I=prt
20=p X .05 X 5
20 = p X .25
20/.25 = p
80 = p
She started with $80
Answer:
Parallel Slope: -3 Perpendicular Slope: 1/3
Step-by-step explanation:
First, solve for y to get the simplified equation for the line.
Once you solve, the equation should be y=-3x+2
Seeing this, we know that the slope of this line is -3. A line parallel will have the same slope as the original equation, and a line perpendicular will have a slope that is the opposite reciprocal.
Hope that helps!
<span>Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as:
W = (2400 - L)/2
And area is:
A = LW
Substitute the equation for width, giving:
A = LW
A = L(2400 - L)/2
And expand:
A = (2400L - L^2)/2
A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
Answer:
18 lawns
Step-by-step explanation:
Expected sum = $515
Bonus for 1 day = $15
Bonus for 5 days = $15 × 5 = $75
Amount to be earned from mowing lawns in 5 days = $515 - $75 = $440
$25 ≡ 1 lawn
$440 ≡ 440 ÷ 25 = 17.6
The minimum number of lawns is 18.
<em>(Note that we take the minimum integer greater than 17.6. If he mows 17 lawns, his earning from 17 lawns = $425 + $75 = $500)</em>
