The perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ has an equation of the form $y = mx + b$. Find $m+b$.

Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$.

  3.5

Step-by-step explanation:

The attached shows the perpendicular bisector to have a slope of m = -1/2 and a y-intercept of b = 4.

  m+b = (-1/2) +4 = 3.5

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The difference of coordinates of the two points is ...

  B-A = (-5, 4) -(-3, 8) = (-2, -4)

Then the rise/run ratio is (-4)/(-2) = 2. The slope of the perpendicular bisector will have a slope (m) that is the negative reciprocal of this:

  m = -1/2

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The average of the coordinates of the two points is ...

  (B+A)/2 = ((-5, 4) +(-3, 8))/2 = (-8, 12)/2 = (-4, 6)

Then the point-slope form of the equation of the perpendicular bisector can be written ...

  y = (-1/2)(x +4) +6 = (-1/2)x -2 +6

  y = (-1/2)x +4

So, the y-intercept is b = 4, and ...

  m + b = (-1/2) +4 = 3 1/2

  m + b = 3.5

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.