Answer:
(x+5/2)^2 = 0
Step-by-step explanation:
4 x^{2} +20x +25 =0
Divide by 4
4/4 x^{2} +20/4x +25/4 =0
x^2 +5x +25/4 =0
Subtract 25/4 from each side
x^2 +5x +25/4 -25/4 =-25/4
x^2 +5x =-25/4
Take the coefficent of x
5
Divide by 2
5/2
Square it
25/4
Add it to each side
x^2 +5x +25/4 =-25/4+25/4
(x+5/2)^2 = 0
Take the square root of each side
x+5/2 = 0
x = -5/2
Answer:
The height of the objects are the same after 2 seconds.
Step-by-step explanation:
In order to calculate at which time both objects have the same height we need to find the value of t that makes both equations equal. Therefore:
![-t^2 + 3t = -t + 4\\t^2 - 3t - t + 4 = 0\\t^2 - 4t + 4 = 0\\t_{1,2} = \frac{-(-4) \pm \sqrt{(-4)^2 - 4*1*4}}{2*1} = \frac{4 \pm \sqrt{16 - 16}}{2}\\t_{1,2} = \frac{4}{2} = 2](https://tex.z-dn.net/?f=-t%5E2%20%2B%203t%20%3D%20-t%20%2B%204%5C%5Ct%5E2%20-%203t%20-%20t%20%2B%204%20%3D%200%5C%5Ct%5E2%20-%204t%20%2B%204%20%3D%200%5C%5Ct_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-%28-4%29%20%5Cpm%20%5Csqrt%7B%28-4%29%5E2%20-%204%2A1%2A4%7D%7D%7B2%2A1%7D%20%3D%20%5Cfrac%7B4%20%5Cpm%20%5Csqrt%7B16%20-%2016%7D%7D%7B2%7D%5C%5Ct_%7B1%2C2%7D%20%3D%20%5Cfrac%7B4%7D%7B2%7D%20%3D%202)
The height of the objects are the same after 2 seconds.
Answer:
y=-1/3
Step-by-step explanation:
first combine like terms:
5/y-3/y=-2-4
2/y=-6
now multiply y on both sides:
2=-6y
solve the equation
y=-1/3
Answer:
Yes. It is an arithmetic sequence.
Step-by-step explanation:
The sequence would be add 5 every time.
-9 + 5 = -4
-4 + 5 = 1
1 + 5 = 6