Which BEST shows where this function is only decreasing?

Triangle A'B'C' is a rotation of triangle ABC by 60 degrees using Q as the center.

butalik [34]

Answer:

The correct options are;

D. Triangles ABC and A'B'C' are congruent

E. Angle ABC is congruent to angle A'B'C'

F. Segment BC is congruent to segment B'C'

H. Segment AQ is congruent to segment A'Q'

Step-by-step explanation:

The given information are;

The angle of rotation of triangle ABC = 60°

Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;

1) The length of the sides of the figure of the preimage and the image are congruent

Therefore;

BC ≅ B'C'

2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image

Therefore;

∠ABC ≅ ∠A'B'C'

3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation

Therefore;

Segment AQ ≅ A'Q'.

4 0

3 years ago

Say you have a tic toe box of 3 by 3 how do you make each diagonal and vertical line equal 15 only using # 1-10

SpyIntel [72]

| 8 | | 1 | | 6 |
-------------------
| 3 | | 5 | | 7 |
-------------------
| 4 | | 9 | | 2 |

7 0

3 years ago

the bleachers at the football game are 7/8 full, and 1/2 of the fans in the bleachers are rooting for the home team. what fracti

wolverine [178]

First you have to find a common denominator which is 8.
1/2 =4/8
7/8 - 4/8 = 3/8
So the answer is 3/8.

5 0

2 years ago

In the accompanying diagram. altitude CD is

Bogdan [553]

Answer: √117

Step-by-step explanation:

Since no diagram present, am assuming hypotenuse AB and right angle C. Let side opp angle B be b, and side opposite angle A be a. Altitude CD is x.

a^2 + b^2 = 22^2 (Pythagorean)

Using Pythag on two smaller triangles,

x^2 + 13^2 = a^2

x^2 + 9^2 = b^2

Substituting in first equation,

x^2 + 13^2 + x^2 + 9^2 = 22^2

x^2 = 117, so x = √117

7 0

2 years ago

A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

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 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 .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

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

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

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

$df=n-1=17-1=16$

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 tabel to find the critical values.