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what is the value of x when f (x)=6

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To find the value of \( x \) when \( f(x) = 6 \), you need to know the expression or function for \( f(x) \). Could you provide the details of the function \( f(x) \)?

use the function to answer the question

f (x) = 1/2x + 3

what is the value of x when f(x)=6

To find the value of \( x \) when \( f(x) = 6 \) using the function \( f(x) = \frac{1}{2}x + 3 \), we can set the equation to 6:

\[ \frac{1}{2}x + 3 = 6 \]

Now, let's solve for \( x \):

  1. Subtract 3 from both sides: \[ \frac{1}{2}x = 6 - 3 \] \[ \frac{1}{2}x = 3 \]

  2. Multiply both sides by 2 to isolate \( x \): \[ x = 3 \times 2 \] \[ x = 6 \]

So, the value of \( x \) when \( f(x) = 6 \) is \( \boxed{6} \).

what is the equation of a line that is parallel to y=-4x-3 and shifted down 3 units?

To find the equation of a line that is parallel to the line given by \( y = -4x - 3 \) and shifted down 3 units, you need to follow these steps:

  1. Identify the slope: The slope of the given line \( y = -4x - 3 \) is \(-4\). Since parallel lines have the same slope, the slope of the new line will also be \(-4\).

  2. Write the new line's equation: Start with the slope-intercept form of the equation of a line, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  3. Shift down 3 units: The original line has a y-intercept of \(-3\). If we shift down 3 units, we subtract 3 from the y-intercept: \[ -3 - 3 = -6 \]

  4. Assemble the new equation: Now, using the same slope and the new y-intercept: \[ y = -4x - 6 \]

Therefore, the equation of the line that is parallel to \( y = -4x - 3 \) and shifted down 3 units is: \[ \boxed{y = -4x - 6} \]

multiply (x-8) (x + 8)

To multiply the expressions \( (x - 8)(x + 8) \), you can use the difference of squares formula, which states that:

\[ (a - b)(a + b) = a^2 - b^2 \]

In this case, \( a = x \) and \( b = 8 \). Therefore, we have:

\[ (x - 8)(x + 8) = x^2 - 8^2 \]

Calculating \( 8^2 \):

\[ 8^2 = 64 \]

So the expression becomes:

\[ x^2 - 64 \]

Thus, the result of multiplying \( (x - 8)(x + 8) \) is:

\[ \boxed{x^2 - 64} \]