Let the lengths of the sides of the rectangle be x and y. Then A(Area) = xy and 2(x+y)=300. You can use substitution to make one equation that gives A in terms of either x or y instead of both.
2(x+y) = 300
x+y = 150
y = 150-x
A=x(150-x) <--(substitution)
The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:
0=x(150-x)
x=0, 150
So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.
A=75(150-75)
A=75*75
A=5625
So the maximum area that can be enclosed is 5625 square feet.
Answer:
All Real Numbers except for 4
Step-by-step explanation:
Objective: Specify domain and range of a function.
The equation is a linear equation. A linear equation range is all real numbers. However x cannot equal 1 so let plug in x to find where the y value CANT be.
So the range is
All Real Numbers except for 4.
Answer:
The answer is 15
Step-by-step explanation:
f(x) = -4x + 3, f(-3)
f(-3) = -4x + 3
f(-3) = -4(-3) + 3
f(-3) = 12 + 3
f(-3) = 15
Thus, The answer is 15
Answer:
$48.66
Step-by-step explanation:
The price of a good is the base cost plus tax. We are given the cost of the skirt, so all we need is the amount of tax. To find it, we multiple the cost of the skirt by the tax rate:
45.99 * 0.058 = 2.67
We now add the tax to the cost of the skirt:
45.99 + 2.67 = 48.66
As you can see, we are adding the price of the skirt to 5.8% of the skirt's price, so we can also solve the problem by simply multiplying the cost by 1.058 as shown below:
45.99 * 1.058 = 48.66
Energy is either released or absorbed
