Answer:
33.89
Step-by-step explanation:
How to Calculate Rounding to the Nearest 100th?
If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit. Example
124.586
The third digit of right of decimal point is 6
The second digit after decimal point is 8 which is greater than 5
So add 1 to 8
Result = 124.59
Answer:
we know that,
y-y1=m(x-x1)
or, y-1=-3(x-5)
or, y-1=15-3x
or 3x+y-16=0 is the required equation
Answer:
yes
Step-by-step explanation:
Answer: ![-4,-15;\ \left(-\dfrac{19}{2},-\dfrac{121}{4}\right)](https://tex.z-dn.net/?f=-4%2C-15%3B%5C%20%5Cleft%28-%5Cdfrac%7B19%7D%7B2%7D%2C-%5Cdfrac%7B121%7D%7B4%7D%5Cright%29)
Step-by-step explanation:
Given
Function is ![F(t)=t^2+19+60](https://tex.z-dn.net/?f=F%28t%29%3Dt%5E2%2B19%2B60)
Zeroes of the function are
![t^2+19t+60=0\\\\\Rightarrow t=\dfrac{-19\pm\sqrt{19^2-4\times 1\times 60}}{2\times 1}\\\\\Rightarrow t=\dfrac{-19\pm \sqrt{121}}{2}\\\\\Rightarrow t=\dfrac{-19\pm 11}{2}\\\\\Rightarrow t=-4,-15](https://tex.z-dn.net/?f=t%5E2%2B19t%2B60%3D0%5C%5C%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7B-19%5Cpm%5Csqrt%7B19%5E2-4%5Ctimes%201%5Ctimes%2060%7D%7D%7B2%5Ctimes%201%7D%5C%5C%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7B-19%5Cpm%20%5Csqrt%7B121%7D%7D%7B2%7D%5C%5C%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7B-19%5Cpm%2011%7D%7B2%7D%5C%5C%5C%5C%5CRightarrow%20t%3D-4%2C-15)
Using completing the square method
![y=t^2+2\times \dfrac{19}{2}t+\dfrac{19^2}{2^2}-\dfrac{19^2}{2^2}+60\\\\y=\left(t+\dfrac{19}{2}\right)^2+60-\dfrac{361}{4}\\\\y=\left(t+\dfrac{19}{2}\right)^2-\dfrac{121}{4}\\\\y+\dfrac{121}{4}=\left(t+\dfrac{19}{2}\right)^2\\\\\left(y-(-\dfrac{121}{4}\right)=\left(t-(-\dfrac{19}{2})\right)^2\\\\\text{The vertex is }\left(-\dfrac{19}{2},-\dfrac{121}{4}\right)](https://tex.z-dn.net/?f=y%3Dt%5E2%2B2%5Ctimes%20%5Cdfrac%7B19%7D%7B2%7Dt%2B%5Cdfrac%7B19%5E2%7D%7B2%5E2%7D-%5Cdfrac%7B19%5E2%7D%7B2%5E2%7D%2B60%5C%5C%5C%5Cy%3D%5Cleft%28t%2B%5Cdfrac%7B19%7D%7B2%7D%5Cright%29%5E2%2B60-%5Cdfrac%7B361%7D%7B4%7D%5C%5C%5C%5Cy%3D%5Cleft%28t%2B%5Cdfrac%7B19%7D%7B2%7D%5Cright%29%5E2-%5Cdfrac%7B121%7D%7B4%7D%5C%5C%5C%5Cy%2B%5Cdfrac%7B121%7D%7B4%7D%3D%5Cleft%28t%2B%5Cdfrac%7B19%7D%7B2%7D%5Cright%29%5E2%5C%5C%5C%5C%5Cleft%28y-%28-%5Cdfrac%7B121%7D%7B4%7D%5Cright%29%3D%5Cleft%28t-%28-%5Cdfrac%7B19%7D%7B2%7D%29%5Cright%29%5E2%5C%5C%5C%5C%5Ctext%7BThe%20vertex%20is%20%7D%5Cleft%28-%5Cdfrac%7B19%7D%7B2%7D%2C-%5Cdfrac%7B121%7D%7B4%7D%5Cright%29)