Answer:
Step-by-step explanation:
I used Cramer's Rule to find y, since we can isolate and solve for individual variables using Cramer's Rule. Do that by finding the determinant of the matrix, |A|. The matrix A looks like this:
2 -2 1
-1 3 2
1 -4 -3
and we find the determinant of a 3x3 by expanding it. Do that by picking up the first 2 columns and throw them on at the end, like this:
2 -2 1 2 -2
-1 3 2 -1 3
1 -4 -3 1 -4
and find the determinant by multiplying along the 3 major axes and subtract from that the product of the 3 minor axes:
[(2*3*-3)+(-2*2*1)+(1*-1*-4)] - [(1*3*1)+(-4*2*2)+(-3*-1*-2)] which simplifies to
-18 - (-19) = 1
So the determinant of the matrix A is |A| = 1.
Now to find the determinant of Ay, we replace the y column with the solutions and so the same thing by expansion and then multiplying and subtracting:
2 -7 1 2 -7
-1 0 2 -1 0
1 1 -3 1 1
and find the determinant of y:
[(2*0*-3)+(-7*2*1)+(1*-1*1)] - [(1*0*1)+(1*2*2)+(-3*-1*-7)] which simplifies to
-15 - (-17) = 2
So the detminant of y is |Ay| = 2
We can solve for the variable now by dividing Ay by A:
2 / 1 = 2
So the solution for y = 2
Brenden. the more plants you test the easier it is to find the average instead of a smaller amount. hope this helped!
Answer:
x=53
Step-by-step explanation:
One way to solve this problem is by using the Pythagorean Theorem.
This states that the square of one "leg" of the triangle plus the square of the other "leg" of the triangle would equal the square of the hypotenuse, or the longest side of a triangle. Keep in mind that this only works for right triangles, where one angle is exactly 90 degrees.
This formula can be written as: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.
So, for this problem, let a=28, and b=45.
This gives us: 28^2 + 45^2 = x^2
And we can simplify this to: 2809 = x^2
Taking the square root of both sides gives us the answer, that x=53 units.
Hope this helps!
Answer:
Step-by-step explanation:
perimeter of a rectangle = twice the length plus twice the width
P = 2L + 2W equation 1 P = 86 ft
Given the length is seven feet more than the width
L = W + 7 equation 2
Substitute equation 2 into equation 1
P = 2(W+7) + 2W = 86 ft
2W +14 + 2W = 86 ft
4W = 86 - 14
W = 72 / 4
W = 18 feet
Answer: 1210.1
Step-by-step explanation: