Find the diagonal of a rectangular solid if the length is 44 inches, the width is 32 inches, and the height is 26 inches.

Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$

Midpoint of given line

$= ( \frac{3 - 9}{2} , \frac{1 - 5}{2} )$

$= ( \frac{ - 6}{2} , \frac{ - 4}{2} )$

$= ( - 3 , - 2)$

Substituting (-3, -2) into the equation:

-2= -2(-3) +c

-2= 6 +c

c= -2 -6 (-6 on both sides)

c= -8

Thus, the equation of the perpendicular bisector is y= -2x -8.

5 0

3 years ago

Chris wants to create a rectangular rose garden in a yard

AnnZ [28]

Answer in picture below:

Step-by-step explanation:

7 0

2 years ago

Estimate a 10% tip on a bill of $158.71 by first rounding the bill amount to the nearest ten dollars.

irga5000 [103]

158.71 rounded to the nearest ten dollars would be $160.00

then to estimate 10% since 10% starts with a 1, just remove the zero from both numbers

so 160 becomes 16

the tip would be $16

5 0

3 years ago

What is 3 dived by 1/2?

Vesna [10]

Answer:

6

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

∠A=6x−18 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #1

denpristay [2]

Using the properties of alternate angles, the value of x = 8 and ∠ A = 30

<h3>What are Alternate Angles?</h3>

A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.

For the given question,

∠A=6x−18

∠B=14x+38

As, both parallel lines are intersected by a transversal,

the value of angle ∠A and ∠180 - B is same as they are alternate angles,

⇒ 6x−18 = 180 - 14x - 38

⇒ 6x + 14x = 142 + 18

⇒ 20x = 160

⇒ x = 8

∠A = 6x−18

⇒ ∠ A = 30

To learn more abut alternate angles from given link

brainly.com/question/26167358

#SPJ13

Correct question -

7 0

1 year ago