we know the segment QP is an angle bisector, namely it divides ∡SQR into two equal angles, thus ∡1 = ∡2, and ∡SQR = ∡1 + ∡2.
![\bf \begin{cases} \measuredangle SQR = \measuredangle 1 + \measuredangle 2\\\\ \measuredangle 2 = \measuredangle 1 = 5x-7 \end{cases}\qquad \qquad \stackrel{\measuredangle SQR}{7x+13} = (\stackrel{\measuredangle 1}{5x-7})+(\stackrel{\measuredangle 2}{5x-7}) \\\\\\ 7x+13 = 10x-14\implies 13=3x-14\implies 27=3x \\\\\\ \cfrac{27}{3}=x\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \measuredangle SQR = 7(9)+13\implies \measuredangle SQR = 76](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20%5Cmeasuredangle%20SQR%20%3D%20%5Cmeasuredangle%201%20%2B%20%5Cmeasuredangle%202%5C%5C%5C%5C%20%5Cmeasuredangle%202%20%3D%20%5Cmeasuredangle%201%20%3D%205x-7%20%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Cmeasuredangle%20SQR%7D%7B7x%2B13%7D%20%3D%20%28%5Cstackrel%7B%5Cmeasuredangle%201%7D%7B5x-7%7D%29%2B%28%5Cstackrel%7B%5Cmeasuredangle%202%7D%7B5x-7%7D%29%20%5C%5C%5C%5C%5C%5C%207x%2B13%20%3D%2010x-14%5Cimplies%2013%3D3x-14%5Cimplies%2027%3D3x%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B27%7D%7B3%7D%3Dx%5Cimplies%209%3Dx%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cmeasuredangle%20SQR%20%3D%207%289%29%2B13%5Cimplies%20%5Cmeasuredangle%20SQR%20%3D%2076)
Answer:
x = -10
Step-by-step explanation:
Step 1: Write equation
180 + 8x = 160 + 6x
Step 2: Solve for <em>x</em>
- Subtract 6x on both sides: 180 + 2x = 160
- Subtract 180 on both sides: 2x = -20
- Divide both sides by 2: x = -10
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
180 + 8(-10) = 160 + 6(-10)
180 - 80 = 160 - 60
100 = 100
Answer:
Step-by-step explanation:
2 1/2 + x = 5 1/3 Change the mixed numbers to improper fractions
5/2 + x = 16/3 The lowest common multiple is 6. Multiply by 6
5*3 + 6x = 16*2
15 + 6x = 32 Subtract 15 from both sides.
6x = 32 - 15
6x = 17 Divide by 6
6x/6 = 17/6
x = 2 5/6
Check
5/2 + 17/6 = 16/3
15/6 + 17/6 = 32/6
32/6 = 32/6 The question checks.
Answer:
543
Step-by-step explanation:
That would be M = 30G where M is in miles and G is in gallons.
