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Irina18 [472]
3 years ago
6

The vertices of ΔABC are A(2, -5), B (-3, 5), and C (3, -3). The triangle is reflected over the x-axis. Use arrow notation to de

scribe the original
triangle and its reflection.
Mathematics
2 answers:
Artyom0805 [142]3 years ago
8 0
Reflected over the x-axis: A'(2,-5),B'(-3,-5),C'(3,3)<span>. Hence, the original triangle is described by A'B'C'.</span>
Nitella [24]3 years ago
8 0
The triangle is reflected over the X- Axis, therefore the arrow notation should be around A, B and C.
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The Hypotenuse is side just opposite to the right angle.

Step-by-step explanation:

By Pythagoras' theorem,

c^2=a^2+b^2

c^2(hypotenuse to be found)= 30^2+ 16^2

<em>c^2=1156 </em>

<em><u>Therefore, c ( i.e. the hypotenuse) will be the square root of 1156. </u></em>

<em><u>The square root of 1156 is 34. </u></em>

<h2><em><u>Thus, c ( hypotenuse) = 34</u></em></h2>

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2 years ago
What is the solution to the system of equations?<br> O (-4,1)<br> O (-2, 1)<br> O (1.4)<br> O (1,-2)
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Answer:

<em></em>(1,-2)<em></em>

<em></em>

Step-by-step explanation:

Given

The attached graph

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The solution here is the intersection points of the two lines. From the attachment, both lines meet

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<em>Hence, the solution is: </em>(1,-2)<em></em>

3 0
2 years ago
The scores of students on the ACT college entrance exam in a recent year had the normal distribution with mean  =18.6 and stand
Maurinko [17]

Answer:

a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 18.6, \sigma = 5.9

a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?

This is 1 subtracted by the pvalue of Z when X = 21. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 18.6}{5.4}

Z = 0.44

Z = 0.44 has a pvalue of 0.67

1 - 0.67 = 0.33

33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?

Now we have n = 76, s = \frac{5.9}{\sqrt{76}} = 0.6768

This probability is 1 subtracted by the pvalue of Z when X = 20.4. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{20.4 - 18.6}{0.6768}

Z = 2.66

Z = 2.66 has a pvalue of 0.9961

1 - 0.9961 = 0.0039

0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

4 0
2 years ago
What is x if 3x+2=5x-8?
anyanavicka [17]
3x + 2 = 5x - 8
Flip
5x - 8 = 3x + 2
Subtract both sides by 3x
2x - 8 = 2
Add both sides by 8
2x = 10
Divide both sides by 2
x = 5

That's your answer.

Have an awesome day! :)

From your friendly Helper-in-Training, collinjun0827
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