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1 year ago

Which triangles are the images of JSK after preforming a reflection?

Mathematics

1 answer:

Jet001 [13]1 year ago

3 0

A reflection is a form of transformation that takes each point in a figure and reflects it over a line

<h3>What is reflection?</h3>

It should be noted that a reflection is a mirror image of the shape. In this case, an image will reflect through a line, known as the line of reflection.

The figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

If A B C is the pre-image, then the triangle, A ′ B ′ C ′ is the resulting image after reflecting the triangle.

Note that an overview was given as the complete information wasn't found.

Learn more about reflection on:

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Solve for x in the given interval.<br><br> sec x= -2√3/3, for π/2 ≤x≤π

drek231 [11]

Answer:

b. $x=\frac{5\pi}{6}$

Step-by-step explanation:

The given function is

$\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi$

Recall that the reciprocal of the cosine ratio is the secant ratio.

This implies that;

$\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}$

$\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }$

$\Rightarrow \cos x=-\frac{\sqrt{3}}{2}$

We take the inverse cosine of both sides to obtain;

$x=\cos^{-1}(-\frac{\sqrt{3}}{2})$

$x=\frac{5\pi}{6}$

4 0

3 years ago

Life Expectancies In a study of the life expectancy of people in a certain geographic region, the mean age at death was years an

Sphinxa [80]

Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean life expectancy, $\sigma$ is the standard deviation and n is the size of the sample.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean $\mu$ , standard deviation $\sigma$ .

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

$Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

Find the probability that the mean life expectancy will be less than years.

8 0

2 years ago

A triangle has a base of 3⅖ inches and an area of 5⅒ square inches. Find the height of the triangle. Show your reasoning

N76 [4]

Answer: 3 in.

Step-by-step explanation:

Given

The base of the triangle is $3\frac{2}{5}\ inches$

The area of the triangle is $5\frac{1}{10}\ inches^2$

Solve mixed fraction

Base is

$=3\dfrac{2}{5}\\\\=\dfrac{17}{5}\ in.$

Area is

$=5\dfrac{1}{10}\\\\=\dfrac{51}{10}\ in.^2$

The area of the triangle is given by

$\Rightarrow \text{Area A=}\dfrac{1}{2}\times \text{base}\times \text{height}$

Insert the values to get the height

$\Rightarrow \dfrac{51}{10}=\dfrac{1}{2}\times \dfrac{17}{5}\times \text{height}\\\\\Rightarrow \text{height}=3\ in.$

8 0

3 years ago

What is the value of a? -2(a-8)+6a=36

Aleksandr [31]

First we expand the brackets:

-2a + 8 + 6a = 36
4a + 8 = 36

We then need to get the a's onto one side and the numbers onto the other:

4a = 28

We can then divide to get an x by itself:

a = 28/4 = 7

6 0

3 years ago

Read 2 more answers

Which is greater, 1 3/4 or 1?

lions [1.4K]

Answer:

1 3/4

Step-by-step explanation:

1 3/4 is 3/4 more than one.

5 0

3 years ago

Read 2 more answers