So,
For number one, there will be an infinite number of solutions, as there are two placeholders.
3x - 2y = 6
It seems we can use the intercept method.
3x - 2(0) = 6
3x = 6
Divide both sides by 3
x = 2
This is one solution: (2,0)
3(0) - 2y = 6
-2y = 6
Divide both sidees by -2
y = -3
This is another solution: (0,-3)
You should now be able to draw the line.
If you want intercept form for this equation, just manipulate the equation in order to get the y = mx + b form.
Subtract 3x from both sides
-2y = -3x + 6
Divide both sides by -2
![y = \frac{3}{2} x + 6](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B2%7D%20x%20%2B%206)
For the second problem, simply manipulate the equation.
![\frac{1}{3} (6x - 9) = \frac{3}{4} (4x - 8)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%286x%20-%209%29%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%284x%20-%208%29)
Distribute
![2x - 3 = 3x - 6](https://tex.z-dn.net/?f=2x%20-%203%20%3D%203x%20-%206)
Subtract 2x from both sides
![-3 = x - 6](https://tex.z-dn.net/?f=-3%20%3D%20x%20-%206)
Add 6 to both sides
![3 = x](https://tex.z-dn.net/?f=3%20%3D%20x)
For the third problem, do the same thing.
![\frac{3(2x-1)}{4} = x + \frac{7}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%282x-1%29%7D%7B4%7D%20%3D%20x%20%2B%20%20%5Cfrac%7B7%7D%7B2%7D%20)
We must first multiply both sides by 4.
![3(2x-1) = 4x + 14](https://tex.z-dn.net/?f=3%282x-1%29%20%3D%204x%20%2B%2014)
Distribute
![6x - 3 = 4x + 14](https://tex.z-dn.net/?f=6x%20-%203%20%3D%204x%20%2B%2014)
Subtract 4x from both sides
![2x - 3 = 14](https://tex.z-dn.net/?f=2x%20-%203%20%3D%2014)
Add 3 to both sides
![2x = 17](https://tex.z-dn.net/?f=2x%20%3D%2017)
Divide both sides by 2
Answer:
C. 31 ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Step-by-step explanation:
1. Convert mixed numbers into improper fractions:
· 2² + (
- 2) ÷ 3
2. Calculate within the parenthesis:
· 2² +
÷ 3
3. Calculate the exponent:
· 4 +
÷ 3
4. Multiply and divide (left to right):
29 +
÷ 3
29 + ![\frac{13}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B6%7D)
5. Add:
![\frac{187}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B187%7D%7B6%7D)
6. Convert the improper fraction to a mixed number:
= 31 ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
hope this helps!
Answer:
24hours divided by 2 is 12
Step-by-step explanation:
Answer:
it will be 14.09
Step-by-step explanation: