Find the midpoint of the segment with the given endpoints. (3,- 9) and (4, -8)

Mathematics

1 answer:

frez [133]3 years ago

3 0

(3,-9)
(4,-8)

$\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\\ \sf\longmapsto \left(\dfrac{3+4}{2},\dfrac{-9+8}{2}\right)$

$\\ \sf\longmapsto \left(\dfrac{7}{2},\dfrac{-1}{2}\right)$

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The system of inequalities are
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7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
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The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
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The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
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Let x represent the number of hours Janine spends babysitting and let y represent the number of hours Janine spends dishwashing
1) From the question, we have;
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) Where
14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
Making, y, the subject of the formula of the above inequalities and plotting as functions is given as follows;
y ≥ 140/9.5 - (14.5/9.5)·x
y ≤ 15 - x
3) In order to earn as much money as possible given that the amount Janine earns from babysitting is more than the amount she earns from dishwashing, Janine should spend the least amount of time dishwashing, which is 7 hours, as given, and then spend the remaining 8 hours babysitting to receive $14.5 × 8 + $9.5×7 = $182.5

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