We can use the point-slope equation:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
m, the slope, is 3/4:
![y = \frac{3}{4} x + b](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20b)
To find b, we plug in the point (4,1/3):
![( \frac{1}{3} ) = \frac{3}{4} (4) + b \\ \frac{1}{3} = 3 + b \\ \frac{1}{3} = \frac{9}{3} + b](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%284%29%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%203%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%20%5Cfrac%7B9%7D%7B3%7D%20%20%2B%20b)
![- \frac{8}{3} = b](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20%20%3D%20b)
Therefore, the point-slope equation is
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
Now we have to see which answer matches.
![y - \frac{3}{4} = \frac{1}{3} (x - 4) \\ y - \frac{3}{4} = \frac{1}{3} x - \frac{4}{3} \\ y - \frac{9}{12} = \frac{1}{3} x - \frac{16}{12}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B9%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B16%7D%7B12%7D)
![y = \frac{1}{3} x - \frac{7}{12}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B7%7D%7B12%7D%20)
Since this is not the same, we try the next one.
![y - \frac{1}{3} = \frac{3}{4} (x - 4) \\ y - \frac{1}{3} = \frac{3}{4} x - 3 \\ y - \frac{1}{3} = \frac{3}{4} x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This is the same, so this is the answer. We should still double-check the other answers.
![y - \frac{1}{3} = 4(x - \frac{3}{4} ) \\ y - \frac{1}{3} = 4x - 3 \\ y - \frac{1}{3} = 4x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204%28x%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = 4x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%204x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This one is not equivalent.
![y - 4 = \frac{3}{4} (x - \frac{1}{3} ) \\ y - 4 = \frac{3}{4} x - \frac{1}{4} \\ y - \frac{16}{4} = \frac{3}{4} x - \frac{1}{4}](https://tex.z-dn.net/?f=y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5C%5C%20y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B16%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20)
![y = \frac{3}{4} x + \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20%20%5Cfrac%7B15%7D%7B4%7D%20)
This one also does not work.
The answer is the second one:
= (-6+2/2, -2-4/2)
= (-4/2, -6/2)
<span>= (-2, -3)</span>
The volume of the sphere is given by:
V1 = (4/3) * (pi) * (r ^ 3)
Where,
r: sphere radio
Substituting values:
V1 = (4/3) * (3.14) * ((1/2) ^ 3)
V1 = 0.523 units ^ 3
The volume of the cube is given by:
V2 = L ^ 3
Where,
L: length of the sides
Substituting values:
V2 = 1 ^ 3
V2 = 1 units ^ 3
The unoccupied space is:
V2-V1 = 1-0.523
V2-V1 = 0.477 units ^ 3
Answer:
The unoccupied volume remaining inside the cube is:
0.477 units ^ 3
Answer:
3 cases
Step-by-step explanation:
Total Money Needed = $850
Each Golf Ball = $2
Total Balls needed = 850/2 = 425 balls
Case = 24 Pack
Pack = 6 balls
So a Case has:
24 * 6 = 144 balls
They need 425 balls to sell and each case has 144 balls, so number of case needed would be:
425/144 = 2.95
We can't have 2.95 cases, so we round up to 3 cases
Answer:
you just rotate the
Step-by-step explanation: