Point m is the midpoint of line segment ab, b is at (20,4), m is at (18, -2) and a is at (p,q). what is p+q?

1 answer:

8 0

The x-value of a midpoint is the average of the x-values of the ends.
The y-value of a midpoint is the average of the y-values of the ends.

The x-value of the end at b is 20 and it's 18 at the middle.
x has decreased by 2 in the course of 1/2 of the line.
So it will decrease another 2 during the other half of the line.
The x-value at the other end, at a, then, is 16.

The y-value of the end at b is 4 and it's -2 at the middle.
y has decreased by 6 in the course of 1/2 of the line.
So it will decrease another 6 during the other half of the line.
The y-value at the other end, at a, then, is -8.

The other end of the line, at a, is at (16, -8) .

The sum of the coordinates at a (p+q) is 8 .

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$\bf \begin{cases}
f(x)=\cfrac{x}{x-9}
\\ \quad \\
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NISA [10]

<h3>Answer: </h3><h3>Overall balance for year 5 after taxes = $1350</h3><h3>The filled out table is shown in the attached image below</h3>

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Work Shown:

10% = 10/100 = 0.10

10% of 1000 = 0.10*1000 = 100 is the amount of interest earned in year 1. This goes in the first row of column 1. The overall balance becomes 1000+100 = 1100 after we add on the interest earned. We will write 1100 in row1,column2.

Next, compute the tax: 30% of 100 = 0.30*100 = 30. The 30 will be written in row1,column3. Finally, we subtract the amount taxed (30) from the overall balance in column 2 (which was 1100). So 1100-30 = 1070 will be written in row1,column4.

After finishing row1, we should have these four values: 100, 1100, 30, 1070

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Now onto row 2

We earn the same amount in interest because we are not compounding. Write 100 in row2,column1.

The overall balance will be different. Instead of using 1000, we will use 1070 which was the figure in row1,column4. Add the amount of interest earned ($100) onto the updated balance ($1070) to get 1170. Write 1170 in row2,column2

The value in row2,column3 is the same as the value above it. This is because the amount of interest does not change, so the amount taxed doesn't change either. Basically we'll have 30s all the way down column 3. We'll also have 100s all the way down column 1.

Subtract 1170 and 30 to get 1140 which is the balance after taxes for year 2.

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Repeat these steps for the third, fourth, and fifth rows and you'll get what you see in the table below.