https://file.aiquickdraw.com/mathbot/file/1726074251586ld38lr0i.jpg

The image contains the following information:

\[
\mathbf{u} = (-2, 9), \quad \mathbf{w} = (-2, -3)
\]

You are asked to compute:

\[
-2\mathbf{u} - 5\mathbf{w} = \, ?
\]

### Step-by-Step Solution:
1. First, let's compute \(-2\mathbf{u}\). To do this, multiply each component of vector \(\mathbf{u} = (-2, 9)\) by \(-2\):

\[
-2\mathbf{u} = -2 \times (-2, 9) = (4, -18)
\]

2. Now, compute \(-5\mathbf{w}\). Multiply each component of vector \(\mathbf{w} = (-2, -3)\) by \(-5\):

\[
-5\mathbf{w} = -5 \times (-2, -3) = (10, 15)
\]

3. Finally, add the results of the two vectors:

\[
-2\mathbf{u} - 5\mathbf{w} = (4, -18) + (10, 15) = (4 + 10, -18 + 15) = (14, -3)
\]

Thus:

\[
-2\mathbf{u} - 5\mathbf{w} = (14, -3)
\]

Would you like further details on this? Here are 5 related questions you can explore:

1. How do you perform vector addition and scalar multiplication?
2. What are some real-world applications of vector operations?
3. How do you calculate the magnitude of a vector?
4. Can vectors in 3D space be solved using similar operations?
5. What is the difference between dot product and cross product?

**Tip:** When working with vectors, always ensure that the operations (like scalar multiplication and addition) are applied component-wise.

Compute -2u - 5w where u = (-2, 9) and w = (-2, -3)

Learn how to compute the vector operation -2u - 5w, where u = (-2, 9) and w = (-2, -3). This problem covers key concepts in vector arithmetic, including scalar multiplication and vector addition. Step-by-step solutions provided for students in Grades 9-12.

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