Answer:
The answer would be 12
Step-by-step explanation:
Answer:
The coordinates of the focus of the parabola is:
![\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)](https://tex.z-dn.net/?f=%5Ctext%7BFocus%7D%3D%28%5Cdfrac%7B3%7D%7B28%7D%2C%5Cdfrac%7B125%7D%7B7%7D%29%3D%280.10714%2C17.8571%29)
Step-by-step explanation:
We know that for any general equation of the parabola of the type:
![(x-h)^2=4p(y-k)](https://tex.z-dn.net/?f=%28x-h%29%5E2%3D4p%28y-k%29)
The focus of the parabola is given by:
Focus= (h,k+p)
Here we are given a equation of the parabola as:
![y=14x^2-3x+18](https://tex.z-dn.net/?f=y%3D14x%5E2-3x%2B18)
On changing the equation to general form as follows:
![y=14(x^2-\dfrac{3}{14}x)+18\\\\\\y=14((x-\dfrac{3}{28})^2-(\dfrac{3}{28})^2)+18\\\\y=14(x-\dfrac{3}{28})^2-\dfrac{9}{56}+18\\\\\\y=14(x-\dfrac{3}{28})^2+\dfrac{999}{56}\\\\y-\dfrac{999}{56}=14(x-\dfrac{3}{28})^2\\\\(x-\dfrac{3}{28})^2=\dfrac{1}{14}(y-\dfrac{999}{56})\\\\(x-\dfrac{3}{28})^2=4\times \dfrac{1}{56}(y-\dfrac{999}{56})](https://tex.z-dn.net/?f=y%3D14%28x%5E2-%5Cdfrac%7B3%7D%7B14%7Dx%29%2B18%5C%5C%5C%5C%5C%5Cy%3D14%28%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2-%28%5Cdfrac%7B3%7D%7B28%7D%29%5E2%29%2B18%5C%5C%5C%5Cy%3D14%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2-%5Cdfrac%7B9%7D%7B56%7D%2B18%5C%5C%5C%5C%5C%5Cy%3D14%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2%2B%5Cdfrac%7B999%7D%7B56%7D%5C%5C%5C%5Cy-%5Cdfrac%7B999%7D%7B56%7D%3D14%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2%5C%5C%5C%5C%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2%3D%5Cdfrac%7B1%7D%7B14%7D%28y-%5Cdfrac%7B999%7D%7B56%7D%29%5C%5C%5C%5C%28x-%5Cdfrac%7B3%7D%7B28%7D%29%5E2%3D4%5Ctimes%20%5Cdfrac%7B1%7D%7B56%7D%28y-%5Cdfrac%7B999%7D%7B56%7D%29)
Hence, we have:
![h=\dfrac{3}{28}\ ,\ k=\dfrac{999}{56}\ ,\ p=\dfrac{1}{56}](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B3%7D%7B28%7D%5C%20%2C%5C%20k%3D%5Cdfrac%7B999%7D%7B56%7D%5C%20%2C%5C%20p%3D%5Cdfrac%7B1%7D%7B56%7D)
Hence,
![k+p=\dfrac{1000}{56}=\dfrac{125}{7}](https://tex.z-dn.net/?f=k%2Bp%3D%5Cdfrac%7B1000%7D%7B56%7D%3D%5Cdfrac%7B125%7D%7B7%7D)
Hence, focus is:
![\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)](https://tex.z-dn.net/?f=%5Ctext%7BFocus%7D%3D%28%5Cdfrac%7B3%7D%7B28%7D%2C%5Cdfrac%7B125%7D%7B7%7D%29%3D%280.10714%2C17.8571%29)
Answer:
19
Step-by-step explanation:
Let the number be 'x'
Given:
The value of 'x' is defined as the quotient of 6 raised to the power of 3 and 9, decrease by 5.
The quotient of
and 9 is given as:
![Q=\frac{6^3}{9}\\Q=\frac{6\times 6\times 6}{9}\\Q=\frac{216}{9}=24](https://tex.z-dn.net/?f=Q%3D%5Cfrac%7B6%5E3%7D%7B9%7D%5C%5CQ%3D%5Cfrac%7B6%5Ctimes%206%5Ctimes%206%7D%7B9%7D%5C%5CQ%3D%5Cfrac%7B216%7D%7B9%7D%3D24)
Now, the quotient is decreased by 5. So, the number 'x' is:
![x=Q-5](https://tex.z-dn.net/?f=x%3DQ-5)
Plug in 24 for 'Q' and solve for 'x'. This gives,
![x=24-5\\x=19](https://tex.z-dn.net/?f=x%3D24-5%5C%5Cx%3D19)
Therefore, the number defined by the statement "<u><em>the quotient of 6 raised to the power of 3 and 9, decrease by 5</em></u>" is 19.
Answer:
-3(3z+91)
Step-by-step explanation:
Hope this helps :)
−12(7z+4)+15(5z−15)
= -3(4(7z+4)-5(5z-15)
= -3(28z+16-25z+75)
= -3(3z+91)
Answer:
3 refers how many tiles in a row
Step-by-step explanation: