Answer:
x /\ y
1 /\ -4
2 /\ -5
3 /\ -6
4 /\ -7
... /\ ...
Step-by-step explanation:
Answer:
x = 30
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
8x - 3(2x - 4) = 3(x - 6)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute: 8x - 6x + 12 = 3x - 18
- Combine like terms: 2x + 12 = 3x - 18
- Subtract 2x on both sides: 12 = x - 18
- Add 18 to both sides: 30 = x
- Rewrite: x = 30
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: 8(30) - 3(2(30) - 4) = 3(30 - 6)
- Multiply: 240 - 3(60 - 4) = 3(30 - 6)
- Subtract: 240 - 3(56) = 3(24)
- Multiply: 240 - 168 = 72
- Subtract: 72 = 72
1. Find the "opposite side," if the angle is 60 degrees and the hyp is 6:
opp opp sqrt(3)
sin 60 deg = ------- = -------- = ----------
hyp 6 2
Cross-multiplying, 2(opp) = 6sqrt(3), so that opp = 3 sqrt(3) (answer)
2. Use the Pyth. Thm. to find the "adjacent side:"
[3sqrt(3)]^2 + x^2 = 6^2, or 9(3) + x^2 = 36, or x^2 = 9, or x = 3.
The lengths of the legs of this 30-60-90 triangle are 3 and 3 sqrt(3).
check: Does 3^2 + [3sqrt(3)]^2 = 6^2?
Does 9 + 9(3) = 6^2? YES
