Answer:
x=16
Step-by-step explanation:
We are given that
![\sqrtx+11=15](https://tex.z-dn.net/?f=%5Csqrtx%2B11%3D15)
we have to solve this equation for x
in order to do that we need to isolate x first
hence
subtracting 11 from both sides we get
![\sqrtx+11-11=15-11](https://tex.z-dn.net/?f=%5Csqrtx%2B11-11%3D15-11)
![\sqrtx=4](https://tex.z-dn.net/?f=%5Csqrtx%3D4)
Now we square on both sides we get
![(\sqrtx)^2=4^2](https://tex.z-dn.net/?f=%28%5Csqrtx%29%5E2%3D4%5E2)
![x=4 \times 4](https://tex.z-dn.net/?f=x%3D4%20%5Ctimes%204)
![x=16](https://tex.z-dn.net/?f=x%3D16)
hence x =16
Answer:
6 ft
Step-by-step explanation:
Given that:
Length of rectangular banner = 18 ft
Total trim of banner available = 48 ft
To find:
Possible widths of the banner = ?
Solution:
Maximum trim available of the banner around the entire border of the banner = 48 ft
i.e. we are given the total perimeter of the rectangular banner.
Formula for perimeter of a rectangle is given as:
![Perimeter = 2 \times (Length + Width)](https://tex.z-dn.net/?f=Perimeter%20%3D%202%20%5Ctimes%20%28Length%20%2B%20Width%29)
Putting the values of perimeter and length to find the value of width.
![48 = 2 \times (18 + Width)\\\Rightarrow 48 =36+2 \times Width\\\Rightarrow 2 \times Width = 48-36\\\Rightarrow 2 \times Width = 12\\\Rightarrow \bold{Width = 6\ ft}](https://tex.z-dn.net/?f=48%20%3D%202%20%5Ctimes%20%2818%20%2B%20Width%29%5C%5C%5CRightarrow%2048%20%3D36%2B2%20%5Ctimes%20Width%5C%5C%5CRightarrow%202%20%5Ctimes%20Width%20%3D%2048-36%5C%5C%5CRightarrow%202%20%5Ctimes%20Width%20%3D%2012%5C%5C%5CRightarrow%20%5Cbold%7BWidth%20%3D%206%5C%20ft%7D)
So, width possible is <em>6ft.</em>
Answer:
A function to represent the height of the ball in terms of its distance from the player's hands is ![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
Step-by-step explanation:
General equation of parabola in vertex form ![y= a(x-h)^2+k](https://tex.z-dn.net/?f=y%3D%20a%28x-h%29%5E2%2Bk)
y represents the height
x represents horizontal distance
(h,k) is the coordinates of vertex of parabola
We are given that The ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.
So,(h,k)=(18,12)
Substitute the value in equation
---1
The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0
So, y = 6
So,![6=a(0-18)^2+12](https://tex.z-dn.net/?f=6%3Da%280-18%29%5E2%2B12)
6=324a+12
-6=324a
![\frac{-6}{324}=a](https://tex.z-dn.net/?f=%5Cfrac%7B-6%7D%7B324%7D%3Da)
![\frac{-1}{54}=a](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B54%7D%3Da)
Substitute the value in 1
So,![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
Hence a function to represent the height of the ball in terms of its distance from the player's hands is ![y=\frac{-1}{54}(x-18)^2+12](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B54%7D%28x-18%29%5E2%2B12)
The correct answer for the question that is being presented above is this one: "C) 1.6." Hank is painting his grandfather's fence. He painted 40 linear feet in 85 minutes. He still has 360 linear feet to paint. His cousins, Sam and Alex, come <span>to help. Sam paints twice as fast and Alex paints half as fast as Hank. The constant of proportionality that relates the current fence painting rate is 1.6.</span>