<span>F for Frank, A or Alice.
F(initial)=1.95 inches
A(initial)=1.50 inches
Frank's equation at .25 inches per year and t representing year variable.
F=1.95+.25t
Alice's equation at .40 inches per year and t representing year variable.
A=1.5+.40t
To figure out how old they will be when their beaks are the same lengths set the equations equal to eachother as the equations are length.
1.95+.25t=1.5+.40t
.45=.15t
t=3 years</span>
48 just count the inside of the triangle which is difficult since all side aren’t a full square or count the outside border of the triangle and just multiply I did 6x8
Answer:
![\frac{1}{2} x - 4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x%20-%204)
Step-by-step explanation:
Perpendicular lines will have slopes that are the multiplicative additive inverse of each other: a line with slope 3/4 is perpendicular to a line with slope -4/3, for example. You need a line that is perpendicular to a line with slope -2 (reading that from the -2 in the -2x portion of the given equation, which is written in slope-intercept form), so your new line must have slope +1/2.
With the slope and a point, we can come up with an equation using this formula:
y - y-coordinate = slope (x - x-coordinate)
So we have y - (-2) = 1/2 (x - 4).
Simplify the equation: y + 2 = 1/2 x - 2
Subtract 2 from both sides: y + 2 - 2 = 1/2 x - 2 - 2
Simplify: y = 1/2 x - 4.
First, we are going to rewrite it as a parabola equation.
Rewrite.
![8y=-x^2+2x+47](https://tex.z-dn.net/?f=8y%3D-x%5E2%2B2x%2B47)
Divide by 8.
![y=-\frac{x^2}{8}+\frac{x}{4}+\frac{47}{8}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7Bx%5E2%7D%7B8%7D%2B%5Cfrac%7Bx%7D%7B4%7D%2B%5Cfrac%7B47%7D%7B8%7D)
Factor out coefficient.
![y=-\frac{1}{8}\left(x^2-2x\right)+\frac{47}{8}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B8%7D%5Cleft%28x%5E2-2x%5Cright%29%2B%5Cfrac%7B47%7D%7B8%7D)
Then, we are going to convert x into square form.
![y=-\frac{1}{8}\left(x^2-2x+1\right)+\frac{1}{8}\cdot \:1+\frac{47}{8}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B8%7D%5Cleft%28x%5E2-2x%2B1%5Cright%29%2B%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5C%3A1%2B%5Cfrac%7B47%7D%7B8%7D)
Convert the whole expression into square form.
![y=-\frac{1}{8}\left(x-1\right)^2+\frac{1}{8}\cdot \:1+\frac{47}{8}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B8%7D%5Cleft%28x-1%5Cright%29%5E2%2B%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%5C%3A1%2B%5Cfrac%7B47%7D%7B8%7D)
Simplify.
![y=-\frac{1}{8}\left(x-1\right)^2+6](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B8%7D%5Cleft%28x-1%5Cright%29%5E2%2B6)
Subtract 6 from both sides.
![y-6=-\frac{1}{8}\left(x-1\right)^2](https://tex.z-dn.net/?f=y-6%3D-%5Cfrac%7B1%7D%7B8%7D%5Cleft%28x-1%5Cright%29%5E2)
Divide by coefficient.
![-8\left(y-6\right)=\left(x-1\right)^2](https://tex.z-dn.net/?f=-8%5Cleft%28y-6%5Cright%29%3D%5Cleft%28x-1%5Cright%29%5E2)
Rewrite in standard form.
The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive.
Have a nice day! :)
Answer:
14.64
Step-by-step explanation:
A negative times a negative equals a positive and there are 2 decimal places.