Question 169082
I'll do the first three to get you started.



# 1


Finding the Midpoint:



{{{2+-4=-2}}} First add the x-coordinates together to get {{{-2}}}



{{{(-2)/2=-1}}} Divide that result by 2



So the x-coordinate of the midpoint is {{{x=-1}}}



{{{7+1=8}}} Now add the y-coordinates together to get {{{8}}}



{{{(8)/2=4}}} Divide that result by 2



So the y-coordinate of the midpoint is {{{y=4}}}



So the midpoint between the points *[Tex \LARGE \left(2,7\right)] and *[Tex \LARGE \left(-4,1\right)] is *[Tex \LARGE \left(-1,4\right)]



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# 2





<h4>x-intercept</h4>

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{3x - 5y = 10}}} Start with the given equation.



{{{3x - 5(0) = 10}}} Plug in {{{y=0}}}.



{{{3x - 0 = 10}}} Multiply {{{5}}} and 0 to get 0.



{{{3x - 0 = 10}}} Simplify.



{{{3x=10+0}}} Add {{{0}}} to both sides.



{{{3x=10}}} Combine like terms on the right side.



{{{x=(10)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



So the x-intercept is *[Tex \LARGE \left(\frac{10}{3},0\right)].



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<h4>y-intercept</h4>

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{3x - 5y = 10}}} Start with the given equation.



{{{3(0) - 5y = 10}}} Plug in {{{x=0}}}.



{{{0 - 5y = 10}}} Multiply {{{3}}} and 0 to get 0.



{{{ - 5y = 10}}} Simplify.



{{{y=(10)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=-2}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-2\right)].



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# 3



{{{2(x+3)>20}}} Start with the given inequality.



{{{x+3>20/2}}} Divide both sides by 2



{{{x+3>10}}} Divide.



{{{x>10-3}}} Subtract {{{3}}} from both sides.



{{{x>7}}} Combine like terms on the right side.



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Answer:


So the answer is {{{x>7}}}