Answer:
x = 8
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 equation</u>
3(x - 2) = 2(x + 1)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute: 3x - 6 = 2x + 2
- Subtract 2x on both sides: x - 6 = 2
- Add 6 to both sides: x = 8
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 3(8 - 2) = 2(8 + 1)
- Subtract/Add: 3(6) = 2(9)
- Multiply: 18 = 18
Here we see that 18 does indeed equal 18.
∴ x = 8 is a solution to the equation.
Answer:
The speed of the first train is 45 mph and the speed of the second train is 75 mph
Step-by-step explanation:
Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).
The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles
The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles
Since the second train overtakes the first at 6:00 pm, hence:
3x + 90 = 5x
2x = 90
x = 45
Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).
It is which ever one adds up to 90
Answer:
130.6 % just move the decimal place 2 places to the right and add the percentage sign
Step-by-step explanation:
<h3>Check the possibilities:</h3><h2>A:</h2>
u(n)=n-1
u(6)=6-1= True
u(10)=10-1≠7 False
<h3>
A is eliminated.</h3>
<h2>
B:</h2>
u(n)=2n-7
u(6)=2(6)-7=12-7=5 True
u(10)=2(10)-7=20-7≠7 False
<h3>
B is eliminated.</h3>
<h2>
C:</h2>
u(n)=0.5n+2
u(6)=0.5(6)+2=3+2=5 True
u(10)=0.5(10)+2=5+2=7 True
<h2>
C is your answer.</h2>
<h3>
Check D although we know it's C:</h3>
u(n)=n/6 +4
u(6)=6/6 +4=1+4=5 True
u(10)=10/6 +4=2.5+4=6.5≠7 False
