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4 years ago

Which pair of triangles MUST be similar?

Mathematics

2 answers:

Naily [24]4 years ago

7 0

Answer:

b.) Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.

Step-by-step explanation:

b.) triangle 7's 3 angles: 40° , 35° and 180° - 40° - 35° = 105°

triangle 8: 40° , 105° and 180° - 40° - 105° = 35°

they have all 3 corresponding angles congruent, triangle and triangle 8 is similar (AAA)

PilotLPTM [1.2K]4 years ago

6 0

Answer:

b.) Triangles 7 and 8 are similar.

Step-by-step explanation:

If triangles have the same angle measurements, they are similar

If we have two angles, we can find the third by using the equation 180 (total of all angles in any triangle) - angle 1 -angle 2 = angle 3.

Let's set up this value with values from triangle 7.

180-40-35=angle 3

105=angle 3

Thus, the angle measurements of triangle 7 are 35, 40, anf 105.

Let's set up the same equation with value for triangle 8.

180-40-105=angle 3

35=angle 3

Thus, the angle measurements of triangle 8 are 35, 40, anf 105, the same as those of triangle 7, meaning the two triangles are similar.

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3 years ago

32. Solve for h. bh-u+g=w

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Answer:

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Step-by-step explanation:

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4 years ago

Solve 2x+4 so that it has no solution

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3 years ago

In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system

Contact [7]

Answer:

n=206

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.09$ , we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.09}{2.58})^2}=205.44$

And rounded up we have that n=206

3 0

3 years ago

Help!! What is arc HLK? Thankyou!

Bezzdna [24]

We know Angle HMK is half the sum of Arc JI and Arc HLK. So, we can set up an equation.

8x - 1 = 1/2 (3x + 2 + 15x - 36)

8x - 1 = 1/2 (18x - 34)

16x - 2 = 18x - 34

32 = 2x

16 = x

Then, we can substitute x into Arc HLK

HLK = 15x - 36

HLK = 240 - 36

Arc HLK = 204°

5 0

3 years ago