Answer:
8x !
Step-by-step explanation:
Answer:
245.1361868
Step-by-step explanation:
126 51.4
___ = ____ 126x100=12600 12600/51.4=245.1361868
x 100
Answer:
2.0 seconds
Step-by-step explanation:
<u>Given quadratic functions</u>:
![\begin{cases}y=-7x^2+26x+3\\y=-6x^2 +23x+5\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3D-7x%5E2%2B26x%2B3%5C%5Cy%3D-6x%5E2%20%2B23x%2B5%5Cend%7Bcases%7D)
To find the time, in seconds, that the balloons collided at the highest point, <u>substitute</u> one equation into the other equation and rearrange to <u>equal zero</u>:
![\begin{aligned}-6x^2+23x+5 & = -7x^2+26x+3\\-6x^2+23x+5+7x^2 & = -7x^2+26x+3+7x^2\\x^2+23x+5 & = 26x+3\\x^2+23x+5-26x & = 26x+3-26x\\x^2-3x+5& = 3\\x^2-3x+5-3& = 3-3\\x^2-3x+2& = 0\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-6x%5E2%2B23x%2B5%20%26%20%3D%20-7x%5E2%2B26x%2B3%5C%5C-6x%5E2%2B23x%2B5%2B7x%5E2%20%26%20%3D%20-7x%5E2%2B26x%2B3%2B7x%5E2%5C%5Cx%5E2%2B23x%2B5%20%26%20%3D%2026x%2B3%5C%5Cx%5E2%2B23x%2B5-26x%20%26%20%3D%2026x%2B3-26x%5C%5Cx%5E2-3x%2B5%26%20%3D%203%5C%5Cx%5E2-3x%2B5-3%26%20%3D%203-3%5C%5Cx%5E2-3x%2B2%26%20%3D%200%5Cend%7Baligned%7D)
<u>Factor</u> the quadratic:
![\begin{aligned}x^2-3x+2 & = 0\\x^2-2x-x+2 & = 0\\x(x-2)-1(x-2) & = 0\\(x-1)(x-2) & = 0\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx%5E2-3x%2B2%20%26%20%3D%200%5C%5Cx%5E2-2x-x%2B2%20%26%20%3D%200%5C%5Cx%28x-2%29-1%28x-2%29%20%26%20%3D%200%5C%5C%28x-1%29%28x-2%29%20%26%20%3D%200%5C%5C%5Cend%7Baligned%7D)
Apply the <u>zero-product property</u> to solve for x:
![\implies (x-1)=0 \implies x=1](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%3D0%20%5Cimplies%20x%3D1)
![\implies (x-2)=0 \implies x=2](https://tex.z-dn.net/?f=%5Cimplies%20%28x-2%29%3D0%20%5Cimplies%20x%3D2)
Therefore, the balloons collided at 1 second and 2 seconds.
To find at which time the highest point of collision occured, substitute both values of x into one of the functions:
![f(1)=-6(1)^2 +23(1)+5=22](https://tex.z-dn.net/?f=f%281%29%3D-6%281%29%5E2%20%2B23%281%29%2B5%3D22)
![f(2)=-6(2)^2 +23(2)+5=27](https://tex.z-dn.net/?f=f%282%29%3D-6%282%29%5E2%20%2B23%282%29%2B5%3D27)
Therefore, the time, in seconds, that the balloons collided at the highest point is 2.0 seconds.
Learn more about quadratic systems of equations here:
brainly.com/question/27930827
Answer:
186.3
To find the answer you have to do inverse operations
9×20.7=186.3
186.3÷20.7=9