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Crank
3 years ago
8

Solve the system of equation below by graphing them y= 2x-3 y=-2x+5

Mathematics
1 answer:
MatroZZZ [7]3 years ago
3 0

Answer:

Step-by-step explanation:

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Given the circle with the equation (x + 1)2 + y2 = 36, determine the location of each point with respect to the graph of the cir
kati45 [8]
\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~
\begin{cases}
\stackrel{center}{(-1,0)}\\
\stackrel{radius}{6}
\end{cases}

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}
\\\\\\
d=\sqrt{0+1}\implies d=1

well, the distance from the center to A is 1, namely is "inside the circle".

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}
\\\\\\
d=\sqrt{0+36}\implies d=6

notice, the distance to B is exactly 6, and you know what that means.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})
\\\\\\
\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}
\\\\\\
d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.
3 0
3 years ago
Read 2 more answers
3 times the sum of a number and 2
kompoz [17]

Answer:

is this actually a question

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
25 POINTS ---need an explanation
olganol [36]
I suggest you look at the work in the pictures I attached. It examplains how you work out the problem and what the answer is

7 0
3 years ago
(05.07) A square pyramid is shown. What is the surface area?
tensa zangetsu [6.8K]
The area of a pyramid is the sum of area of the base and the area of slant triangles. 
The area of the base is 1.5 × 1.5 = 2.25 cm²
The slant height of each triangle, s is 3 cm
The area of the triangles = 1/2 × 1.5 × 3 × 4
                                        = 9 cm²
Therefore, the area of the pyramid
 =9 +2.25 
= 11.25 cm²

                                         
4 0
3 years ago
Write the equation of a line that is parallel with a y = -2/3 x + 2 and goes
zhannawk [14.2K]

Answer:

y = -2/3x - 2

Step-by-step explanation:

Parallel lines have the same slope so slope = -2/3

Given (-3,0)

Slope-intercept: y = mx + b

0 = -2/3(-3) + b

0 = 2 + b

b = -2

then y = -2/3x - 2

5 0
2 years ago
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