Answer:
7. r = -5
8. x = -1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define</u>
r + 2 - 8r = -3 - 8r
<u>Step 2: Solve for </u><em><u>r</u></em>
- Combine like terms: -7r + 2 = -3 - 8r
- Add 8r to both sides: r + 2 = -3
- Subtract 2 on both sides: r = -5
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: -5 + 2 - 8(-5) = -3 - 8(-5)
- Multiply: -5 + 2 + 40 = -3 + 40
- Add: -3 + 40 = -3 + 40
- Add: 37 = 37
Here we see that 37 does indeed equal 37.
∴ r = -5 is a solution of the equation.
<u>Step 4: Define equation</u>
-4x = x + 5
<u>Step 5: Solve for </u><em><u>x</u></em>
- Subtract <em>x</em> on both sides: -5x = 5
- Divide -5 on both sides: x = -1
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: -4(-1) = -1 + 5
- Multiply: 4 = -1 + 5
- Add: 4 = 4
Here we see that 4 does indeed equal 4.
∴ x = -1 is a solution of the equation.
Answer:
Step-by-step explanation:
Given the equation = 
Required: To factor out 1/3;
1/3 is common to both sides;
So, 1/3 is a common factor
To solve for the value of p;
= 0
X = 5.
Pythagorus Theorem:
c^2 = b^2 + a^2
(13)^2 = (12)^2 + a^2
a = sqrt((13)^2 - (12)^2))
a = 5
Answer:
30 gallons of 6% milk, and 45 gallons of 1% milk.
x=quarts of 6% butterfat
First, write an equation.
0.06x+0.01(75-x)=0.03*75
Multiply both sides by 100.
0.06x*100+0.01*100(75-x)=100*0.03*75
Simplify
6x+75-x=3*75
6x+75-x=225
Solve
5x=225-75=150
5x=150
x=30
75-30=45
So, we need 30 gallons of 6% milk, and 45 gallons of 1% milk.
Step-by-step explanation:
