Answer:
Step-by-step explanation:
Let's use the addition/elimination method to solve this. If we multiply the first equation through by -1 we can eliminate the x terms. Doing that gives us:
-x + 3y = 3
x + 3y = 9
The x's subtract each other away leaving us with
6y = 12 so
y = 2.
Now we will plug in 2 for y in either of the original equations to solve for x:
x + 3(2) = 9 and
x + 6 = 9 so
x = 3
The coordinate for the solution is (3, 2) or x = 3, y = 2
The second choice down is the one you want.
Answer:
Step-by-step explanation:
Recall that the notion of the derivative of a function is the rate of change of it. So it kind of tells us how much the value of functioin changes as the independt variable increases or decreases. If it is positive, this means that the function will increase as the indepent variable increases, and if it is negative, that means that the function will decrease as the indepent variable increases.
a) Since f(x) is the number of units you can make out of x units of raw material, it is natural to think that the more material you have, the more units you can make, so we expect f'(x) to be positive.
b) The company buys each unit of raw material at the price w. So the product wx represents the total cost of the raw material used to produce f(x) units. Since each produced unit is sell at the price of p, then the product pf(x) represents the total income for selling all f(x) units.Recall that the profit is the difference between the total income and the total cost of production. Hence, the profit in this case is represented by the formula pf(x)-wx.
c) Recall that a function h(x) that is differentiable attains it's maximum when it's derivative is 0 and it's second derivative is negative.
In this case, we know that the derivative of the profit function, evaluated at x* must be 0, since it is a maximum. So, using the rules of derivation, we know that the derivative of the profit function is pf'(x)-w. Hence,
pf'(x*)-w =0. From where we know that f'(x*)=w/p.
ANSWER
The simplest form of the ratio
is
EXPLANATION
The ratio given to us is
We can divide each term in ratio by the same number.
To find the ratio in the simplest form we divide the terms in the ratio by their highest common factor, which is
This implies that,
We simplify this to obtain,
The correct answer is C.
Alternatively,
This implies that,
The formula in solving the area of a square is Area = a² where "a" is for the length of the side. The area formula in solving a cube is Area = 6a² where "a" is for the length of its side.
Area of square = a²
64 = a²
a = 8 units
Area of cube = 6a²
64= 6a²
a = 3.27 units
The difference of side of the square and side of the cube is shown below:
Difference = 8 - 3.27
Difference = 4.73 units.
The answer is 4.73 units.
3% of x = 354
<span>3%∗<span>1<span>100%</span></span>∗x=354</span><span><span><span>3x</span>100</span>=354</span>Can you solve that for x<span>?</span>
