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Licemer1 [7]
3 years ago
6

Find x and y, given that line WS and line VT are parallel. Show all work!

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.

\frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU}..........(Equation 1)

Checking the diagram given, we see that:

VT=y, WS=22, VU=8, ST=x-2

WU=WV+VU=12+8=20

TU=5

SU=ST+TU=(x-2)+5=x+3

Thus, substituting the required values in (Equation 1) we get:

\frac{y}{22}=\frac{8}{20}=\frac{5}{x+3}

Now, as can be clearly seen, to find y we will use the first two ratios as:

\frac{y}{22}=\frac{8}{20}

y=\frac{8\times 22}{20}=8.8

In a similar manner, to find the value of x we can use the last two ratios:

\frac{8}{20}=\frac{5}{x+3}

After cross multiplication we get:

5\times 20=8(x+3)

Which can be simplified as:

x+3=\frac{100}{8} =12.5

Thus, x=12.5-3=9.5

Therefore, the required answer is:

x=9.5 and y=8.8



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5 0
2 years ago
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and
olchik [2.2K]

Answer:

12 boys

Step-by-step explanation:

From the above question:

Number of boys = 3

Number of girls = 2

Boys: Girls

3:2

Let :

a = boys

b = girls

Hence, a : b = 3 : 2

a/b = 3/2  

Cross Multiply

2a = 3b .......... Equation 1

a = 3b/2

If four more girls join the class, there will be the same number of boys and girls

Hence,

a: b + 4 = 3 : 3

a/b + 4 = 3/3

Cross Multiply

3a = 3(b + 4)

3a = 3b + 12 ........ Equation (2)

From Equation 1: a = 3b/2

Substitute 3b/2 for a in Equation 2 we have:

3a = 3b + 12 .........Equation 2

3(3b/2) = 3b + 12

9b/2 = 3b + 12

Cross Multiply

9b = 2(3b + 12)

9b= 6b + 24

9b - 6b = 24

3b = 24

b = 8

Substitute 8 for b in Equation 1

a = 3b/2

a = 3 × 8/2

a = 24/2

a = 12

Therefore, the number of boys in the class is 12

7 0
3 years ago
What is the value of 27÷(−34⋅−45)?<br> 4<br><br> 16/15<br><br> 28 4/5<br><br> 45
MakcuM [25]

Answer:

It would not be any of those answers. it would be 106 :) Its negative numbers divided

5 0
2 years ago
How many and what is the solution to 2(x − 1) + 3 = 3x − (x + 4)?
Licemer1 [7]

Answer:

0=−5

Step-by-step explanation:

5 0
3 years ago
Do this for me and I will give 42 points, it is 9th grade prob and stats.
Hitman42 [59]

answer what question?

6 0
3 years ago
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