All categories

3 years ago

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.

You might be interested in

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.