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Gekata [30.6K]
3 years ago
13

As a membership fee a health club charges a one time amount of $40 and charges $25 for each month. The total fee after m months

is $240. What is the value of m
A runner warms up for ten minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes. How many miles are run?
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
3 0
First you need to set up an equation y = mx + b. m would be the monthly charge and b would be the one time fee. x represents the number of months.
To solve for the number of months with a total price of 240 we substitute 240 in for y and solve for x.
240 = 25x + 40
subtract 40 from each side
200= 25x
divide by 25
8 = x
8 months

10 + 7r = 45
7r = 35
r = 5
5 miles
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Answer:

A

Step-by-step explanation:

We want to solve the equation:

2\sin^2(x)=\sin(x)

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First, we can move all the terms to one side. Start off by subtracting sin(x) from both sides:

2\sin^2(x)-\sin(x)=0

We can factor:

\sin(x)\left(2\sin(x)-1\right)=0

By the Zero Product Property:

\sin(x)=0\text{ or } 2\sin(x)-1=0

Solve for each case:

\displaystyle \sin(x)=0\text{ or } \sin(x)=\frac{1}{2}

Use the unit circle to solve:

\displaystyle x=\left\{0, \frac{\pi}{6},\frac{5\pi}{6}, \pi\right\}

Hence, our answer is A.

*Please note that we should not simply divide both sides by sin(x) to acquire 2sin(x) = 1. The problem with the operation is that we are dividing by sin(x), yet we do not know what the value of x is. Thus, one or more values of x may result in sin(x) = 0, and we cannot divide by 0. Hence, we are required to subtract and then factor, unless the question specifically states that sin(x) ≠ 0.

8 0
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The rule to use: when dividing fractions, invert and multiply.

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Answer:

Step-by-step explanation:

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the answer is 3,500

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