Answer:
y = -1/2 + 2 (Slope intercept)
Step-by-step explanation:
Y-intercept is when the x-value is 0.
So the y-intercept is (0, 2)
To find slope, find two random points:
(0, 2) , (2, 1)
Slope (m) =ΔY/ΔX = -1/2 = -0.5
Equation of the line:
y = -0.5x + 2
or
y = -1/2 + 2
When x=0, y = 2
When y=0, x = 4
The system of inequalities are
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) 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
3) 8 hours babysitting, 7 hours dishwashing
Step-by-step explanation:
The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
The minimum number of hours Janine can spend dishwashing = 7 hours
The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
The minimum amount she wants to make each week = $140
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
For this case we have that by definition, the perimeter of the rectangle is given by:
Where:
W: Is the width of the rectangle
L: is the length of the rectangle
According to the data we have:
Substituting:
So, the width of the rectangle is 9 inches
So, the length of the rectangle is 15 inches
Answer:
the width of the rectangle is 9 inches
the length of the rectangle is 15 inches
