Answer:
Proved
Step-by-step explanation:
Given
![B =(-2,-1)](https://tex.z-dn.net/?f=B%20%3D%28-2%2C-1%29)
![U = (0,3)](https://tex.z-dn.net/?f=U%20%3D%20%280%2C3%29)
![G = (3,2)](https://tex.z-dn.net/?f=G%20%3D%20%283%2C2%29)
![S = (4,-3)](https://tex.z-dn.net/?f=S%20%3D%20%284%2C-3%29)
Required
Prove BUGS is a trapezoid
Given the coordinates, to prove a trapezoid; all we need to do is to check if one pair of sides is parallel.
<u></u>
<u>Taking BU and GS as a pair</u>
First, we calculate the slope using:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
For BU
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{3 - -1}{0- -2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%20-%20-1%7D%7B0-%20-2%7D)
![m = \frac{4}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%7D%7B2%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
For GS
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{-3-2}{4-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3-2%7D%7B4-3%7D)
![m = \frac{-5}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-5%7D%7B1%7D)
![m = -5](https://tex.z-dn.net/?f=m%20%3D%20-5)
<em>The slope of BU and GS are not the same; hence, they are not parallel.</em>
<u>Taking BS and GU as a pair</u>
Calculate the slope
For BS
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{-3 - -1}{4- -2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-3%20-%20-1%7D%7B4-%20-2%7D)
![m = \frac{-2}{6}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-2%7D%7B6%7D)
![m = -\frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
For GU
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So, we have:
![m = \frac{3-2}{0-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3-2%7D%7B0-3%7D)
![m = \frac{1}{-3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B1%7D%7B-3%7D)
![m = -\frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
The slope of BS and GU are the same; hence, they are parallel.
<em>BUGS is a trapezoid because BS and GU have the same slope</em>
2 is the square root of 4
Easily putting the equation into Google, I found a graph for you! :)
Answer:
a)
and ![c=\frac{-1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B-1-%5Csqrt%7B13%7D%7D%7B2%7D)
Step-by-step explanation:
The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:
![3-x^{2}=x](https://tex.z-dn.net/?f=3-x%5E%7B2%7D%3Dx)
and then solve for x. We move everything to one side of the equation so we get:
![x^{2}+x-3=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2Bx-3%3D0)
and we use the quadratic formula:
![x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
and we substitute:
![x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B%281%29%5E2-4%281%29%28-3%29%7D%7D%7B2%281%29%7D)
and solve
![x=\frac{-1\pm \sqrt{1+12}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%2B12%7D%7D%7B2%7D)
![x=\frac{-1\pm \sqrt{13}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B13%7D%7D%7B2%7D)
so our two answers are:
a)
and ![c=\frac{-1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B-1-%5Csqrt%7B13%7D%7D%7B2%7D)
Answer:
250 Cookies
Step-by-step explanation:
First calculate the cookies decorated per hour
100 ÷ 2 = 50 cookies per hour
Number of cookies in 5 hours = 50 × 5
= 250 Cookies