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Taya2010 [7]
3 years ago
8

Evaluate the summation of 2 n plus 5, from n equals 1 to 12..

Mathematics
1 answer:
kirza4 [7]3 years ago
4 0
<span>Let f(n) = 2n + 5. Then we must simply calculate (f1), f(2), ..., (f12). And we have that f(1) = 2*1 + 5 <=> f(1) = 7; f(2) = 2*2 + 5 <=> f(2) = 9; f(3) = 2*3 + 5 <=> f(3) = 11. And so on. It's easy to see that the rest of the results will be 13, 15, 17, 19, 21 and so on. So the summation will be S = 7 + 9 + 11 +... + 29 <=> S = 216</span>
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3 years ago
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Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $27
SOVA2 [1]
Part A: To get an equation into standard form to represent the total amount  rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.

Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}

Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.
<span>
This means that the line modeling this situation crosses points at (2, 125) and (5, 275).
</span>
The equation modeling <span>the total rent (y) that Marguerite has to pay for renting the truck for x days is given by
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y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50
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But if you are writing the equation in standard form it would be <span>
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50x - y = -25


Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).
</span>
If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.<span>
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Writing the equation using the function notation would give us this
f(x) = 50x + 25


Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of </span>(2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
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