All categories

3 years ago

The angles shown above form a linear pair. Show all of your work for full credit.

Mathematics

1 answer:

Akimi4 [234]3 years ago

7 0

Answer:

A. $(4n + 22) + (8n - 10) = 180$

B. $n = 14$

C. 78° and 102°

Step-by-step explanation:

A. The relationship between the two angles that are a linear pair is: their sum gives us 180°. That is:

$(4n + 22) + (8n - 10) = 180$

B. $(4n + 22) + (8n - 10) = 180$

Solve for n.

$4n + 22 + 8n - 10 = 180$

Collect like terms

$12n + 12 = 180$

Subtract 12 from both sides

$12n + 12 - 12 = 180 - 12$

$12n = 168$

Divide both sides by 12

$\frac{12n}{12} = \frac{168}{12}$

$n = 14$

C. Plug in the value of 14 to get the measurement of both angles

$(4n + 22) = 4(14) + 22 = 56 + 22 = 78$

$(8n - 10) = 8(14) - 10 = 112 - 10 = 102$

You might be interested in

The conditional relative frequency table was generated using data that compares the favorite subjects of male and female student

Leona [35]

Answer: Using the information of the conditional relative frequency table, 123 students in the survey said that math was their favorite subject.

Solution:

1. The survey was given to 120 male students.

Acconding with the table, the proportion of male students with Math as favorite subject is 0.35. The quantity of male students with Math as favorite subject would be:

0.35(120)=42 male students

2. The survey was given to 180 female students.

Acconding with the table, the proportion of female students with Math as favorite subject is 0.45. The quantity of female students with Math as favorite subject would be:

0.45(180)=81 female students

Then the total of students in the survey said that math was their favorite subject would be:

42 male students + 81 female students = 123 students

3 0

3 years ago

Read 2 more answers

What does this mean f(5)=-10

Ghella [55]

You have to find f. F= -2

8 0

3 years ago

Solve the equation.<br><br> x − 12.3 = 8.7

lesya [120]

Answer is 3.6
I check it

3 0

3 years ago

Read 2 more answers

The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,750 per day. FSF supplies hot dogs to local restaurants a

NARA [144]

Answer:

A) 22812 hotdogs per run

B) 75 runs/yr

C) 4 days in a run

Step-by-step explanation:

We are given;

Production rate;p = 5750 per day

Steady Usage rate;u = 270 per day

Setup cost of hotdog;S = $67

Annual carrying cost (H) = 47 cents = $0.47 per hot dog

No. of Production days; d = 297 days

A) Let's first find the annual demand given by the formula;

Annual demand;D = pd

D = 5750 × 297

D = 1707750 hot dogs/yr

Now, formula for optimal run size is given by;

Q_o = √[(2DS/H) × (p/(p - u))]

Plugging in the relevant values gives;

Q_o = √[(2 × 1707750 × 67/0.47) × (5750/(5650 - 270))]

Q_o =√520375454.7971209

Q_o = 22812 hotdogs per run

B) formula for Number of runs per year is given as;

No. of Runs = D/Q₀

Thus;

no. of runs = 1707750/22812

no. of runs ≈ 75 runs/yr

C) Length of a run is given by the formula;

Length = Q₀/p

Length = 22812/5750

Length ≈ 4 days in a run

6 0

3 years ago

On a game show, a contestant randomly chooses a chip from a bag that contains numbers and stripes. The theoretical probability o

Lapatulllka [165]

*I'm going to assume you meant stripes.

Answer:

So in total there are 15 chips in the bag.

9 of them are stripes and 6 are numbers.

Step-by-step explanation:

So there are 9 stripes in the bag.

The probability of getting a stripe is 3/5

This means that for every 5 chips that the contestant pulls out, 3 of them should be stripes. This also means 2 of them are numbers.

So we know that 9 of the chips in the bag are stripes. To find the total number of stripes we should divide 9 by 3/5:

$\frac{9}{\frac{3}{5}} = 9 * \frac{5}{3}$

So we get:

$\frac{45}{3} = 15$

8 0

3 years ago