The Answer is 8.75 x 10¹²
Answer:
w = -4
Step-by-step explanation:
Solve for w:
17 - 3 (w + 5) = 6 (w + 5) - 2 w
-3 (w + 5) = -3 w - 15:
-3 w - 15 + 17 = 6 (w + 5) - 2 w
Grouping like terms, -3 w - 15 + 17 = (17 - 15) - 3 w:
(17 - 15) - 3 w = 6 (w + 5) - 2 w
17 - 15 = 2:
2 - 3 w = 6 (w + 5) - 2 w
6 (w + 5) = 6 w + 30:
2 - 3 w = 6 w + 30 - 2 w
Grouping like terms, 6 w - 2 w + 30 = (6 w - 2 w) + 30:
2 - 3 w = (6 w - 2 w) + 30
6 w - 2 w = 4 w:
2 - 3 w = 4 w + 30
Subtract 4 w from both sides:
2 + (-3 w - 4 w) = (4 w - 4 w) + 30
-3 w - 4 w = -7 w:
-7 w + 2 = (4 w - 4 w) + 30
4 w - 4 w = 0:
2 - 7 w = 30
Subtract 2 from both sides:
(2 - 2) - 7 w = 30 - 2
2 - 2 = 0:
-7 w = 30 - 2
30 - 2 = 28:
-7 w = 28
Divide both sides of -7 w = 28 by -7:
(-7 w)/(-7) = 28/(-7)
(-7)/(-7) = 1:
w = 28/(-7)
The gcd of 28 and -7 is 7, so 28/(-7) = (7×4)/(7 (-1)) = 7/7×4/(-1) = 4/(-1):
w = 4/(-1)
Multiply numerator and denominator of 4/(-1) by -1:
Answer: w = -4
9514 1404 393
Explanation:
Finish the Given statement, make use of the relationships of angles and parallel lines, then finish the algebra.
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2. m∠6 = (1/8)m∠4 . . . . Given
3. m∠6 + m∠4 = 180° . . . . 3. same-side interior angles are supplementary
4. m∠6 + 8·m∠6 = 180° . . . . 4. Substitution (from 2, above: 8·m∠6 = m∠4)
Here is the "algebra" that gets you to line 5:
4a. 9m∠6 = 180° . . . collect terms
4b. m∠6 = 20° . . . . . divide by 9
4c. m∠4 = 8·20° = 160° . . . use the same relation as in step 4
5. m∠6 = 20°, m∠4 = 160° . . . . Algebra
