Question

use matrix multiplication to double side 1 (left), triple side 3 (right) of each triangle and find the new perimeter of each triangle. what has the greatest perimeter?

1. multi - step a mechanic bought a part for $4.25 and marked the price up by 200% to sell to a customer. how much did the customer pay for the part? how much would the customer have paid if she had used a 5% off coupon?

solve for x.

1. 3x - 5 = 2 - 4x

*27. \\(\frac{3}{4}x-\frac{1}{5}x = 2\frac{3}{4}\\)

1. 5x - 2 = 7 + 2x
2. coordinate geometry the coordinates for a triangle are a(-3,7), b(6,8), and c(2,-3).

a. write the coordinates as a matrix such that row one is x - values, row two is y - values, and each column is a coordinate.
b. add the transformation matrix \\(\

$$\begin{bmatrix}-2&-2&-2\\\\3&3&3\\end{bmatrix}$$

\\).
c. what are the coordinates of the transformation?

Explanation:

Step1: Write the coordinate matrix

The coordinates of the triangle are \(A(-3,7)\), \(B(6,8)\), and \(C(2, - 3)\). The coordinate - matrix \(M\) with row one as \(x\) - values and row two as \(y\) - values is:
\[M=

$$\begin{bmatrix}-3&6&2\\7&8& - 3\end{bmatrix}$$

\]

Step2: Add the transformation matrix

The transformation matrix \(T=

$$\begin{bmatrix}-2&-2&-2\\3&3&3\end{bmatrix}$$

\). To find the new coordinates, we add the two matrices element - by - element.
\[M + T=

$$\begin{bmatrix}-3+( - 2)&6+( - 2)&2+( - 2)\\7 + 3&8+3&-3 + 3\end{bmatrix}$$

=

$$\begin{bmatrix}-5&4&0\\10&11&0\end{bmatrix}$$

\]

Answer:

The coordinates of the transformation are \(A'(-5,10)\), \(B'(4,11)\), and \(C'(0,0)\)