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2 years ago

Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)

Mathematics

1 answer:

stiv31 [10]2 years ago

6 0

9514 1404 393

Answer:

2x +y = -2

Step-by-step explanation:

The bisector must have a slope that is the negative reciprocal of the slope of the line between these points. It must pass through the midpoint of the segment.

The slope of the line through the given points is ...

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

= (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

The slope of the required bisector is then ...

m = -1/(1/2) = -2

The midpoint of the given segment is ...

((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

Then the point-slope form of the equation of the bisector is ...

y -y1 = m(x -x1)

y -2 = -2(x -(-2))

y = -2x -4 +2

y = -2x -2 . . . . . . . slope-intercept form equation

2x +y = -2 . . . . . . . standard form equation

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A professor has recorded exam grades for 10 students in his class, but one of the grades is no longer readable. If the mean sco

Nostrana [21]

Answer:

unreadable score = 35

Step-by-step explanation:

We are trying to find the score of one exam that is no longer readable, let's give that score the name "x". we can also give the addition of the rest of 9 readable s scores the letter "R".

There are two things we know, and for which we are going to create equations containing the unknowns "x", and "R":

1) The mean score of ALL exams (including the unreadable one) is 80

so the equation to represent this statement is:

mean of ALL exams = 80

By writing the mean of ALL scores (as the total of all scores added including "x") we can re-write the equation as:

$\frac{R+x}{10} =80$

since the mean is the addition of all values divided the total number of exams.

in a similar way we can write what the mean of just the readable exams is:

$\frac{R}{9} = 85\\$ (notice that this time we don't include the grade x in the addition, and we divide by 9 instead of 10 because only 9 exams are being considered for this mean.

Based on the equation above, we can find what "R" is by multiplying both sides by 9:

$\frac{R}{9} = 85\\R=85*9= 765$

Therefore we can now use this value of R in the very first equation we created, and solve for "x":

$\frac{R+x}{10} =80\\\frac{765+x}{10} =80\\765+x=80*10=800\\765+x=800\\x=800-765=35$

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2 years ago

Which graph represents the following system of inequalities? y<1/4x+4 y ≥5x+1

Readme [11.4K]

Answer:

3rd

Step-by-step explanation:

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2 years ago

Find the surface area of composite figure. Please help

Ivan

Answer:

The surface area of the composite figure is $410\ m^{2}$

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to the surface area of the rectangular prism of the bottom plus the lateral area o the rectangular prism of the top

Step 1

Find the surface area of the rectangular prism of the bottom

The surface area is equal to

$SA=2B+Ph$