2(x-3)=7x-31
2x-6=7x-31
-7x -7x
----------------
-5x-6=-31
+6 +6
--------------
-5x=-25
Divide by -5
x=5

3x-2(x+5)=-3+18
15
3x-2(x+5)=15
3x-2x-10=15
x-10=15
+10 +10
--------------
x=25

3 0

3 years ago

Find k so that the distance from (–1, 1) to (2, k) is 5 units. k= k= *there are two solutions for 2*

dalvyx [7]

Answer:

k = -3

k =5

Step-by-step explanation:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\$

$5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\$

$\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3$

7 0

3 years ago

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