https://file.aiquickdraw.com/mathbot/file/1728050705518azrndgyu.jpg

Let's go through the questions from the image one by one.

### Question 21:
You are given a line equation \( y = -6x + 3 \) and a series of matrix transformations. The first matrix transformation is:

\[
\begin{pmatrix}
2 & 1 \\
-1 & -2
\end{pmatrix}
\]

This is followed by another transformation with the matrix:

\[
\begin{pmatrix}
1 & 0 \\
1 & -2
\end{pmatrix}
\]

You are asked to find the resulting equation after these transformations.

**Steps**:
1. Rewrite the line equation in matrix form and apply each matrix transformation step by step.
2. After applying the matrices, convert the resulting points back to the line equation form.

### Question 22:
You are asked to find the equation of the transformed circle after a series of matrix transformations.

The original equation of the circle is:
\[
(x - 2)^2 + (y + 3)^2 = 25
\]

It undergoes transformations by:
\[
\begin{pmatrix}
1 & 0 \\
1 & 0
\end{pmatrix}
\]
and then:
\[
\begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix}
\]

The task is to determine the equation of the resulting curve.

### Question 23:
Given an exponential function \( y = 5^{-3x - 2} \), you are asked to find the reflection of this function across the x-axis.

### Question 24:
The function \( y = 3^{2x - 1} \) is rotated 90° clockwise. You are required to find the resulting equation.

### Question 25:
The curve \( y = x^2 + 3 \) undergoes dilation with respect to the point \( P(-1, 2) \) by a factor of 3. Then, it is rotated \( \frac{\pi}{2} \) radians around the origin.

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Solve the series of matrix transformations, curve equations, and other related math problems.

Solve matrix transformations, linear and circle equations, exponential function reflections, and curve rotations. This problem set covers advanced algebra and geometry topics for students in Grades 11-12.

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