Sierra has plotted two vertices of a rectangle at (3,2) and (8,2). What is the length of the sides of the rectangle

Use the diagram and given information to answer the questions and prove the statement.

Greeley [361]

Answer:

See explanation

Step-by-step explanation:

<u> ASA Postulate (Angle-Side-Angle):</u>

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Consider triangles XYB and ZYA. In these triangles

∠X≅∠Z (given)
XY≅ZY (given)
∠Y is common angle

By ASA Postulate, triangles XYB and ZYA are congruent. Congruent triangles have congruent corresponding sides, so

BX≅AZ

6 0

3 years ago

What is the equation of a line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ? Enter your equation in th

ANTONII [103]

Perpendicular lines have slopes that multiply to get -1
y=mx+b is the slope intercept equation
m=slope

so get into y=mx+b form
-x+2y=4
solve for y
add x both sides
2y=x+4
divide by 2 both sides
y=(1/2)x+2
the slope is 1/2

perppendicular line slope multiplies to -1
1/2 times what=-1
times 2/1 both sides
what=-2/1=-2

y=-2x+b
find b
we are given a point is (-2,1)
when x=-2, y=1
1=-2(-2)+b
1=4+b
minus 3 both sides
-3=b

so the equation is
y=-2x-3

your teacher might want it in standard form (ax+by=c) so
add 2x both sides
2x+y=-3 is an equation

so y=-2x-3 is correct (slope intercept form)
2x+y=-3 is also correct (standard form)

6 0

3 years ago

How to convert 80 kilometers per hour is 60 miles per hour?

Tatiana [17]

1 km = 0.62 mi
1 mi = 1.6 km

80*0.62
-or-
60*1.6

Hope this helps

5 0

3 years ago

I only need help with #17 pls

Sholpan [36]

Answer:

I'm pretty sure the answer is A) Dilation.

7 0

3 years ago

Read 2 more answers

The current process has a mean of 2.50 and a std deviation of 0.05. A new process has been suggested by research. What sample si

Novay_Z [31]

Answer:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(0.05)}{0.02})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=0.05$ represent the population standard deviation

n represent the sample size (variable of interest)

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =0.02 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(0.05)}{0.02})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

7 0

3 years ago