Answer: 8
The point E in the parallelogram is located at the crossing point of the diagonal line. It can be concluded that the distance of AE is equal to CE, or equal to 1/2 AC. Then you can get three equation like this:
AE=CE
<span>AE=x^2−8
CE=2x .
Using these equation you can find the value of x
AE= CE
</span>x^2−8 = 2x
x^2−2x-8 = 0
(x- 4) (x+2)
x1= 4 x2= -2
Excluding the minus result, you can get that AE= CE= 4
Then AC would be:
AC= AE+CE
AC= 4 + 4= 8
If we translate the word problems to mathematical equation,
2x + 3y = 60
The second equation is,
P = xy³
From the first equation, we get the value of y in terms of x.
y = (60 - 2x) / 3
Then, substitute the expression of y to the second equation,
P = x (60-2x) / 3
P = (60x - 2x²) / 3 = 20x - 2x²/3
We derive the equation and equate the derivative to zero.
dP/dx = 0 = 20 - 4x/3
The value of x from the equation is 15.
Hence, the value of x for the value of the second expression to be maximum is equal to 15.
Answer:
The answer is Option B
Step-by-step explanation:
<u>Step 1: Find the points</u>
The leftmost point is: <em>(-3, -1)</em>
The next point is: <em>(-2, 2)</em>
The next point is: <em>(1, 0)</em>
The next point is: <em>(3, 1)</em>
The rightmost point is: <em> (4, -2)</em>
<em />
Answer: The answer is Option B
Answer:
The answer is 9in.
Step-by-step explanation:
To solve this problem, you must use the Pythagorean Theorem.
Since we already have the Hypotenuse (
), which is 15in, we must solve the following:
+ 
= 
Now, we find that = 225, so we subtract that from , which is 114.
Then, that leaves us with 81, and the sqaure root of 81 is 9, which is your answer.
