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hoa [83]
2 years ago
15

What is the measure of Zr?

Mathematics
1 answer:
pishuonlain [190]2 years ago
3 0

Answer:

  24°

Step-by-step explanation:

Two angles that form a linear pair are supplementary. That is, their total is 180°.

  x° +156° = 180°

  x° = 180° -156° = 24°

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Solve the following system of equations by the substitution method. 2x = 10y - 8 3x + 4y + 5 = 0
Natali [406]

Answer:

x = -\frac{41}{19}

y = \frac{7}{19}

Step-by-step explanation:

2x = 10y - 8

3x + 4y + 5 = 0

2x = 10y - 8

x = 5y - 4

3x + 4y + 5 = 0

3 ( 5y - 4 ) + 4y + 5 = 0

19y - 7 = 0

19y = 7

y = \frac{7}{19}

x = 5y - 4

x = 5 ( \frac{7}{19} ) - 4

x = -\frac{41}{19}

5 0
3 years ago
What is the greatest common factor of 250, 45, and 30?
kupik [55]
I'm pretty sure that it is 3.5 or even 45
3 0
3 years ago
A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 12ft^3
zheka24 [161]

The height of the container should be equal to 2.57 cm, so as to minimize cost.

<h3>How to calculate the height?</h3>

First of all, we would determine the volume of the rectangular container by using this formula:

Volume = l × w × h

Where:

  • l represents the length.
  • w represents the width.
  • h represents the height.

Substituting the given parameters into the formula, we have;

Volume = x × 4x × h

Volume = 4x²h

At a volume of 12 ft³, we have:

12 = 4x²h

h = 12/4x²

h = 3/x²

For the total area of top and bottom, we have:

Area = (x × 4x) + (x × 4x)

Area = 4x² + 4x²

Area = 8x² sq. units.

Thus, the cost of top and bottom is given by:

Cost = 8x² × 1.50

Cost = $12x²

For the total area of all four sides, we have:

Area = (x × h) + (x × h) + (4x × h) + (4x × h)

Area = xh + xh + 4xh + 4xh

Area = 10xh sq. units.

Thus, the cost of all four sides is given by:

Cost = 10xh × 4.50

Cost = $45xh.

Also, the cost function would be given by:

C(x) = 12x² + 10xh

C(x) = 12x² + 10x(3/x²)

C(x) = 12x² + 30/x

Taking the first derivative, we have:

dC/dx = 24x - 30/x²

24x = 30/x²

24x³ = 30

x³ = 30/24

x = 1.08

Therefore, the height will be:

h = 3/x²

h = 3/1.08²

h = 3/1.1664

Height, h = 2.57 cm.

Read more on minimum height here: brainly.com/question/27308167

#SPJ1

5 0
2 years ago
Match the following
Roman55 [17]

Answer:

No picture

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What number can you use to simplify 5 and 15?
pshichka [43]

Answer:

You can use 5 to simplify 5 and 15, giving you 1 and 3

If this answer was helpful please consider giving brainliest!

7 0
2 years ago
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