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sashaice [31]
3 years ago
15

If triangle VWZ is congruent to triangle XWY, find the length of YX.

Mathematics
1 answer:
valkas [14]3 years ago
8 0

Answer:

Measure of side YX is 22 units.

Step-by-step explanation:

Since ΔVWZ ~ ΔXWY, their corresponding sides will be in the same ratio.

\frac{VW}{XW}=\frac{VZ}{XY}=\frac{WZ}{WY}

By substituting the values given in the picture in the ratio,

\frac{45}{30}=\frac{(3x-9)}{(x+8)}=\frac{36}{24}

\frac{(3x-9)}{(x+8)}=\frac{3}{2}

By cross multiplication,

2(3x - 9) = 3(x + 8)

6x - 18 = 3x + 24

(6x -18) + 18 = 3x + 24 + 18

6x - 3x = (3x + 42) - 3x

6x - 3x = 42

3x = 42

x = \frac{42}{3}

x = 14

m(YX) = x + 8

          = 14 + 8

          = 22

Therefore, measure of side YX is 22 units.

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The vertices of a square are located at (0,4), (4,0), (0, -4) and (-4,0).
kozerog [31]
The answer is: (4,0), (0,4)

4 0
2 years ago
A random sample of 9 wheels of cheese yielded the following weights in pounds has a sample mean of 20.90 and a sample variance o
Ronch [10]

Answer:

2.002 \leq \sigma^2 \leq 11.365

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

s^2 represent the sample variance

n=9 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

On this case we need to find the sample standard deviation with the following formula:

s=sqrt{\frac{\sum_{i=1}^9 (x_i -\bar x)^2}{n-1}}
The sample variance given was [tex]s^2=3.45

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=9-1=8

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,8)" "=CHISQ.INV(0.95,8)". so for this case the critical values are:

\chi^2_{\alpha/2}=15.507

\chi^2_{1- \alpha/2}=2.732

And replacing into the formula for the interval we got:

\frac{(9)(3.45)}{15.507} \leq \sigma \frac{(9)(3.45)}{2.732}

2.002 \leq \sigma^2 \leq 11.365

7 0
3 years ago
A system of equations is shown on the graph below.how many solutions does this system have
lisabon 2012 [21]

Answer:

1

Step-by-step explanation:

A solution to a system of equations is the point where the 2 lines meet.

6 0
3 years ago
Marco needs to buy some cat food. At the nearest​ store, 5 bags of cat food cost ​$18.75. How much would Marco spend on 3 bags o
Ira Lisetskai [31]

Answer:

$11.25

Step-by-step explanation:

5 bags = $18.75

To find the amount for three bags, we need to find the price for <em>each </em>bag.

Divide 18.75 by 5.

18.75/5 = 3.75

So each bag is 3.75, and since we need to know the price for 3 bags, we need to multiply 3.75 by 3, which is 11.25.

7 0
3 years ago
Which of these ratios is not a rate?
Doss [256]

Answer:

i think it is B

Step-by-step explanation:

because that one isn't really a rate as much as the other ones are, its more of a ratio, i'm bad at explaining things, hope its correct :D

6 0
3 years ago
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