Does a hexagon contain rays
1 answer:
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Answer:
(3, 1)
Step-by-step explanation:
(a) Algebraic solution
(1) y = -⅔x + 3
(2) y = 2x - 5
Set Equation (1) equal to Equation (2)
-⅔x + 3 = 2x - 5
Multiply each side by 3
-2x + 9 = 6x - 15
Add 15 to each side
-2x + 24 = 6x
Add 2x to each side
24 = 8x
Divide each side by 3
(3) x = 3
Substitute (3) into (2)
y = 2×3 - 5 = 6 - 5 = 1
The ordered pair that makes both equations true is (3, 1).
(b) Graphical solution
In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).
Distance between points 
and 
is
Distance from H to B:
![[tex]d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}](https://tex.z-dn.net/?f=%5Btex%5Dd%3D%5Csqrt%7B%2810-%28-3%29%29%5E2%2B%281-%28-9%29%29%5E2%7D%3D%5Csqrt%7B169%2B100%7D%3D%5Csqrt%7B269%7D)
d=\sqrt{(1-(-3))^2+(10-(-9))^2}=\sqrt{16+361}=\sqrt{376}[/tex] units.
Distance from Z to B:
units.
Horse Z is closer to the barn.
(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)
Distance from H to B:
Distance from Z to B:
Horse Z is closer to the barn.
(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)