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Karo-lina-s [1.5K]
3 years ago
11

Two different cross sections are taken parallel to the base of a three-dimensional figure. The two cross sections are the same s

hape, but are not congruent.
Which could be the three-dimensional figure? Select three options.

cone
cylinder
triangular prism
triangular pyramid
square pyramid
Mathematics
2 answers:
Ilia_Sergeevich [38]3 years ago
6 0
<h2>Answer:</h2>

A. cone

D. triangular pyramid

E. square pyramid

(Look at the photo at the bottom.)

<h2>Step-by-step explanation:</h2>

First, know what a cross section is. A cross section is the exposed shape or surface when a straight cut is made through a 3D figure. For example, if I make a cross section, or cut, through a sphere, the cross section will be a circle. The newly exposed surface is in the shape of a circle.

We want to know which 3D figures can make 2 different cross sections, parallel to the base, that are congruent. Congruent means <em>same shape but different size.</em> <em>Parallel to the base</em> means the cut is completely horizontal.

  • A cone is one, because no matter where you horizontally cut this, the cross section will always be a circle, but different sizes.
  • A triangular pyramid is another, because no matter where you horizontally cut this, the cross section will always be a triangle, but different sizes.
  • A square pyramid is another, because no matter where you horizontally cut this, the cross section will always be a square, but different sizes.

Here's a photo of Edge incase you're doubtful.

Vlad [161]3 years ago
5 0

Answer:

<u>A. </u>Cone

<u>D. </u>Triangular Pyramid

<u>E. </u>Square Pyramid

Explanation:

A cone is one, because no matter where you horizontally cut this, the cross section will always be a circle, but different sizes.

A triangular pyramid is another, because no matter where you horizontally cut this, the cross section will always be a triangle, but different sizes.

A square pyramid is another, because no matter where you horizontally cut this, the cross section will always be a square, but different sizes.

Hope this helps! :)

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State whether the lines are parallel, perpendicular,or neither.
cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

  • Two lines are parallel if their slopes are equal.
  • Two lines are perpendicular if the product of their slope is -1

We also know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept

Given the lines

1)

  • y = 6х - 3

Comparing with y=mx+b, the slope of y = 6х - 3:

m₁=6  

  • y = - 1/6x + 7

Comparing with y=mx+b, the slope of y = - 1/6x + 7:

m₂=-1/6

As

m₁ × m₂ = -1

6 ×  - 1/6 = -1

-1 = -1

Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.

2)

  • y = 3x + 2

Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3  

  • 2y = 6x - 6

simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.

i.e. m₁ = m₂ → 3 = 3

Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

3)

  • 8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4  

  • x + 4y = - 1

simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

As

m₁ × m₂ = -1

4 ×  - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

4)

  • 3x+2y = 5

simplifying to write in slope-intercept form

y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

m₁=-3/2  

  • 3y + 2x = - 3

simplifying to write in slope-intercept form

y = -2/3x - 1

Comparing with y=mx+b, the slope of y = -2/3x - 1:

m₂=-2/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

5)

  • y - 5 = 6x

simplifying to write in slope-intercept form

y=6x+5

Comparing with y=mx+b, the slope of y=6x+5:

m₁=6  

  • y - 6x = - 1

simplifying to write in slope-intercept form

y=6x-1

Comparing with y=mx+b, the slope of y=6x-1:

m₂=6

As the slopes of y - 5 = 6x and y - 6x = -1 are equal.

i.e. m₁ = m₂ → 6 = 6

Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

6)

  • y = 3х + 9

Comparing with y=mx+b, the slope of y = 3х + 9:

m₁=3  

  • y = -1/3x - 4

Comparing with y=mx+b, the slope of y =  1/3x - 4:

m₂=1/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

8 0
2 years ago
9) 4 = K/42<br> Solve that for me pls I’m writing here because I need twenty words
DaniilM [7]

Answer:

k = 168

Step-by-step explanation:

4= \frac{k}{42} rewrite the equation

42 * 4=\frac{k}{42} *42 Multiply 42 to isolate k. Do the same on the other side

42 * 4 = 168 When you do that you get 168.

8 0
3 years ago
Three-fourths of the tickets had been sold, and there were 420 tickets left. How many tickets were printed?
BabaBlast [244]

Answer: 560 tickets

Step-by-step explanation:

3/4 = 420/x; now cross multiply:

3x = 4(420)

3x = 1,680; now divide both sides by 3, and you get x = 560

3 0
3 years ago
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Fudgin [204]

Hey mate hope its help you...

5 0
3 years ago
Read 2 more answers
Write an equatiob of line in slope intercept from passing through (-10,-8) and parallel to y=1/5x-3
IgorC [24]
Parallel = same slope
Y = 1/5x + b
Plug in point
-8 = 1/5(-10) + b
-8 = -2 + b, b = -6
Equation: y = 1/5x - 6
7 0
3 years ago
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