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sergeinik [125]
1 year ago
11

Which lines must be parallel?

Mathematics
1 answer:
Oduvanchick [21]1 year ago
5 0

The lines that must be parallel are lines r and s. The correct option is A) r and s

<h3>Parallel lines </h3>

From the question, we are to determine the lines that must be parallel to satisfy the given condition

The given condition is

∠5 ≅∠13

In the given diagram,

∠5 and ∠13 are corresponding angles

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

In the diagram,

The transversal is line p which intersects lines r and s.

Therefore,

Lines r and s must be parallel lines

Hence, the lines that must be parallel are lines r and s. The correct option is A) r and s

Learn more on Parallel lines here: brainly.com/question/24213000

#SPJ1

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Factorise<br>a^4+a^2b^2+b^4​
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Answer:

a^6*b^6

Step-by-step explanation:

I think that's correct, but I'm not sure

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The length of XY the minor arc is 48 cm what is the circumference of Z
Amanda [17]
If found the image that accompanies this problem, the central angle was 60°. Since the circumference of a circle is always 360°, the minor arc represents 60°/360° of the circle.

48 cm / (60°/360°) = 48 cm / (1/6) = 48 cm * 6/1 = 48 cm * 6 =  288 cm

The circumference of circle Z is 288 cm.

4 0
3 years ago
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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
3 years ago
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frosja888 [35]

Answer:

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Step-by-step explanation:

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