In the triangle below, calculate the value of x.

Unit 3 parallel and perpendicular lines Homework 3 proving lines are parallel

IrinaK [193]

Step-by-step explanation:

Since, lines l and m are parallel and a transverse is intersecting these lines.

5). (9x + 2)° = 119° [Alternate intrior angles]

9x = 117 ⇒ x = 13

6). (12x - 8)° + 104° = 180°

12x = 180 - 96

x = ⇒ x = 7

7). (5x + 7) = (8x - 71) [Alternate exterior angles]

8x - 5x = 71 + 7

3x = 78

x = 26

8). (4x - 7) = (7x - 61) [Corresponding angles]

7x - 4x = -7 + 61

3x = 54

x = 18

9). (9x + 25) = (13x - 19) [Corresponding angles]

13x - 9x = 25 + 19

4x = 44

(13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary]

(13×11) - 19 + 17y + 5 = 180

129 + 17y = 180

17y = 180 - 129

y = 3

10). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]

3x + 8y = 180 + 12

3x + 8y = 192 -----(1)

(8y + 17) = (6x - 7) [Alternate exterior angles]

6x - 8y = 24

3x - 4y = 12 -----(2)

Equation (1) - equation (2)

(3x + 8y) - (3x - 4y) = 192 - 12

12y = 180

y = 15

From equation (1),

3x + 8(15) = 192

3x + 120 = 192

x = 24

11). (3x + 49)° = (7x - 23)° [Corresponding angles]

7x - 3x = 49 + 23

4x = 72 ⇒ x = 18

(11y - 1)° = (3x)° [Corresponding angles]

11y = 3×18 + 1

11y = 55 ⇒ y = 5

12). (5x - 38)° = (3x - 4)° [Corresponding angles]

5x - 3x = 38 - 4

2x = 34

x = 17

(7y - 20)° + (5x - 38)° + 90° = 180°

[Sum of interior angles of a triangle = 180°]

5x + 7y = 148

5×17 + 7y = 148

85 + 7y = 148

7y = 148 - 85

y =

5 0

3 years ago

Please answer I will mark brainliest

77julia77 [94]

Answer:

3,466.32

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A researcher collected data from a sample of correctional officers and found that on average they made 47,173 dollars a year wit

ollegr [7]

Answer:

a) $z = \frac{40000- 47173}{6364} = -1.127$

b) $z = \frac{50000- 47173}{6364} = 0.444$

c) $P(X>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)$

And we can find this probability using the complement rule and the normal standard distribution or excel and we got:

$P(z>-1.127)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of money of a population of interet, and we know the following info:

Where $\bar X=47173$ and $s=6364$

We can assume that the sample size is large and the estimators can be used as a good description for the parameters $\mu \sigma$

The z score for 40000 would be:

$z = \frac{40000- 47173}{6364} = -1.127$

Part b

The z score for 50000 would be:

$z = \frac{50000- 47173}{6364} = 0.444$

Part c

We are interested on this probability

$P(X>40000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)$

And we can find this probability using the complement rule and the normal standard distribution or excel and we got:

$P(z>-1.127)=1-P(z$

8 0

3 years ago

Which statements are true about the rectangular pyramid below? Select three options .

sp2606 [1]

Answer:

First, second, and fourth are true.

Step-by-step explanation:

Ok, so let's get to it.

The first statement is true, since 6 * 4 = 24.

The second statement is also true, since the 4 triangles are the 4 sides.

The third statement is false since they aren't congruent since they don't have a consistent ratio.

The fourth one is true, since 24(2) + 18.4 does indeed equal to 66.4

The fifth one is false since only the <u>base </u>has an area of 24.

:)

8 0

3 years ago

In a board game, students draw a number do not replace it, and then draw a second number. Determine the probability of each even

murzikaleks [220]

The figure depicting the board game is attached below.

Answer:

Step-by-step explanation:

Kindly note that selections done without replacement.

Count of numbers on the board game = 8

Count of odd numbers = (1, 9, 1) = 3

Count of digit 6 = 3

Probability = required outcome / Total possible outcomes

P(picking an odd number) = 3 / 8

Without replacement

Numbers left on board game = 8 - 1 = 7

P(picking a 6) = 3 / 7

Hence,

P(picking an odd number then, a 6) = 3/8 * 3/7 = 9 / 56

7 0

3 years ago