Question 684406: I want to first say, thank you for your service, and that this is not homeowrk for me but a study review for an exam so your help would be amazing so I can prepare well for it.
Find the distance PQ and the coordinates of the midpoint for the following ordered pairs.
1) p(-3,9), Q(2,7)
2)p(2x,-4x), Q(4x,2x^2)
Find the x-intercept and y-intercept for each line. use the intercepts to graph the equations
3) x/2+y/3=1
4)4x-5y=20
Graph the linear inequality
5)2x-y less then and equal to 1
6)x/2+y/4>1
7) x<2y
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the distance PQ and the coordinates of the midpoint for the following ordered pairs.
1) p(-3,9), Q(2,7)
d = sqrt[(9-7)^2+(2--3)^2] = sqrt[4+25] = sqrt(29)
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2)p(2x,-4x), Q(4x,2x^2)
d = sqrt[(2x^2-2x)^2 + (4x--4x)^2] = sqrt[4x^4-8x^3+4x^2+64x^2]
= sqrt[4x^4-8x^3+68x^2]
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Find the x-intercept and y-intercept for each line. use the intercepts to graph the equations
3) x/2+y/3=1
x-intercept: Let y = 0, then x = 2
y-intercept: Let x = 0, then y = 3
-----
Graph the line that passes thru (0,3) and (2,0)
-----------------------------------------
4)4x-5y=20
x-intercept: Let y = 0, then x = 5
y-intercept: Let x = 0, then y = -4
----
Graph the line that passes thru (0,-4) and (5,0)
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Graph the linear inequality
5)2x-y less then and equal to 1
Graph the boundary y = 2x-1
Shade the half-plane above that boundary.
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6)x/2+y/4>1
y/4 > (-x/2)+1
y > -2x+4
Graph the boundary y = -2x+4 as a dashed line.
Shade the half-plane above that boundary.
--------------------------------
7) x<2y
y > (1/2)x
----
Draw the boudary y = (1/2)x as a dashed line.
Shade the half-plane above the boundary.
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Cheers,
Stan H.
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