Step-by-step explanation:
![6x+3y=12\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x-6x+3y=12-6x\\\\3y=12-6x\qquad\text{divide both sides by 3}\\\\\dfrac{3y}{3}=\dfrac{12}{3}-\dfrac{6y}{3}\\\\\large\boxed{y=4-2y}\\\\===================](https://tex.z-dn.net/?f=6x%2B3y%3D12%5Cqquad%5Ctext%7Bsubtract%7D%5C%206x%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C6x-6x%2B3y%3D12-6x%5C%5C%5C%5C3y%3D12-6x%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cdfrac%7B3y%7D%7B3%7D%3D%5Cdfrac%7B12%7D%7B3%7D-%5Cdfrac%7B6y%7D%7B3%7D%5C%5C%5C%5C%5Clarge%5Cboxed%7By%3D4-2y%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![2p-k=3\qquad\text{subtract}\ 2p\ \text{from both sides}\\\\2p-2p-k=3-2p\\\\-k=3-2p\qquad\text{change the signs}\\\\k=-3+2p\\\\\large\boxed{k=2p-3}\\\\===================](https://tex.z-dn.net/?f=2p-k%3D3%5Cqquad%5Ctext%7Bsubtract%7D%5C%202p%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C2p-2p-k%3D3-2p%5C%5C%5C%5C-k%3D3-2p%5Cqquad%5Ctext%7Bchange%20the%20signs%7D%5C%5C%5C%5Ck%3D-3%2B2p%5C%5C%5C%5C%5Clarge%5Cboxed%7Bk%3D2p-3%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![6v-2w=10\qquad\text{subtract}\ 6v\ \text{from both sides}\\\\6v-6v-2w=10\\\\-2w=10-6v\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2w}{-2}=\dfrac{10}{-2}-\dfrac{6v}{-2}\\\\w=-5+3v\\\\\large\boxed{w=3v-5}\\\\===================](https://tex.z-dn.net/?f=6v-2w%3D10%5Cqquad%5Ctext%7Bsubtract%7D%5C%206v%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5C6v-6v-2w%3D10%5C%5C%5C%5C-2w%3D10-6v%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-2%29%7D%5C%5C%5C%5C%5Cdfrac%7B-2w%7D%7B-2%7D%3D%5Cdfrac%7B10%7D%7B-2%7D-%5Cdfrac%7B6v%7D%7B-2%7D%5C%5C%5C%5Cw%3D-5%2B3v%5C%5C%5C%5C%5Clarge%5Cboxed%7Bw%3D3v-5%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
Answer:
For 20 tickets its 35 dollars
For 50 tickets its 87.50 dollars
For r tickets its 140 dollars
Step-by-step explanation:
So the formula would be -1856 +98[n-1]
9514 1404 393
Answer:
x ≈ 32.4
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between angle, adjacent side, and hypotenuse:
Cos = Adjacent/Hypotenuse
cos(72°) = 10/x
x = 10/cos(72°)
x ≈ 32.4
Answer:
80 × 30 = 2,400
Step-by-step explanation:
We can easily round 79 up to 80 and round 31 down to 30. This would make our expression 80 × 30, which is much easier to compute. We just take 8 × 3 (which is 24) and add two zeros onto the end of the number. This yields us an answer of 2,400 which is very close to the actual multiplication of 79 × 31 which is 2,449 (only 49 more than our estimation).