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murzikaleks [220]
2 years ago
5

tudents are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are

15 questions on the test, and students are given 51 minutes to take it. The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test. m + f = 15 3m + 5f = 51 How many multiple-choice questions are on the test? 3 5 12 14
Mathematics
1 answer:
AlladinOne [14]2 years ago
6 0
In this question, they gave you the system of equations. You just need to use the two of them.

We want to find the m or the number of the multiple-choice questions. So we need to turn our last equation in the form of 'm's by translating the 'f's into 'm's.

m + f = 15
f = 15 - m

If we know the m form of f, we can convert the second equation and find the answer: 3m + 5f = 51

Plug in the m value of f: 3m + 5(15 - m) = 51

Distribute the 5: 3m + 75 - 5m = 51

Subtract -75 from both sides: 3m - 5m= 51 - 75

Combine like terms: - 2m = - 24

Divide both sides by -2: m = 12

So, we learned that the number of the multiple-choice questions is 12.
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What is the answer to this equation <br><br> h(x)= -9 - x; h(2k-5
dezoksy [38]

The answer is h(2k - 5) = -4 - 2k

Step-by-step explanation:

In a function f(x) = y, we can find the value of y for any given value of x

Examples:

  • If f(x) = 2x - 3, and we need to find f(3), that means substitute x by 3 in f(x), so f(3) = 2(3) - 3 = 6 - 3 = 3, that means f(x) = 3 at x = 3
  • If f(x) = 8 - 5x, and we need to find f(a - 2), substitute x by (a - 2) in f(x), so f(a - 2) = 8 - 5(a - 2) = 8 - 5a + 10 = 18 - 5a, that means f(a - 2) = 18 - 5a at x = a - 2

∵ h(x) = -9 - x

- We need to find h(2k - 5), that means substitute x by 2k - 5

∵ x = 2k - 5

∴ h(2k - 5) = -9 - (2k - 5)

- Simplify the right hand side

∴ h(2k - 5) = -9 - 2k - (-5)

- Remember (-)(-) = (+)

∴ h(2k - 5) = -9 - 2k + 5

- Add the like terms in the right hand side

∴ h(2k - 5) = (-9 + 5) - 2k

∴ h(2k - 5) = -4 - 2k

The answer is h(2k - 5) = -4 - 2k

Learn more:

You can learn ore about the functions in brainly.com/question/5337932

#LearnwithBrainly

7 0
3 years ago
Easy math for smart people problem: 7w-6=3(w+6)
LenKa [72]

Answer:

<h2>w=6</h2>

Step-by-step explanation:

7w-6=3w+18                     I expanded the bracket

+6 on both sides

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-3w on both sides

4w=24

divide both sides by 4

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Answer:

Step-by-step explanation: 4848474838387398437939743927938<em>5</em>

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Solve r + (-8) = 10<br><br> ———————-
Yuliya22 [10]

Answer:

r = 18

Step-by-step explanation:

r -8 = 10

r -8 + 8 = 10 + 8

r = 18

4 0
3 years ago
a traveling salesman drives his car 30000 miles a year. His car travels 16 miles to the gallon of gas. How many gallons of gas d
DENIUS [597]

Answer:

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Step-by-step explanation:

Make a proportion

\frac{16 miles}{1 gallon} = \frac{3000 miles}{x}

3000/16 = 187.5, so multiply 1 by 187.5 to find the gallons used in a year

This gets you 187.5 gallons used in a year

4 0
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