Question

The slope of the line passing through points (X,, Y,) and X2, Y2) is found using the formula
У2 — У1
22 - 11
The line passing through the points (1, 2) and (x, 5) is perpendicular to a line that has a slope of
-. What is the value of x?
10
- 2
-4
D

Answer 1

simplify:%20(2-4)%20(3%20-6i)%0A-18%20-%2024i%0AB%0A6%20-%2024%D1%96%0AD%0A6%20-%2012i%0A-18%20-%2012i

Answer 2

To find the value of \( x \) such that the line passing through points (1, 2) and (x, 5) is perpendicular to a line with a slope of -10, we need to use the properties of slopes of perpendicular lines.

1. **Identify the slope of the line with points (1, 2) and (x, 5)**:
The slope \( m_1 \) of the line connecting points (1, 2) and (x, 5) is given by the formula:
\[
m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 2}{x - 1} = \frac{3}{x - 1}
\]

2. **Find the slope of the line that is required to be perpendicular**:
Given that the slope of the other line is -10, we know that if two lines are perpendicular, the product of their slopes is -1:
\[
m_1 \cdot m_2 = -1
\]
Here, \( m_2 = -10 \). So we have:
\[
\frac{3}{x - 1} \cdot (-10) = -1
\]

3. **Solve for \( x \)**:
This leads to the equation:
\[
-\frac{30}{x - 1} = -1
\]
Removing the negative signs:
\[
\frac{30}{x - 1} = 1
\]
Cross-multiplying gives:
\[
30 = x - 1
\]
Solving for \( x \):
\[
x = 30 + 1 = 31
\]

However, upon review, it appears my initial conditions should yield a scenario where we equate \( m_1 \) to \(\frac{1}{10}\) as the slope perpendicular to the given slope of -10 (as slopes of perpendicular lines are negative reciprocals). Thus, the initial equation can be restated correctly as:

\[
\frac{3}{x - 1} = \frac{1}{10}
\]

Redoing the calculation here gives us:
Cross-multiplying results in:
\[
3 \cdot 10 = (x - 1) \cdot 1
\]
\[
30 = x - 1
\]
Thus,
\[
x = 31
\]

From this, we arrive at your understanding that the value of \( x \) does not match those provided as options.

Based on further calculations or consideration, if we want it to yield a coefficient from one of the given choices, you may review options for a specific value perhaps as related to error detection vs slope, however for clarity, the correct \( x \) for the derived line towards -10 slope is **31**.

In essence:
**If the choice is to retrieve explicitly one of the initial provided options**, they may need adjusting reliably based on slope recalibrations.

Answer 3

To simplify the expression \((2 - 4)(3 - 6i) - 18 - 24i\), let's go through the calculations step by step.

1. **Calculate \((2 - 4)(3 - 6i)\)**:

\[
(2 - 4)(3 - 6i) = (-2)(3) + (-2)(-6i) = -6 + 12i
\]

2. **Combine this result with \(-18 - 24i\)**:

Now, we substitute this result back into the expression:

\[
-6 + 12i - 18 - 24i
\]

3. **Combine like terms**:

Combine the real parts and the imaginary parts:

\[
(-6 - 18) + (12i - 24i) = -24 - 12i
\]

Thus, the simplified expression is:

\[
\boxed{-24 - 12i}
\]