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.
Answer:
(x+7)^2+4
Step-by-step explanation:
(x+7)^2 + 4
x^2+14x+49+4
x^2+24x+53
Step-by-step explanation:
by considering how many inches (") are in one foot (').
the answer is 12. there are 12 in in every ft.
so, now we can convert everything to the smallest scale (inches) and do the calculation based on inches :
(8×12 + 4) - (2×12 + 6) = 96 + 4 - 24 - 6 = 100 - 30 = 70"
and now to translate 70" back into ft and in :
70/12 = 5 with a remainder of 10
70" = 5' 10"
Answer:
$3 off which is $27
Step-by-step explanation:
10% of 30 is 3 so you would subtract 30 - 3
and you get $27
Let θ = m∡I
tan θ = 20/21
tan⁻¹ (20/21) = θ
θ ≈ 43.60° or if you need to round to another decimal point, plug the equation I put in bold into a calculator.
