Answer:
150
Step-by-step explanation:
The statement “3, 9, 81, 243 is an example of an infinite
arithmetic series” is FALSE. I am hoping that this answer has satisfied your
query and it will be able to help you in your endeavor, and if you would like,
feel free to ask another question.
This question seems to me to be an exercise in applying the rule for a difference of squares in order to rewrite the difference of two relatively large numbers as the "simpler" product of other integers.
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.
If x represents the mass of 1 ball in kg, then the balance shows ...
... 6x = x + 9 kg
... 5x = 9 kg
Then 6x is ...
... (6/5)·5x = (6/5)·9 kg = 10.8 kg
0.8 kg = 0.8·1000 g = 800 g
so 10.8 kg is ...
... D. 10 kg 800 g
