What is the volume, in cubic m, of a rectangular prism with a height of 15m, a width of 4m, and a length of 13m?

9966 [12]

Based on the above, the segments that are perpendicular to EF are LM and NP.

<h3>Why is the segment are LM and NP perpendicular to EF ?</h3>

Note that when two lines are perpendicular, we can say that;

M1 * M2 = -1 As M1 and M2 are known to be the slopes of the lines.

Therefore, when the the slope of EF is said to be −5/2, then one can say that the slope of the segment that is said to be perpendicular to EF will have to be equal to m1*m2=-1, m2=-1/m1, m2=-1/(-5/2) or m2=2/5.

Scenario one:

JK , if J is at (3, −2) and K is at (5, −7)

To find the slope JK, then

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

m=(-7+2)/(5-3)

m=-5/2

-5/2 is not equal to 2/5

Therefore, JK is not perpendicular to EF

Scenario 2

Find GH , when G is at (6, 7) and H is at (4, 12)

To find the slope GH

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

m=(12-7)/(4-6)

m=5/-2

m=-5/2

Since -5/2 is not equal to 2/5 then GH is not perpendicular to EF

Scenario 3:

Find LM , If L is at (1, 9) and M is at (6, 11)

To find the slope LM, then

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

m=(11-9)/(6-1)

m=2/5

Since 2/5 is equal to 2/5

Then LM is perpendicular to EF

Scenario 4:

Find NP , if N is at (−3, 4) and P is at (−8, 2)

To find the slope NP, then

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

m=(2-4)/(-8+3)

m=-2/-5

m=2/5

Since 2/5 is equal to 2/5.

Therefore, NP is perpendicular to EF

Based on the above calculations, the segments that are perpendicular to EF are LM and NP.

See correct format of question written below

The slope of EF is −5/2 .

Which segments are perpendicular to EF?

Select all the right answers please

1. JK , where J is at (3, −2) and K is at (5, −7)

2. GH , where G is at (6, 7) and H is at (4, 12)

3. LM , where L is at (1, 9) and M is at (6, 11)

4. NP , where N is at (−3, 4) and P is at (−8, 2)

Learn more about segments from

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5 0

2 years ago

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.

ycow [4]

The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: $y = k \times f(x)$

Horizontal stretch by a factor k: $y = f\left(\dfrac{x}{k}\right)$

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

Learn more about Transforming functions:

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5 0

2 years ago

Georgia wants to purchase a piece of fabric that is between 64 and 68 inches long. She can choose between three pieces of fabric

sineoko [7]

The answer is B. Mark as brainliest if this helped you out :). (It would be 66 inches long)

6 0

3 years ago

Read 2 more answers

Find the difference: <br> 2(x-2) - 3(x-4)

cluponka [151]

Answer:

brainliest plzzzzz

Step-by-step explanation:

2(x-2) - 3(x-4)

Simplify:

2(x-2)-3(x-4)

2x-4-3(x-4)

Distribute:

2x-4-3(x-4)

2x-4-3x+12

Add the numbers:

2x-4-3x+12

2x+8-3x

Combine like terms:

2x+8-3x

-x+8

Hence Solution = -x+8

4 0

3 years ago

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism. What is the volume of the rectangular prism? Show

Tju [1.3M]

Answer:

The volume of the rectangular prism is <u>19.25 inches³</u>.

Step-by-step explanation:

Given:

It takes 154 cubes with side lengths of 1/2 inch to fill a rectangular prism.

Now, to find the rectangular prism's volume.

We first find the volume of a cube to fill in the rectangular prism.

The side length of the cube = $\frac{1}{2}\ inch.$

Now, to get the volume of cube we put formula:

$Volume=(side)^3\\\\Volume=(\frac{1}{2})^3 \\\\Volume=\frac{1}{8}\ inch^3.$

<em>Thus, the volume of a cube is </em> $\frac{1}{8} \ inch^3.$ <em />

<em>Number of cubes = 154.</em>

<u><em>According to question, it takes 154 cubes to fill the rectangular prism.</em></u>

<u><em>So, to get the volume of prism we need to find the volume of 154 cubes.</em></u>

Now, to get the volume of 154 such cubes we multiply the volume of a cube by number of cubes:

$\frac{1}{8}\times 154\\\\ =\frac{154}{8}\\\\ =19.25\ inches^3.$

Therefore, the volume of the rectangular prism is 19.25 inches³.

3 0

3 years ago