Answer:
360 red cars
Step-by-step explanation:
your welcome (yw)
Step-by-step explanation:
A quadrilateral is made up of four sides. This means the sum of all the side equals 43. This is given as;
(x + 7) + (x² - 2x
) + (x +3) + (2x - 2) = 43
x² - 2x + 4x + 8 = 43
x² - 2x - 35 = 0
Upon solving for x by factorization;
( x - 5) ( x + 7) = 0
The values of x are; 5 and - 7
Since the side of shape cannot have a negative value, -7 is ignored.
x = 5
The length of the sides are;
- X+7 = 5 + 7 = 12
- x² - 2x = 5² - 2(5) = 25 - 10 = 15
- X+3 = 5 + 3 = 8
2x-2 = 2(5) - 2 = 10 -2 = 8
Check:
8 + 8 + 15 + 12 = 43
Answer:
Simplifying
5x + 7y = -6
Solving
5x + 7y = -6
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7y' to each side of the equation.
5x + 7y + -7y = -6 + -7y
Combine like terms: 7y + -7y = 0
5x + 0 = -6 + -7y
5x = -6 + -7y
Divide each side by '5'.
x = -1.2 + -1.4y
Simplifying
x = -1.2 + -1.4y
__________________________________
Simplifying
4x + 7y = -9
Solving
4x + 7y = -9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7y' to each side of the equation.
4x + 7y + -7y = -9 + -7y
Combine like terms: 7y + -7y = 0
4x + 0 = -9 + -7y
4x = -9 + -7y
Divide each side by '4'.
x = -2.25 + -1.75y
Simplifying
x = -2.25 + -1.75y
Answer:
C.) y is greater than or equal to -6
Step-by-step explanation:
The range are all the set of y-values that are plotted on the vertical axis (y-axis).
The range starts from -6 and above. Which is y ≥ -6
Therefore, range of the function is said to be:
C.) y is greater than or equal to -6
Answer:
![A = \left[\begin{array}{ccc}1&-4&2\\2&6&-6\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-4%262%5C%5C2%266%26-6%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given
Required
Find the standard matrix
The standard matrix (A) is given by
Where
![T(x) = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]](https://tex.z-dn.net/?f=T%28x%29%20%3D%20%5BT%28e_1%29%5C%20T%28e_2%29%5C%20T%28e_3%29%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%26x_2%26x_3%5C%5C-%26%26x_n%5Cend%7Barray%7D%5Cright%5D)
becomes
![Ax = [T(e_1)\ T(e_2)\ T(e_3)]\left[\begin{array}{c}x_1&x_2&x_3\\-&&x_n\end{array}\right]](https://tex.z-dn.net/?f=Ax%20%3D%20%5BT%28e_1%29%5C%20T%28e_2%29%5C%20T%28e_3%29%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%26x_2%26x_3%5C%5C-%26%26x_n%5Cend%7Barray%7D%5Cright%5D)
The x on both sides cancel out; and, we're left with:
![A = [T(e_1)\ T(e_2)\ T(e_3)]](https://tex.z-dn.net/?f=A%20%3D%20%5BT%28e_1%29%5C%20T%28e_2%29%5C%20T%28e_3%29%5D)
Recall that:
In matrix:
is represented as: ![\left[\begin{array}{c}a\\b\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%5C%5Cb%5Cend%7Barray%7D%5Cright%5D)
So:
![T(e_1) = (1,2) = \left[\begin{array}{c}1\\2\end{array}\right]](https://tex.z-dn.net/?f=T%28e_1%29%20%3D%20%281%2C2%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
![T(e_2) = (-4,6)=\left[\begin{array}{c}-4\\6\end{array}\right]](https://tex.z-dn.net/?f=T%28e_2%29%20%3D%20%28-4%2C6%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-4%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
![T(e_3) = (2,-6)=\left[\begin{array}{c}2\\-6\end{array}\right]](https://tex.z-dn.net/?f=T%28e_3%29%20%3D%20%282%2C-6%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-6%5Cend%7Barray%7D%5Cright%5D)
Substitute the above expressions in
Hence, the standard of the matrix A is:
