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zavuch27 [327]
3 years ago
5

In one year Megan spent 359.94 on her gym membership at the same monthly rate of 59.99. Write an equation to represent this situ

ation. Identify and define your variable
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0

Answer:

359.94 = 59.99 * X

Step-by-step explanation:

The situation is determined by the following equation:

T = M * X

Being M the monthly value, that is to say 59.99

T the total value, that is 359.94

And X would be the number of months, and at the same time the variable.

In this case it would be like this:

359.94 = 59.99 * X

If we solve for X, we are left with:

X = 359.94 / 59.99

X = 6

That is to say that Megan went to the gym for 6 months of the year

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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
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Answer:

<u>b(n) = -11 + (n-1)*8</u>

<u></u>

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

<u><em>b(1)</em></u><em>   -11</em>         + 8 =   -3

<u><em>b(2)</em></u><em>   -3</em>          + 8 =    5

<u><em>b(3)</em></u>   <em> 5 </em>         + 8 =   13

<u><em>b(4)</em></u><em> </em> <em>13</em>

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

<u>b(n) = -11 + (n-1)*8</u>

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   <u><em>YES</em></u>

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