The mass of the gold bar is = 13.896 kg.
To acheive this answer you have to multiply the area of the trapezium and the length of the bar. Hope this helped x :)
Answer:
B or A but i worked it out on a paper and its leading me towards A
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
5(x+2)=6x+3x-14
5x+10=6x+3x-14. distributive property
10+14=8x-5x. combine like term
24=3x. addition and subtraction property
24/3 = 3x/3. division property
8=x
> x = 8
Hello,
Answer B
a) Δ=8²+4*2=72
b)36-4*3*2=12
c)4²+4*1=20
d)4-4*4*1=-12
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).