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3 years ago

Given <3 and <4 are supplementary. If m<3 =5x+22 and m<4=7x+2, find the measures of each angle.

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

4 0

Answer:

m<3 = 87

m<4 = 93

Step-by-step explanation:

The sum of the measures of supplementary angles is 180 deg.

m<3 + m<4 = 180

5x + 22 + 7x + 2 = 180

12x + 24 = 180

12x = 156

x = 13

m<3 = 5x + 22 = 5(13) + 22 = 65 + 22 = 87

m<4 = 7x + 2 = 7(13) = 91 + 2 = 93

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If Kevin wants a 90 average in math after 5 tests and his first 4 tests are 76, 92, 89 and 97 what does he need on the fifth tes

Keith_Richards [23]

You need to understand that you're solving for the average, which you already know: 90. Since you know the values of the first three exams, and you know what your final value needs to be, just set up the problem like you would any time you're averaging something.
Solving for the average is simple:
Add up all of the exam scores and divide that number by the number of exams you took.
(87 + 88 + 92) / 3 = your average if you didn't count that fourth exam.
Since you know you have that fourth exam, just substitute it into the total value as an unknown, X:
(87 + 88 + 92 + X) / 4 = 90
Now you need to solve for X, the unknown:
87
+
88
+
92
+
X
4
(4) = 90 (4)
Multiplying for four on each side cancels out the fraction.
So now you have:
87 + 88 + 92 + X = 360
This can be simplified as:
267 + X = 360
Negating the 267 on each side will isolate the X value, and give you your final answer:
X = 93
Now that you have an answer, ask yourself, "does it make sense?"
I say that it does, because there were two tests that were below average, and one that was just slightly above average. So, it makes sense that you'd want to have a higher-ish test score on the fourth exam.

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4 years ago

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Rosamaria is setting up a 20 gallon saltwater fish tank that needs to have a salt content of 3.5%. If rosamaria has water that h

Eduardwww [97]

She should use 0.74 gallons you have to take 20 and timed it by 3.7 % and thats how you get to see whats left that she need.

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3 years ago

The radius of a circle is 19 miles. What is the circle's circumference?<br> Use 3.14 for .

insens350 [35]

Answer:

119.38

Step-by-step explanation:

the circumference is πd so it is 19 X 2, which is 38, times π, which is 38π. this equals 119.38

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3 years ago

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When a force of 30 N acts on a certain object the acceleration of the object is 5m/s2 if the force is changed to 54 N what will

PtichkaEL [24]

Answer:

The correct answer is 9 m per $second^{2}$

Step-by-step explanation:

Force is defined by mass of an object times it's acceleration.

Let the mass of the object be m kilograms.

When a force of 30 N acts on a certain object the acceleration of the object is 5 m per $second^{2}$

∴ 30 = m × 5

⇒ m = 6.

If the force is changed to 54 N, let the acceleration of the object be x m per $second^{2}$ .

∴ 54 = m × x

⇒ x = $\frac{54}{6}$ = 9

Thus when the force is 54 N, the acceleration of the object is 9 m per $second^{2}$ .

6 0

4 years ago

A football team plays in a large stadium. With a ticket price of $17, the average attendance at recent games has been 50,000.

Verizon [17]

Answer:

a. N(x) = 50000 - 200x

b. R(x) = (50000-200x)(17+x)

Step-by-step explanation:

a. Given,

The the original price of each ticket = $ 17,

Also, the average attendance = 50,000

Let x be the number of times the original price of each ticket is increased by $ 1,

Also, for each $1 increase in the ticket price, attendance decreases by 200,

Thus, decrements in the attendance = 200x,

If N(x) represents the new average attendance,

Then,

N(x) = 50000 - 200x

Which is the required function,

b. Now,

Revenue = average attendance × price of each ticket

R(x) = N(x) × ( 17 + x )

⇒ R(x) = (50000-200x)(17+x)

Which is the required function.

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3 years ago