Equivalent equations help you to knock out the <span> choices and solve the problems more easier.
for example
</span>x + 6y = 8
<span>2x + 4y = 8
</span>multiply first equation to get rid of from x
2x+12y=16
2x+4y=8
now subtract second equation from first
8y=8
y=1
now put value of y in seond equation
2x+4(1)=8
2x=8-4
2x=4
x=2
hence,
<span>equivalent equations help you to solve a system of equations</span>
Let's try to tease out a function for the area of our hypothetical rectangle:
We know that the area of a rectangle is Base x Height, and the base will be the length of the x-axis portion of the rectangle. Looking at a graph of y=27 - x^2 will help with intuition on this.
The length of the base will be 2x, since it will be the distance from the (0,0) axis in the positive direction and in the negative direction.
So our rectangle will have an area of 2x, multiplied by the height.
What is the height? The height will be our y value.
Therefore,
A = 2x * y, where x is x-value of the positive vertex.
We already know what y is as a function of x:
y= 27 - x^2
That means our equation for the area of the rectangle is:
A = 2x (27 - x^2) Distribute the terms....
A = 54x - 2x^3
This is essentially a calculus optimization problem. We want to find the Maximum for A, so let's find where the derivative of A is equal to zero.
First, we find the derivative:
A = 54x - 2x^3
A' = 54 - 6x^2
Set A' equal to zero to find the maximum value for A
0 = 54 - 6x^2
6x^2 = 54
x^2 = 9
x = 3
We got our x-value! Now let's find the y value at that point:
y= 27 - x^2
y = 27 - 9
y = 18
The height our rectangle will be 18, and our base will be 2*x = 2*3 = 6
Area = base x height = 18 * 6 = 108
The answer is B) 108.
(1) C = 15x + 40000 ...............because it cost $15 to produce each CD with a one-time cost of $40,000
(2) R = 59x ......................because each CD will sell for $59
(3) P = R - C → P = 59x - (15x + 40000) → P = 44x - 40000
(4) 44x = 40000 → x = 909 ........ They must sell 909 in order to break even
Answer:
Step-by-step explanation:
d = - 9
a = 4
n = 95
tn = a + (n - 1)*d
t95 = 4 + (94)*(-9)
t95 = 4 -846
t95 = - 842
Answer:
I haven't done this in a while but I'm pretty sure it's C.
Step-by-step explanation:
A triangle has to have 180 degrees. angle a and c are congruent. angle b is slightly smaller. therofore, istead of all the angles biegh 60, a and c are 65 thus leaving angle b 50 degrees
