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Nataliya [291]
2 years ago
14

Help me please

Mathematics
1 answer:
Olenka [21]2 years ago
4 0
The answer is D $32,000
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Describe how to determine which side of the boundary line should be shaded
iogann1982 [59]
Hello Bri,

If you are talking about a boundary line on a coordinate plane, the best way to determine which side to shade is to start by selecting a coordinate point (x, y) that is not on the line.

Then, substitute those values into your inequality. Simplify the inequality. If the resulting statement is true, then shade the side with your point. If the resulting statement is false, then shade the other side.

Testing a point like this shows the side of the inequality that is the solution and needs to be shaded.

Good luck!
8 0
3 years ago
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
2 years ago
A rectangle is 5 inches long and 7 inches wide.How many one-square-inch tiles are needed to cover its area?
Ket [755]

Answer:

35 square inches

Step-by-step explanation:

The formula is bh

b being base and h being height. In this, the width is height and length is base.

5 times 7 is 35

Mark me as brainliest if this helps!

5 0
3 years ago
What is the slope of the line that passes through the points (1, -6)(1,−6) and (-8, 9) ?(−8,9)?
Monica [59]

Answer:

The answer to your question is  m = -5/3      

Step-by-step explanation:

Data

Point 1 = (1, -6)

Point 2 = (-8, 9)

Process

To find the slope just substitute the values in the formula and simplify.

Formula

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

-Identify x1, y1, x2 and y2

  x1 = 1    y1 = -6   x2 = -8  y2 = 9

-Substitution

             m = (9 + 6) / (-8 - 1)

-Simplification

             m = 15/-9

-Result

             m = -5/3            

4 0
3 years ago
A cave explorer is at an elevation of negative 38 feet. The explorer starts moving at a rate of negative 12 feet per minute. Ide
Ksivusya [100]

Answer:

-38 - 12x < 200

Step-by-step explanation:

Given,

The original elevation = -38 feet,

Also, the explorer starts moving at a rate of negative 12 feet per minute.

So, the distance covered by explorer after x minutes = -12x feet,

Thus, the final elevation = original elevation +  distance covered by explorer

= -38 - 12x

According to the question,

final elevation < -200 feet

⇒ -38 - 12x < 200

Which is the required inequality.

8 0
3 years ago
Read 2 more answers
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