Answer:
![a=\frac{2S -2v_ot-2s_o}{t^2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B2S%20-2v_ot-2s_o%7D%7Bt%5E2%7D)
Step-by-step explanation:
We have the equation of the position of the object
![S = \frac{1}{2}at ^2 + v_ot+s_o](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B1%7D%7B2%7Dat%20%5E2%20%2B%20v_ot%2Bs_o)
We need to solve the equation for the variable a
![S = \frac{1}{2}at ^2 + v_ot+s_o](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7B1%7D%7B2%7Dat%20%5E2%20%2B%20v_ot%2Bs_o)
Subtract
and
on both sides of the equality
![S -v_ot-s_o = \frac{1}{2}at ^2 + v_ot+s_o - v_ot- s_o](https://tex.z-dn.net/?f=S%20-v_ot-s_o%20%3D%20%5Cfrac%7B1%7D%7B2%7Dat%20%5E2%20%2B%20v_ot%2Bs_o%20-%20v_ot-%20s_o)
![S -v_ot-s_o = \frac{1}{2}at ^2](https://tex.z-dn.net/?f=S%20-v_ot-s_o%20%3D%20%5Cfrac%7B1%7D%7B2%7Dat%20%5E2)
multiply by 2 on both sides of equality
![2S -2v_ot-2s_o = 2*\frac{1}{2}at ^2](https://tex.z-dn.net/?f=2S%20-2v_ot-2s_o%20%3D%202%2A%5Cfrac%7B1%7D%7B2%7Dat%20%5E2)
![2S -2v_ot-2s_o =at ^2](https://tex.z-dn.net/?f=2S%20-2v_ot-2s_o%20%3Dat%20%5E2)
Divide between
on both sides of the equation
![\frac{2S -2v_ot-2s_o}{t^2} =a\frac{t^2}{t^2}](https://tex.z-dn.net/?f=%5Cfrac%7B2S%20-2v_ot-2s_o%7D%7Bt%5E2%7D%20%3Da%5Cfrac%7Bt%5E2%7D%7Bt%5E2%7D)
Finally
![a=\frac{2S -2v_ot-2s_o}{t^2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B2S%20-2v_ot-2s_o%7D%7Bt%5E2%7D)
Answer:
(4,9)
Step-by-step explanation:
If f(x) is a function, the function f(x) + a is a function translated a units up vertically. <em>Hence, all the y-coordinates of the coordinates of the points on the function will shift up by a.</em>
<em />
For this problem, we need to find corresponding coordinate of (4,4) of f(x) + 5. <em>This means that the y-coordinate of this coordinate will increase by 5 and x will stay the same</em>.
Hence, corresponding point for f(x) + 5 for the point (4,4) would be (4,4+5) OR (4,9).
Answer:
Jelly beans: $6 for 1 kg
Gummy worms: $7 for 1 kg
Step-by-step explanation:
In this question, we need to find the cost of 1kg of jelly beans and gummy worms.
To do this, make equations for both scenarios and solve:
2j + 2g = 26
2j + 3g = 33
Turn the bottom equation negative, as we will first solve for gummy worms (g).
2j + 2g = 26
-2j - 3g = -33
Solve:
-g = -7
Divide both sides by -1.
g = 7
We now know that gummy worms cost $7 for 1 kg
To solve for jellybeans (j), plug in 7 to g in one of the equations and solve:
2j + 2(7) = 26
2j + 14 = 26
Subtract 14 from both sides.
2j = 12
Divide both sides by 2.
j = 6
Jellybeans cost $6 for 1 kg.
Check answer by plugging in values to one of the equations:
2(6) + 2(7) = 26
12 + 14 = 26
26 = 26
Twelve and six hundred seven thousandths