Answer:
n = 1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
-41 = -2/5(45n + 60) + n
<u>Step 2: Solve for </u><em><u>n</u></em>
- Distribute -2/5: -41 = -18n - 24 + n
- Combine like terms: -41 = -17n - 24
- [Addition Property of Equality] Add 24 on both sides: -17 = -17n
- [Division Property of Equality] Divide -17 on both sides: 1 = n
- Rewrite/Rearrange: n = 1
<u>Step 3: Check</u>
<em>Plug in n into the original equation to verify it's a solution.</em>
- Substitute in <em>n</em>: -41 = -2/5(45(1) + 60) + 1
- (Parenthesis) Multiply: -41 = -2/5(45 + 60) + 1
- (Parenthesis) Add: -41 = -2/5(105) + 1
- Multiply: -41 = -42 + 1
- Add: -41 = -41
Here we see that -41 does indeed equal -41.
∴ n = 1 is the solution to the equation.
First we have to write these words in math. This now looks like 3x^2 = 15x. We can also write this as 3x^2 - 15x = 0. This looks like a quadratic, and it is! We can factor this quadratic into the product of two binomials, or (3x + 0)(x - 15).
In order to make (3x)(x - 15) equal to 0, either (3x) or (x-15) has to be equal to zero. This is because the product of a number and 0 always equals the number 0.
If 3x = 0, x needs to equal 0. But because x is a non zero number, x can't be zero.
Moving on to x-15 = 0, we see that x can equal 15. So the two possible values of x in our equation (3x)(x-15) are 0 and 15. We can eliminate 0 because x is a non zero number to get 15 as our final value for x.
Answer:
5.5, 9.5
Step-by-step explanation:
Let x and y be the numbers
x+y = 15
x-y = 4
Add the two equations together to eliminate y
x+y = 15
x-y = 4
------------------
2x = 19
Divide by 2
2x/2 =19/2
x = 9.5
Now find y
x+y = 15
9.5+y = 15
Subtract 9.5
x = 15-9.5
x =5.5
Answer:
20/
9
Step-by-step explanation:
80/
36
=
20/
9
=
2 wholes and 2/
9
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