Logarhythm

Since the slope of that line is -2, the the perpendicular one would be its negative reciprocal, which is \(\frac{1}{2}\)

This means you can use the equation and plug in the point (-4, -4) to find the y intercept:
\(y = mx + b\)

\(-4 = \frac{1}{2} \cdot (-4) + b\)

\(-4 = -2 + b\)

\(b = -2\)

This means the equation of the line, and your answer, is: \(y = \frac{1}{2}x -2\)

y - 6 = -5(x + 2)

First distribute the brackets:

y - 6 = -5x - 10

Move over the 6

y  = -5x - 4

Finally move over the 5x

5x + y = -4

\(\frac{2x + 4}{5} = \frac{3x + 5}{7}\)

\(14x + 28 = 15x + 25\)

\(x = 3\)

\((x-h)^2 + (y - k)^2 = r^2\)

The center point of the circle is: (-3, -2)

The radius of the circle is: 5

Which means the equation is:

\((x -(-3))^2 + (y -(-2))^2 = 5^2\)

\((x+3)^2 + (y + 2)^2 = 25\)

7x + 20 + 5x + 2y + 7x + 20 + 90 = 360

19x + 2y + 130 = 360

19x + 2y = 230

7x + 90 + 20 = 180

7x = 70

x = 10

19x + 2y = 230

19(10) + 2y = 230

190 + 2y = 230

2y = 40

y = 20

By pythagoras' theorem: 

the slant height of the cone \((l) = \sqrt{18^2 + 5^2}\)

\(l = \sqrt{349}\)

This means the slant height is √349 inches, or about 18.68 inches

The volume is the length times the width times the height:
4 x 5 x 6 = 120 m³

22x + 8 + 24x + 6 + 12x - 2 = 360

58x + 12 = 360

58x = 348

x = 6 

By pythagoras' theorem:

\(x = \sqrt{10^2 + 24^2}\)

\(x = \sqrt{676}\)

\(x = 26\)

The two points are: (-5, 3) and (3, 5)

To find the slope, use this equation:
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{5 - 3}{3 - (-5)}\)

\(m = \frac{2}{8}\)

\(m = \frac{1}{4}\)

Now we can plug in one of the points and find the y intercept:

(3, 5)
\(y = mx + b\)

\(5 = \frac{1}{4} \cdot 3 + b\)

\(5 = \frac{3}{4} + b\)

\(b = \frac{17}{4}\)

This means the equation of the line is:
\(y = \frac{1}{4}x + \frac{17}{4}\)