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MariettaO [177]
3 years ago
10

Solve each equation for the missing variable. If your answer is not an integer, write it as an improper fraction.

Mathematics
2 answers:
Andre45 [30]3 years ago
8 0
To start the problem, you will want to move the numbers with variables and the ones without to the other side, then combine them together so that there is only one thing on each side. Then divide on both sides by the variable's coefficient and you will get your answer. Here is it done for the 1st problem.
5n - 14 = 8n + 4 \\ 5n - 14 - 5n = 8n + 4 - 5n \\  - 14 = 3n + 4 \\  - 14 - 4 = 3n + 4 - 4 \\  - 18 = 3n \\  \frac{3}{3} n =   \frac{ - 18}{6}  \\ n =  - 6
For the second one you will want to start by simplifying everything on both sides since you can combine the constants (numbers without any variables). It should look like this:
- 15 + 4 - 5a =  - 2 + 26 + 30a \\  - 11 - 5a = 24 + 30a
What you can do from here is push constants to one side and variables to the other like before. Here is how it would look:
- 11 - 5a = 24 + 30a \\  - 11 - 5a - 24 = 24 - 24 + 30a \\  - 35 - 5a = 30a \\  - 35 - 5a + 5a = 30a + 5a \\  - 35 = 35a
Once there is only one thing on both side, you can divide both sides by the coefficient (the number attached to a variable) to get the variable alone.
35a =  - 35 \\  \frac{35}{35} a =  \frac{ - 35}{35}  \\ a =  - 1
Thus, a is equal to -1.

For the third problem, it is more of the same type of problem that we have done before. Since there are no multiples of anything (variables or constants) on each side, we can start pushing variables to one side and constants to the others like so:
- 8x + 25 = 3 - 9x \\   - 8x + 9x  + 25 = 3 - 9x + 9x \\ x + 25 = 3 \\ x + 25 - 25 = 3  - 25 \\ x =  - 22
Since x's coefficient is 1, there is no need to divide and your answer is -22.
FromTheMoon [43]3 years ago
4 0

First example:

Subtract the 8n on both sides to get the variable on one side of the equation. Do the same for the regular numbers. Then divide by -3.

5n-14=8n+4\\ \\ 5n-8n=4+14 \\ \\ -3n=18\\ \\ n=-6

This should be your final answer.

Second Example:

Do the same thing as explained in Example 1. Here's some work to help guide you.

-15 - 5a + 4 = -2 + 30a + 26\\ \\ -5a-30a=-2+26+15\\ \\ -35a=39\\ \\ a = \frac{39}{-35}

That should be your final answer here.

Third Example:

3 - 9x = -8x + 25\\ \\ -9x+8x=25-3\\ \\ -x=22\\ \\ x=-22

Hope this helps and its understandable! Let me know if you still don't understand.

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Question 1
Alexxx [7]

Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

                               = (Area of the rectangle + Area of the trapezoid)× depth  

Area of the trapezoid = \frac{1}{2}(b_{1}+b_{2})\times h

                                    = \frac{1}{2}(11+9)\times (12-1.5)

                                    = 105 ft²

Area of the rectangle = Length × width

                                    = 11 × 1.5

                                    = 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

                                          = 121.5 × 4

                                          = 486 cubic feet

b). Liner required = surface area of the pool excluding top

                             = Surface area of the walls + Area of the pool base

                             = (Perimeter of the pool) × depth + area of the base

                             = (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

                             = 176.8 + 121.5

                             = 298.3 square feet

Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet                                  

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KIM [24]

Answer:

2n+10=-2

2n=-2-10

2n= -12

N= -12/2

n=-6

Step-by-step explanation:

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