Answer:
![y=-\frac{1}{2}x+\frac{5}{2}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B5%7D%7B2%7D)
Step-by-step explanation:
slope = -1/2
y - int. = 5/2
<em>good luck, i hope this helps :)</em>
Joe ate 7/30 more of pizza than Jane. You can just subtract 2 uneven denominators. So you would turn them into 30 because that’s the closest highest number that can go with 5 and 6. Then multiply 2 with 6 which is 12 and then multiply 1 with 5 which is 5 now you can subtract it. 12/30-5/30=7/30.
Final Result: 7/30
Answer:
Yes. No graph paper.
Step-by-step explanation:
Let's say the 3 points are A, B, C.
If A, B and C lie on one line then ![m_{AB} = m_{BC} = m_{AC}](https://tex.z-dn.net/?f=m_%7BAB%7D%20%3D%20m_%7BBC%7D%20%3D%20m_%7BAC%7D)
![m_{AB} = \frac{y_{B}-y_{A} }{x_{B}-x_{A}} = \frac{2-6}{3-5} = \frac{-4}{-2} = 2\\m_{BC} = \frac{y_{C}-y_{B} }{x_{C}-x_{B}} = \frac{8-2}{6-3} = \frac{6}{3} = 2\\\\m_{AC} = \frac{y_{C}-y_{A} }{x_{C}-x_{A}} = \frac{8-6}{6-5} = \frac{2}{1} = 2\\\\](https://tex.z-dn.net/?f=m_%7BAB%7D%20%3D%20%5Cfrac%7By_%7BB%7D-y_%7BA%7D%20%7D%7Bx_%7BB%7D-x_%7BA%7D%7D%20%3D%20%5Cfrac%7B2-6%7D%7B3-5%7D%20%3D%20%5Cfrac%7B-4%7D%7B-2%7D%20%3D%202%5C%5Cm_%7BBC%7D%20%3D%20%5Cfrac%7By_%7BC%7D-y_%7BB%7D%20%7D%7Bx_%7BC%7D-x_%7BB%7D%7D%20%3D%20%5Cfrac%7B8-2%7D%7B6-3%7D%20%3D%20%5Cfrac%7B6%7D%7B3%7D%20%3D%202%5C%5C%5C%5Cm_%7BAC%7D%20%3D%20%5Cfrac%7By_%7BC%7D-y_%7BA%7D%20%7D%7Bx_%7BC%7D-x_%7BA%7D%7D%20%3D%20%5Cfrac%7B8-6%7D%7B6-5%7D%20%3D%20%5Cfrac%7B2%7D%7B1%7D%20%3D%202%5C%5C%5C%5C)
Hence, they lie on one line.
You don't need to use a graph paper to prove it.
Answer:
AC ≈ 2.87
Step-by-step explanation:
Using the sine ratio in the right triangle
sin35° =
=
= ![\frac{AC}{5}](https://tex.z-dn.net/?f=%5Cfrac%7BAC%7D%7B5%7D)
Multiply both sides by 5
5 × sin35° = AC , thus
AC ≈ 2.87 ( to the nearest hundredth )
Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.