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3 years ago

In this figure, AB || CD and mZ6 = 75" What is mZ3? Enter your answer in the box.

Mathematics

1 answer:

grandymaker [24]3 years ago

8 0

Answer:

105

Step-by-step explanation:

Theorem:

If parallel lines are cut by a transversal, then same-side interior angles are supplementary.

Lines AB and CD are parallel, and angles 3 and 6 are same-side interior angles, so by the theorem above, angles 3 and 6 are supplementary. That means that the sum of their measures is 180 deg.

m<3 + m<6 = 180

m<3 + 75 = 180

Subtract 75 from both sides.

m<3 = 105

Answer: 105 degrees

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A box of Munchkins contains chocolate and glazed donut holes. If Jacob ate 2 chocolate

neonofarm [45]

Answer:

24 munchkins.

Step-by-step explanation:

Let C be the number of chocolate and D be number of glazed donut holes in the original box.

We are told if Jacob ate 2 chocolate munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:

$C-2=\frac{1}{11}*(C+D-2)...(1)$

We are also told if he instead added 4 glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:

$C=\frac{1}{7}*(C+D+4)...(2)$

Upon substituting C's value from equation (2) in equation (1) we will get,

$\frac{1}{7}*(C+D+4)-2=\frac{1}{11}*(C+D-2)$

Let us have a common denominator on right side of equation.

$\frac{1}{7}*(C+D+4)-\frac{7*2}{7}=\frac{1}{11}*(C+D-2)$

$\frac{C+D+4-14}{7}=\frac{1}{11}*(C+D-2)$

Multiplying both sides of our equation by 7, we will get,

$7*\frac{C+D-10}{7}=7*\frac{1}{11}*(C+D-2)$

$C+D-10=\frac{7}{11}*(C+D-2)$

Multiplying both sides of our equation by 11, we will get,

$11*(C+D-10)=11*\frac{7}{11}*(C+D-2)$

$11*(C+D-10)=7*(C+D-2)$

$11C+11D-110=7C+7D-14$

$11C-7C+11D-7D=-14+110$

$4C+4D=96$

$4(C+D)=96$

$(C+D)=\frac{96}{4}$

$(C+D)=24$

Therefore, the total number of Munchkins in original box is 24.

3 0

3 years ago

each year lizza school purchased agenda books, which are sold in the school this year the school purchased 350 books at a cost o

Inga [223]

Old price: 1,137.50 / 350 = 3.25
New price (at least): 1,500 / 350 = 4.3 (result is rounded)

7 0

3 years ago

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected resi

mihalych1998 [28]

Answer:

Mean = 910.2

Standard deviation = 12.8

Step-by-step explanation:

82% over the age of 25 are high school graduates.

A survey randomly selected students of certain country included 1110 who were over the age of 25 and 871 of them were high school.

n = 1110

p = 82% = 0.82

q = 1 - 0. 82

q = 0.18

Mean = np

= 1110*0.82

= 910.2

Standard deviation = √npq

= √ 1110*0.82*0.18

=√163.836

= 12.8

6 0

3 years ago

Dusty has a summer lawn-moving business.In one-week,he mows 20 lawns and earns a total of $450.If he charges the same amount for

Dmitriy789 [7]

Answer:

He mows 80 yards.

Make meh happy pls ;)

Step-by-step explanation:

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3 years ago

The sum of two numbers is at least 30 and the difference between the two numbers is less than 8. X and y are the two numbers suc

vaieri [72.5K]

Answer:

1 Expert Answer

Let x and y be the two numbers. Then by assumptions we have x+y=30 and x-y=20. Hence, y=x-20 and by plugging this into the first equation we obtain x+x-20=30 or 2x=50 or x=25 and y=5

Step-by-step explanation:

So, divide 30 by 2 . That gives you 15 for x, 15 for y. Now, you have difference of six, divide by two, that equals 3.

3 0

3 years ago