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Morgarella [4.7K]
2 years ago
14

4. Solve each equation for x. (8 points: 2 points each)

Mathematics
1 answer:
maksim [4K]2 years ago
8 0

Answer:

a. x = 9 + 4y

b. x = (7y-2)/6

c. x = (17 + k)/4

d. x = (9-c)/k

Step-by-step explanation:

In each of the equations, we want to make x the formula subject

a) 3x-12y = 27

3x = 27 + 12y

3x = 3(9 + 4y)

x = 9 + 4y

b) 6x-7y = -2

6x = 7y-2

x = (7y-2)/6

c) 4x - k = 17

4x = 17 + k

x = (17 + k)/4

d) kx + c = 9

kx = 9-c

x = (9-c)/k

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The volume of a sphere can be described by the following formula, where V = volume and r = radius of the sphere.
Anika [276]

Option C: r = \sqrt[3]{\frac{3V}{4\pi} } is the right answer

Step-by-step explanation:

Given formula for volume of a sphere is:

V = \frac{4}{3}\pi r^3

We have to make r the subject of the formula

Multiplying equation by 3/4

\frac{3}{4}V = \frac{4}{3} * \frac{3}{4} \pi r^3\\\frac{3}{4}V = \pi r^3

Dividing both sides by pi

\frac{3}{4\pi}V =\frac{ \pi r^3}{\pi}\\\frac{3V}{4\pi} = r^3

Taking cube root on both sides

\sqrt[3]{\frac{3V}{4\pi} } = \sqrt[3]{r^3} \\ r = \sqrt[3]{\frac{3V}{4\pi} }

Hence,

Option C: r = \sqrt[3]{\frac{3V}{4\pi} } is the right answer

Keywords: Volume, Sphere

Learn more about volume at:

  • brainly.com/question/12973601
  • brainly.com/question/13063819

#LearnwithBrainly

5 0
3 years ago
Please help i need this answer quick for a test
Oksi-84 [34.3K]

Answer: the depth of the trench is 3685 ft

Step-by-step explanation:

The hole is approximately 347 yards wide. This means that the diameter of the hole is 347 yards.

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder or hole.

h represents the height or depth of the cylinder or hole.

π is a constant whose value is 3.14

From the information given,

Volume = 348289500 ft³

Radius = diameter/2 = 347/2 = 173.5 ft

Therefore,

348289500 = 3.14 × 173.5² × h

348289500 = 94521.065h

h = 348289500/94521.065

h = 3685 feet

4 0
3 years ago
What is the sum of the first 37 terms of the arithmetic sequence?
lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

a_{n+1} = a_{n} + d

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

a_{n} = a_{1} + (n-1)*d

The sum of the first n terms of an arithmetic sequence is given by:

S_{n} = \frac{n(a_{1} + a_{n})}{2}

In this question:

a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6

We want the sum of the first 37 terms, so we have to find a_{37}

a_{n} = a_{1} + (n-1)*d

a_{37} = a_{1} + (36)*d

a_{37} = -27 + 36*6

a_{37} = 189

Then

S_{37} = \frac{37(-27 + 189)}{2} = 2997

The sum of the first 37 terms of the arithmetic sequence is 2997.

6 0
3 years ago
The original price of an audio jukebox was 280 it is on sale for 220 what percent discount does this represent
solong [7]

Answer:

The answer would be 12%

Step-by-step explanation:

250-220=30 and 30 is 12% of 250

4 0
2 years ago
Read 2 more answers
Write a system<br> of linear inequalities represented by the graph.
Helga [31]
2,3 or 4,1 either one
6 0
2 years ago
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