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3 years ago

15

How are pairs of alternate interior angles related to one another? How are pairs of alternate exterior angles related to one ano

ther? Describe the relationship between these pairs using geometric terms.

1 answer:

eduard3 years ago

4 0

Answer:Each pair of alternate interior angles is congruent, and each pair of alternate exterior angles is congruent.

Step-by-step explanation:

You might be interested in

A loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency.

Law Incorporation [45]

Answer:

4.4

Step-by-step explanation:

The sum of the probabilities of all possible outcomes is 1.

As the die is loaded so that the number 4 occurs 3/10 of the time, and the other numbers occur with equal frequency, then the probability of numbers 1, 2, 3, 5, 6, 7 and 8 being rolled is 1/10.

Create a probability distribution table for X, where X is the score on the loaded 8-sided die:

$\begin{array}{ | c | c | c | c | c | c | c | c | c |}\cline{1-9}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\cline{1-9} & & & & & & & &\\ \text{P}(X=x) & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{3}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10}\\& & & & & & & &\\\cline{1-9}\end{array}$

Add a product row and a totals column:

$\begin{array}{ | c | c | c | c | c | c | c | c | c | c |}\cline{1-10}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 &\text{Total} \\ \cline{1-10} &&&&&&&&& \\ \text{P}(X=x) & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{3}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & 1\\ &&&&&&&&&\\ \cline{1-10} &&&&&&&&&\\\text{Product} & \frac{1}{10} & \frac{2}{10} & \frac{3}{10} & \frac{12}{10} & \frac{5}{10} & \frac{6}{10} & \frac{7}{10} & \frac{8}{10} & \frac{44}{10} \\ &&&&&&&&&\\\cline{1-10}\end{array}$

(The Product is row is the product of the <u>score on the die</u> and <u>its probability</u>).

The expected value (EV) is the sum of the product of each outcome and its probability.

Therefore, the expected value (EV) of this die is 44/10 = 4.4

6 0

2 years ago

Help please will give brainliest

vampirchik [111]

Answer:

R=0.25

Step-by-step explanation:

Y=RX

2=R×8

2/8=8R/8

R=0.25

7 0

3 years ago

Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).

seraphim [82]

Answer:

Choice B. $\displaystyle y - 7 = -\frac{6}{11} \, (x + 7)$ .

Step-by-step explanation:

Start by finding the slope of this line. Let $(x_1,\, y_1)$ and $(x_2,\, y_2)$ represent two distinct points on a line on a Cartesian Plane. (That is, $x_1 \ne x_2$ .) The slope of this line would be:

$\displaystyle \frac{y_2 - y_1}{x_2 - x_1}$ .

For the line in this question:

$x_1 = -7$ ,
$y_1 = 7$ ;

$x_2 = 4,$
$y_2 = 1$ .

Indeed, $x_1 \ne x_2$ . The slope of this line would thus be $\displaystyle \frac{1 - 7}{4 - (-7)}$ , which is equal to $\displaystyle -\frac{6}{11}$ .

On a Cartesian Plane, the point-slope form of a line that has a slope of $m$ and includes the point $(x_0,\, y_0)$ can be written as:

$y - y_0 = m\, (x - x_0)$ .

(Note the minus signs in this form.)

For the line in this question, $m = \displaystyle -\frac{6}{11}$ . There are two equivalent expressions for its point-slope form:

Using the first point, $y - 7 = \displaystyle -\frac{6}{11}\, (x - (-7))$ . This equation is equivalent to $y - 7 = \displaystyle -\frac{6}{11}\, (x + 7)$ .
Using the second point, $y - 1 = \displaystyle -\frac{6}{11}\, (x - 4)$ .

7 0

4 years ago

For the function f(x)=2x+1 and g(x)=3x-2, find (f-g)(4)

icang [17]

Answer:

-5

Step-by-step explanation:

Here is how you solve this problem:

First, you set it up like this: 2x+1-3x+2

Second:You are finding f(4) and g(4) so you just plug in 4 for both problems:

2(4)+1-3(4)-2= 9-14= -5

4 0

4 years ago

If the cube shown is 5 inches on all sides, what is the length of the diagonal, x, of the cube?

Pavel [41]

Answer:

$5\sqrt{3} inches$

Step-by-step explanation:

3 0

3 years ago