Answer: D
(7, -5)
The X axis is the horizontal follow to point A than go down from there then bam answer
Answer:
20days
Step-by-step explanation:
1 bag feed : 5/2 = 2.5 days
8 bags feed : 2.5*8 = 20 days
Part A.
We could take, for example:
![\begin{cases}x\geq-3\\y\geq3\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%5Cgeq-3%5C%5Cy%5Cgeq3%5Cend%7Bcases%7D)
For x ≥ -3 we have vertical line (x-intercept = -3) and shaded region on the right side of the line.
For y ≥ 3 we have horizontal line (y-intercept = 3) and shaded region above that line.
Part B.
Simply, substitute x and y coordinates of D and E <span>to the system of inequalities from part A, and check if its is true, what we get.
</span>
![D=(-2,4)\\\\\begin{cases}x\geq-3\\y\geq3\end{cases}\quad\implies\quad\begin{cases}-2\geq-3\qquad\text{True}\\4\geq3\qquad\text{True}\end{cases}](https://tex.z-dn.net/?f=D%3D%28-2%2C4%29%5C%5C%5C%5C%5Cbegin%7Bcases%7Dx%5Cgeq-3%5C%5Cy%5Cgeq3%5Cend%7Bcases%7D%5Cquad%5Cimplies%5Cquad%5Cbegin%7Bcases%7D-2%5Cgeq-3%5Cqquad%5Ctext%7BTrue%7D%5C%5C4%5Cgeq3%5Cqquad%5Ctext%7BTrue%7D%5Cend%7Bcases%7D)
so point D is a solution,
![E=(2,4)\\\\\begin{cases}x\geq-3\\y\geq3\end{cases}\quad\implies\quad\begin{cases}2\geq-3\qquad\text{True}\\4\geq3\qquad\text{True}\end{cases}](https://tex.z-dn.net/?f=E%3D%282%2C4%29%5C%5C%5C%5C%5Cbegin%7Bcases%7Dx%5Cgeq-3%5C%5Cy%5Cgeq3%5Cend%7Bcases%7D%5Cquad%5Cimplies%5Cquad%5Cbegin%7Bcases%7D2%5Cgeq-3%5Cqquad%5Ctext%7BTrue%7D%5C%5C4%5Cgeq3%5Cqquad%5Ctext%7BTrue%7D%5Cend%7Bcases%7D)
and point E is also a solution to <span>our system of inequalities.
</span>
Part C.
There are two ways we could do that. First is the same as in part B. We substitute x and y coordinates of each school and check if inequality is true or false:
![A=(-5,5)\\\\y\ \textless \ 3x-3\quad\implies\quad5\ \textless \ 3\cdot(-5)-3\quad\implies\quad5\ \textless \ -18\quad\text{False}\\\\\\ B=(-4,-2)\\\\y\ \textless \ 3x-3\quad\implies\quad-2\ \textless \ 3\cdot(-4)-3\quad\implies\quad-2\ \textless \ -15\quad\text{False}\\\\\\ C=(2,1)\\\\y\ \textless \ 3x-3\quad\implies\quad1\ \textless \ 3\cdot2-3\quad\implies\quad1\ \textless \ 3\quad\text{True}\\\\\\ D=(-2,4)\\\\y\ \textless \ 3x-3\quad\implies\quad4\ \textless \ 3\cdot(-2)-3\quad\implies\quad4\ \textless \ -9\quad\text{False}\\\\\\ E=(2,4)\\\\y\ \textless \ 3x-3\quad\implies\quad4\ \textless \ 3\cdot2-3\quad\implies\quad4\ \textless \ 3\quad\text{False}\\\\\\](https://tex.z-dn.net/?f=A%3D%28-5%2C5%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad5%5C%20%5Ctextless%20%5C%203%5Ccdot%28-5%29-3%5Cquad%5Cimplies%5Cquad5%5C%20%5Ctextless%20%5C%20-18%5Cquad%5Ctext%7BFalse%7D%5C%5C%5C%5C%5C%5C%0AB%3D%28-4%2C-2%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad-2%5C%20%5Ctextless%20%5C%203%5Ccdot%28-4%29-3%5Cquad%5Cimplies%5Cquad-2%5C%20%5Ctextless%20%5C%20-15%5Cquad%5Ctext%7BFalse%7D%5C%5C%5C%5C%5C%5C%0AC%3D%282%2C1%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad1%5C%20%5Ctextless%20%5C%203%5Ccdot2-3%5Cquad%5Cimplies%5Cquad1%5C%20%5Ctextless%20%5C%203%5Cquad%5Ctext%7BTrue%7D%5C%5C%5C%5C%5C%5C%0AD%3D%28-2%2C4%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad4%5C%20%5Ctextless%20%5C%203%5Ccdot%28-2%29-3%5Cquad%5Cimplies%5Cquad4%5C%20%5Ctextless%20%5C%20-9%5Cquad%5Ctext%7BFalse%7D%5C%5C%5C%5C%5C%5C%0AE%3D%282%2C4%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad4%5C%20%5Ctextless%20%5C%203%5Ccdot2-3%5Cquad%5Cimplies%5Cquad4%5C%20%5Ctextless%20%5C%203%5Cquad%5Ctext%7BFalse%7D%5C%5C%5C%5C%5C%5C)
![F=(3,-4)\\\\y\ \textless \ 3x-3\quad\implies\quad-4\ \textless \ 3\cdot3-3\quad\implies\quad-4\ \textless \ 6\quad\text{True}\\\\\\](https://tex.z-dn.net/?f=F%3D%283%2C-4%29%5C%5C%5C%5Cy%5C%20%5Ctextless%20%5C%203x-3%5Cquad%5Cimplies%5Cquad-4%5C%20%5Ctextless%20%5C%203%5Ccdot3-3%5Cquad%5Cimplies%5Cquad-4%5C%20%5Ctextless%20%5C%206%5Cquad%5Ctext%7BTrue%7D%5C%5C%5C%5C%5C%5C)
So Timothy can attend schools C and F.
We can also draw a graph of that inequality (pic 2).
Erica will take 4.5 minutes to run from home to school
<h3><u>Solution:</u></h3>
Given that , Arica can run
of a kilometer in a minute
Her school is
th of a kilometer away from her home
We have to find at this speed how long will it take Erica to run from home to school
<em><u>The relation between speed distance and time is given as:</u></em>
![\text { Distance }=\text { speed } \times \text { time }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Distance%20%7D%3D%5Ctext%20%7B%20speed%20%7D%20%5Ctimes%20%5Ctext%20%7B%20time%20%7D)
Plugging in values, we get
![\frac{3}{4}=\frac{1}{6} \times \text { time taken }](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B6%7D%20%5Ctimes%20%5Ctext%20%7B%20time%20taken%20%7D)
![\begin{array}{l}{\text { Time taken to reach school }=\frac{3}{4} \times 6} \\\\ {\text { Time taken to reach home }=\frac{3}{2} \times 3} \\\\ {\text { Time taken to reach home }=\frac{9}{2}=4.5}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Ctext%20%7B%20Time%20taken%20to%20reach%20school%20%7D%3D%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%206%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Time%20taken%20to%20reach%20home%20%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%203%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Time%20taken%20to%20reach%20home%20%7D%3D%5Cfrac%7B9%7D%7B2%7D%3D4.5%7D%5Cend%7Barray%7D)
Hence, she takes 4.5 minutes to reach school from her home
<u>Find amount spent on magazines:</u>
1 magazine = $3.95
3 magazines = $3.95 x 3 = $11.85
<u>Find amount spent on books:</u>
Amount spent on books = $47.65 - $11.85 = $35.80
<u>Find number of books:</u>
Number of books = $35.80 ÷ $8.95 = 4
Answer: Huge bought 4 books