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Hitman42 [59]
3 years ago
8

Two angles are supplementary if their sum is​ 180°. the larger angle measures five degrees more than four times the measure of a

smaller angle. if x represents the measure of the smaller angle and these two angles are​ supplementary, find the measure of each angle.
Mathematics
1 answer:
wlad13 [49]3 years ago
5 0
Let x represent the smaller angle.
Let y represent the larger angle.

The problem states that the larger angle measures five degrees more than four times the measure of the smaller angle.
With this given information, we can create the following equation.

y=4x+5

Also, they a supplementary, meaning that they add up to 180. We can create another equation.

x+y=180

Since we have two linear equations and we want to find the solution, we have a system of linear equations. Let's solve this system by using the substitution method.

Substitute y=4x+5 into x+y=180

x+y=180

After substituting, you get

x+4x+5=180

Now, combine the x's

5x+5=180

Subtract both sides by 5

5x=175

Divide both sides by 5.

x=35

Now, we can solve for y using the equation x+y=180 since we know the value of x.

35+y=180

Subtract both sides by 35.

y=145

The smaller angle has a measure of 35 degrees and the larger one has a measure of 145 degrees. Have an awesome day! :)
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iren2701 [21]
Answer: 14.5

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4 0
2 years ago
among a group of students 50 played cricket 50 played hockey and 40 played volleyball. 15 played both cricket and hockey 20 play
kondaur [170]

Answer:

Cricket only= 30

Volleyball only = 15

Hockey only = 25

Explanation:

Number of students that play cricket= n(C)

Number of students that play hockey= n(H)

Number of students that play volleyball = n(V)

From the question, we have that;

n(C) = 50, n(H) = 50, n(V) = 40

Number of students that play cricket and hockey= n(C∩H)

Number of students that play hockey and volleyball= n(H∩V)

Number of students that play cricket and volleyball = n(C∩V)

Number of students that play all three games= n(C∩H∩V)

From the question; we have,

n(C∩H) = 15

n(H∩V) = 20

n(C∩V) = 15

n(C∩H∩V) = 10

Therefore, number of students that play at least one game

n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)

= 50 + 50 + 40 – 15 – 20 – 15 + 10

Thus, total number of students n(U)= 100.

Note;n(U)= the universal set

Let a = number of people who played cricket and volleyball only.

Let b = number of people who played cricket and hockey only.

Let c = number of people who played hockey and volleyball only.

Let d = number of people who played all three games.

This implies that,

d = n (CnHnV) = 10

n(CnV) = a + d = 15

n(CnH) = b + d = 15

n(HnV) = c + d = 20

Hence,

a = 15 – 10 = 5

b = 15 – 10 = 5

c = 20 – 10 = 10

Therefore;

For number of students that play cricket only;

n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30

For number of students that play hockey only

n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25

For number of students that play volleyball only

n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15

3 0
3 years ago
In the number 3,287,854 how many times greater is the value of the 8 in the ten thousands place compared to the value of the 8 i
olga55 [171]

8 in the 10,000s place is worth 80,000.

8 in the hundreds place is worth 800.

80,000/800 = 100

Answer: 100 times.

6 0
3 years ago
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It is in the attachment.
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Answer:

you would have to pay $43.20

Step-by-step explanation:

15+32.50=47.50

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47-3.80=43.20

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Rotation 180 degrees about the origin
WITCHER [35]

Answer:

<u>Rule for rotation 180° about the origin:</u>

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<u>Given coordinates:</u>

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<u>Coordinates of the image, apply the rule above:</u>

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