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3 years ago

10. What is the distance between (8,7) and (3,-5)?

Mathematics

1 answer:

Anarel [89]3 years ago

8 0

Answer:

distance between points=13 units

Step-by-step explanation:

distance between points= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

put $(x_1,x_2)$ =(8,7) and $(y_1,y_2)$ =(3,-5)

distance between points= $\sqrt{(3-8)^2+(-5-7)^2}$

distance between points= $\sqrt{(-5)^2+(-12)^2}$

distance between points= $\sqrt{25+144}$

distance between points= $\sqrt{169}$

distance between points=13 units answer

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Part A.

We could take, for example:

$\begin{cases}x\geq-3\\y\geq3\end{cases}$

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 to the system of inequalities from part A, and check if its is true, what we get.

$D=(-2,4)\\\\\begin{cases}x\geq-3\\y\geq3\end{cases}\quad\implies\quad\begin{cases}-2\geq-3\qquad\text{True}\\4\geq3\qquad\text{True}\end{cases}$

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and point E is also a solution to our system of inequalities.

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}\\\\\\
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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}\\\\\\
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So Timothy can attend schools C and F.

We can also draw a graph of that inequality (pic 2).

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