-> First, we want to put it into more of a slope-intercept form so we can graph.
y - 4 = 1/3 (x + 2)
y = 1/3 (x + 2) + 4
y = 1/3x + 2/3 + 4
y = 1/3x + 14/3
-> Next, we will plot the point (0, 14/3) because it is the y-intercept of our equation
-> Last, we will move up one and to the right three, following the pattern of "rise over run" with our slope of 1/3
[] The finished graph is attached
[] I have also graphed the original equation to show that they overlap, showing that our simplification works
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
Assuming this little game of catch took place on planet earth, negative acceleration due to gravity is -9.8 m/s .
Converting 30ft/s to m/s, initial velocity was 30ft/s x 0.305ft/meter = 9.14m/s
Let's find how long it took for the velocity to equal zero, meaning when the ball reached it's highest point and, for a split second, stopped in mid-air before falling back down.
V(t) = Vi + a*t , where V(t) is velocity as a function of time, a is acceleration due to gravity, and t is time. Set V(t) = 0
0 = 9.14 + (-9.8)* t Add -9.8t to both sides
9.8t = 9.14 Divide both sides by 9.8
t = 0.93 seconds
Let's say your hand is the base point, or where h=zero. We want to find how high above your hand the ball went before it started coming down. Using the distance, or in this case height, formula:
h = Vi*t + (1/2)at² Plug in Vi, a, and our t value, 0.93
h= 9.14 * 0.93 + (1/2)(9.8)(0.93²)
h= 8.5 + 4.9 (0.865)
h = 8.5+ 4.27
h = 12.74 meters
The ball made it 12.74 meters above your hand. Your friends had was one foot above yours, so let's subtract .305 meters to see how far it dropped from the peak height to his hand.
12.74-.305 = 12.43 meters
Let's use the distance formula again to see how long it took to come down. Remember that this time, initial velocity is zero, since the ball starts off suspended in the air.
-12.43 = 0*t + (1/2)(-9.8)(t²) Divide both sides by -9.8/2, or -4.9
2.5374 = t²
t = 1.59
The ball took .93 seconds to go up, and 1.59 seconds to come down to your friend's glove. The total time the ball was in the air:
.93 + 1.59 = 2.52 seconds
The total value of the uniform Aileen sold is x= 2260 on monthly Commission sells.
Given,
Let us assume the all little League uniform = x
Aileen first commission 10% of 2000$ in sales.
Aileen Second Commission 12% of (x-2000)$
Total Commission Aileen Earner = 10% ×2000 + 12% × (x-2000)
231.2 = 0.1× 2000 + 0.12× (x-2000)
231.2 = 200 + (0.12x - 240 )
231.2 = 200 + 0.12x - 240
After Transformation, we get
0.12x = 231.2 - 200 +240
0.12x = 271.2
x = 271.2/.12
x = 2260
Aileen Sell the total value of Lopez Sporting Goods Uniform is 2260.
So the final Answer is x = 2260$.
Learn more about the Commission here.
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