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2 years ago

14

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and cos ∠X = 2.5 over 5 and 59 hundredths. Triangles XYZ

and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent. Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB. You must show all work and calculations to receive full credit. (5 points) Part B: Explain how to find the measures of segments AC and AB. You must show all work and calculations to receive full credit. (5 points)

1 answer:

adell [148]2 years ago

5 0

Dilation involves changing the size of a shape

<h3>How to determine the relationship between the trigonometry ratios</h3>

From the question, we understand that:

The dilation of triangle XYZ gives triangle ACB

This means that, the following are corresponding points

Points X and A
Points Y and C
Points Z and B

The above means that:

The relationships between the trigonometry ratios of both triangles are:

cos(X) = cos(A), cos(Y) = cos(C) and cos(Z) = cos(B)

<h3>How to determine the measures of segments AC and AB</h3>

In (a), segments XY and XZ corresponds to the segments AC and AB

So, the product of the lengths of XY and XZ and the scale factor will result in the lengths of AC and AB,

i.e.

AC = 2 * XY and AB = 2 * XZ

Read more about dilation at:

brainly.com/question/26332230

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(-1/3) to the power of five?

Bumek [7]

$\bf \left( -\cfrac{1}{3} \right)^5\implies \left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\implies -\cfrac{1^5}{3^5}\implies -\cfrac{1}{243}$

recall minus * minus * minus * minus * minus is minus.

8 0

3 years ago

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

a

$\= x = 13.4$ . $E = 2.3$

b

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

3 years ago

Lacey deposited $4,860 in a new credit union savings account on the first day of the quarter. The principal earns 4% interest co

Softa [21]

Answer:

$4956.23 approx

Step-by-step explanation:

Given data

P= $4860

R= 4%

T= 6 months = 0.5 years

Applying the compound interest formula we have

A=P(1+r)^t

Substitute

A=4860(1+0.04)^0.5

A= 4860(1.04)^0.5

A=4860*1.0198

A=4956.228

Hence the balance will be $4956.23 approx

7 0

3 years ago

NEED HELP ASAP PLEASE

kati45 [8]

Answer: its (0,2/3)

Step-by-step explanation: i say this because 2/3 equal 0.6 so 0.6 will be on the y-axis and 0 will be on the x-axis, this will equal a line that meats up wit R and is parallel to PQ. I hope this helps.

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3 years ago

What is the slope of a line that is perpendicular to the line y=-1/3x-6?

max2010maxim [7]

Y=-1/3x-6, for this line, the slope (m) is -1/3.
This is because the equation is in the slope intercept form: y = mx + b.
The perpendicular line to one with m = -1/3, is the negative reciprocal of m, we'll call it m2.
m2 = --3/1 = +3/1 = 3

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3 years ago