Find the value of the expression 9.16 + k for k = 9.

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

<h3>Midpoint</h3>

The midpoint of XZ is the average of the coordinates of X and Z.

M = (X +Z)/2

M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

<h3>Line through two points</h3>

The slope of the median can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

5(y -4) -17(x -7) = 0

5y -17x +99 = 0 . . . . equation of the median through Y

3 0

2 years ago

Write each number as a logarithm with base 2:-3

expeople1 [14]

The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)

<h3>What are logarithms?</h3>

As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms

<h3>How to rewrite the number as a logarithm?</h3>

The number is given as:

x = -3

The base of the logarithm is given as:

Base = 2

To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2

This is represented as:

Number =2^-3

Apply the power rule of indices

Number =1/2^3

Evaluate the exponent

Number = 1/8

Evaluate the quotient

Number = 0.125

Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)