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solong [7]
1 year ago
12

Given the following information, determine which lines, if any, are parallel. State the

Mathematics
1 answer:
Leokris [45]1 year ago
4 0

Answer:

parallel lines a and b

parallel lines l and m

Step-by-step explanation:

25 A.

Angles 3 and 7 are alternate interior angles of lines a and b cut by transversal l.

Since angles 3 and 7 are congruent, lines a and b are parallel by the theorem:

<em>If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.</em>

25 B.

Angles 5 and 12 are same side interior angles of lines l and m and transversal b.

Since the sum of the measures of the angles 5 and 12 is 180, then angles 5 and 12 are supplementary angles making lines l and m parallel by the theorem:

<em>If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.</em>

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1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she fi
AleksAgata [21]

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x

The table is:

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}

3 0
3 years ago
PLEASE HELP!!!
zaharov [31]
Do you have a picture I can use for reference?
3 0
3 years ago
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Identify all the intercepts for the following function
Triss [41]
Where are the intercepts
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3 years ago
Confused!! consider the polar axes with the points plotted below. Write the coordinates of point A in polar form. Be sure to wri
irinina [24]

Point A is on the 4th circle from the center, each circle has a radius of 1, so the 4th circle has a radius of 4. The point is also on the angle labeled 5PI/6.

The polar coordinate would be (4, 5PI/6)

Point C, you are given (-3,pi/3)

Because the radius is positive find the 3rd circle, which would be r = 3, Then find where PI/3 is on the circle and find the value opposite that which is 4pi/3

7 0
3 years ago
What is the angle measurement of angle P?
Solnce55 [7]

Answer:

60

Step-by-step explanation:

p = 180 - [ 360 - ( 130 + 110 ) ]

  = 180 - [ 360 - 240 ]

  = 180 - 120

p = 60

5 0
2 years ago
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