) = 12(-1)-6


f(3) = 7

g(-1) = -18


7 + (-18) = -11


Question 3:


This is similar to question 1, plug in the variables and simplify.


9x - (7x+3)


Remember to distribute the "-"


9x - 7x - 3

2x - 3

6 0
3 years ago
Read 2 more answers
Other questions:
  • 7) 19 = 9 + 2(x – 7)
    13·2 answers
  • The table below represents a linear function f(x) and the equation represents a function g(x):
    8·2 answers
  • I need help on this!!!
    8·2 answers
  • A quarter, a nickel,and a penny are flipped. Find the probability of each of the following:-
    13·1 answer
  • Tonysha has two bags. Each bag has three objects in it. The first bag has one dime, one nickel, and one penny. The second bag ha
    5·2 answers
  • Mr. Garner’s gas tank holds 17.5 gallons of gasoline. How much will it cost him to fill up his gas tank if gasoline costs $2.48
    9·1 answer
  • Help please ASAP!!!!!!
    6·2 answers
  • 9. Select one of the factors of 3x + 4x -4.
    12·1 answer
  • Solution
    12·1 answer
  • Domain range function explained
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!