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2 years ago

ΔABC and ΔDEF appear to be similar. Which set of measurements prove that the two triangles are similar?

Mathematics

1 answer:

Triss [41]2 years ago

5 0

Answer:

Step-by-step explanation:

Similar triangles have congruent corresponding angles, and proportional corresponding sides.

The only angle given is angle A, which will correspond to angle D if the similarity statement is true. That is, angle D must be 35°. (Eliminates choice D)

The ratios of the given sides are AB:AC = 9:12 = 3:4. The corresponding sides would be DE:DF. (Eliminates choice A)

The remaining choices have side ratios of ...

B. DE : DF = 16 : 21 ≠ 3 : 4

C. DE : DF = 12 : 16 = 3 : 4

The set of measurements that would make ΔABC ~ ΔDEF is ...

DE = 12, DF = 16, and ∠D = 35°

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4 years ago

Let △ABC be a right triangle with m∠C = 90°. Given tan ∠B = 1, find tan ∠A.

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3 years ago

Find the perimeter and area of the figure.

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4 years ago

Read 2 more answers

What is the answer for AC =

Triss [41]

Answer:

The length of AC is 2.33 units.

Step-by-step explanation:

You have to use Tangent Rule, tanθ = opposite/adjacent :

$\tan(θ) = \frac{oppo.}{adj.}$

Let oppo. = AC,

Let adj. = BC = 5,

Let θ = 25°,

$\tan(25) = \frac{ac}{5}$

$ac = 5 \tan(25)$

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3 years ago

A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const

Ludmilka [50]

Answer:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation

s=0.68 represent the sample standard deviation

$\bar x =98.90$ represent the sample mean

n=98 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:

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

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

$df=n-1=98-1=97$

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.