The answer is C.
4x-y=-8
-y=-4x-8
y=4x+8
y=4x+8
0=4x+8
-8=4x
-2=x
Answer:
Step-by-step explanation:
n(30/100)=27
n=100(27)/30
n=90
Answer:
11.547 ft wide by 5.774 ft high
769.800 ft³ capacity
Step-by-step explanation:
Volume is maximized for a given area by having the area of a pair of opposite sides equal the area of the bottom. That means the overall area of the container is 3 times the area of the bottom. Then the square bottom will have a width of ...
w = √(400/3) ≈ 11.547 . . . feet
The height is half that, so is ...
h = w/2 = 11.547/2 ≈ 5.774 . . . feet
The capacity is then ...
w²h = (11.547 ft)²(5.774 ft) = 769.800 ft³
The container is 11.547 ft wide by 5.774 ft high. It has a capacity of 769.800 cubic feet.
_____
You want to maximize w^2h subject to w^2 + 4wh = 400. Solving the constraint equation for h, we get h = (400 -w^2)/(4w) and the volume we want to maximize can be written as ...
V = w(400-w^2)/4
This will be an extreme when dV/dw = 0, so we want to solve ...
dV/dw = 0 = 100 -(3/4)w^2
w^2 = 400/3
w = √(400/3) . . . . . as above
Answer:
10
Step-by-step explanation:
We will use a system of equations to solve this. We do not know how much of the 25% bleach solution is used; we will use x to represent this. We know that 5 cups of the 10% solution was used. We do not know how much of the resulting solution we have; we will use y to represent this. This gives us the equation
x+5 = y
Using the decimal forms of the percentages for each solution, we have 0.25x (25% solution for x cups), 0.1(5) (10% solution for 5 cups) and 0.2y (20% solution for y cups); this gives us the equation
0.25x+0.1(5) = 0.2y
This gives us the system

To use elimination, we will make the coefficients of x the same by multiplying the top equation by 0.25:

We will now subtract the second equation from the first:

Divide both sides by 0.05:
0.75/0.05 = 0.05y/0.05
15 = y
There were 15 cups of the resulting 20% solution. Substituting this into the first equation, we have
x+5=15
Subtract 5 from each side:
x+5-5=15-5
x = 10