Answer:
3. r = -8
4. x = -5
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>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<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>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<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>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
False — if it doesn’t cross, it has no real roots.
1800000000000000000000000
Answer:
She has 23 nickels and 5 dimes.
Step-by-step explanation:
Let n = the number of nickles and d = the number of dimes.
The number of each = 28. Set up the equation:
n + d = 28
Solve for n:
n = 28 - d
The total amount is $1.65 or 165 cents:
5n + 10d = 165
Substitute:
5(28 - d) + 10d = 165
140 - 5d + 10d = 165
140 + 5d = 165
5d = 165 - 140
5d = 25
d = 5, the number of dimes.
Solve for n:
n = 28 - d
n = 28 - 5 = 23, the number of nickles.
Proof:
5n + 10d = 165
5(23) + 10(5) = 165
115 + 50 = 165
165 = 165
Hope this Helps! Have an Awesome Day!!! <3
Step-by-step explanation:
Answer:
Y=5x+8
Step-by-step explanation:
43=5(7)+b Substitute in the ordered pair and solve in parathensis
43=35+b Subtract 35 from both sides
43-35=-35+b Did you subtract?
8=b The variable is 8.
y= 5x+8 Rewrite the equation in slope intercept form
