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:
hi Step-by-step explanation:April 12, 1861: Battle of Fort Sumter. ...
June 30, 1861: Battle of Philippi. ...
July 21, 1861: First Battle of Bull Run/First Battle of Manassas. ...
August 28-29, 1861: Battle of Hatteras Inlet Batteries. ...
October 21, 1861: Battle of Ball's Bluff. ...
November 7, 1861: Battle of Belmont. ...
January 19, 1862: Battle of Mill Springs.
The negative externalities must be present.
Answer:
y=4
Step-by-step explanation:
if y+2=6, you can subtract 2 from both sides, giving you y=6-2. 6-2=4, which is y.
Answer:
C(x) = 12x + 1680
Slope = 12
Intercept = 1680
Step-by-step explanation:
Given that:
X1 = 60 chairs ; y1 = 2400
X2 = 260 chairs ; y2 = 4800
Obtain the slope ; m
m = y2 - y1 / x2 - x1
m = 4800 - 2400 / 260 - 60
m = 2400 / 200
m = 12
Using the point slope relation:
y - y1 = m(x - x1)
y - 2400 = 12(x - 60)
y - 2400 = 12x - 720
y = 12x - 720 + 2400
y = 12x + 1680
C(x) = 12x + 1680
From the general slope intercept equation :
y = mx + c
m = slope ; c = intercept
Hence,
C(x) = 12x + 1680
Slope = 12
Intercept = 1680
