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ZanzabumX [31]
3 years ago
6

What are the measures of angles M and N?

Mathematics
1 answer:
romanna [79]3 years ago
7 0

Answer:

mM = 113 and mN = 61

Step-by-step explanation:

In a Cyclic quadrilateral, the rule states that:

The sum opposite interior angles is equal to 180°

In the above diagram, we have cyclic quadrilateral KLMN

According to the rule stated above:

Angle K is Opposite to Angle M

So, Angle K + Angle M = 180°

Angle K = 67°

67° + Angle M = 180°

Angle M = 180° - 67°

Angle M = 113°

Angle L is Opposite to Angle N

so Angle L + Angle N = 180°

Angle L is given as = 119°

119° + Angle N = 180°

Angle N = 180° - 119°

Angle N = 61°

Therefore, Angle M = 113° and Angle N = 61°

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y=-3/7x +1/7

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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
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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

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

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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}

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