Straight

Hi Guest,

   hi asinus,

Maybe he is just meaning that:

$\sqrt[3]{6x}-12+4=12$

Then would be the solution:

$\approx {\frac{4000}{3}} \mbox { (wolframalpha)}$

Straight

Hello Guest,

x = 1/12

Hello Guest,

 ...

I got a solution, here is it:

$\sqrt{5x}-5+5=6$

$x = \frac{36}{5}=7\frac{1}{5}=7.2$

Straight

Hello Guest,

D) is correct. Here is why:

$16\%= 16:100=4:25$

$100\%-16\%=84\%$

$84\%=84:100=21:25$

Which represents the ratio of books that have never been checked out to the total number of books in the libary?

Straight

Hello Guest,

$\frac{5}{4}k-\frac{3}{4}+\frac{1}{2}k=-\frac{1}{4}k-\frac{1}{2}$

$\mbox {Now multiply both sides by 4}$

$5k-3+2k=-k-2$

$7k-3=-k-2$

$7k-3+k=-2$

$7k+k=-2+3$

$8k=-2+3$

$8k=1$

$k=\frac{1}{8}=0.125$

Easy!

Hello Guest,

$(x,y)=(0,0)$ AND

$(x,y)=(245,49)$

Hello Guest,

so that's an easy question:

$3.5x-5.7=2.5x+4.1$

$3.5x-5.7-2.5x=4.1$

$3.5x-2.5x=4.1+5.7$

$x=4.1+5.7$

$x=9.8=\frac{49}{5}=9\frac{4}{5}$

Easy!

Hello Guest,

$r=\sqrt{\frac{45}{4}}$

center: $(\frac{1}{2},-1)$

Hello Guest,

$x^2+y^2=2-x-6y+6-18x+2y$

$\mbox {Move the variables to the left side and change their signs}$

$x^2+y^2-2x+6y+18x-2y=6$

$x^2+y^2+16x+6y-2y=6$

$x^2+y^2+16x+4y=6$

$\mbox {Use the commutative property to reorder the terms}$

$x^2+16x+y^2+4y=6$

$\mbox {To complete the square, the same value needs to be added to both sides}$

$x^2+16x+?+y^2+4y=6+?$

$\mbox {To complete the square } x^2+16x+64=(x+8)^2 \mbox { add 64 to the expression}$

$x^2+16x+64+y^2+4y=6+?$

$\mbox {Since 64 was added to the left side, also add 64 to the right side}$

$x^2+16x+64+y^2+4y=6+64$

$\mbox {Use the first binomial } a^2+2ab+b^2=(a+b)^2 \mbox { to factor the expression}$

$(x+8)^2+y^2+4y=6+64$

$(x+8)^2+y^2+4y=70$

$\mbox {To complete the square, the same value needs to be added to both sides}$

$(x+8)^2+y^2+4y+?=70+?$

$\mbox {To complete the square } y^2+4y+4=(y+2)^2 \mbox { add 4 to the expression}$

$(x+8)+y^2+4y+4=70+?$

$\mbox {Since 4 was added to the left side, also add 4 to the right side}$

$(x+8)+y^2+4y+4=70+4$

$\mbox {Use the first binomial } a^2+2ab+b^2=(a+b)^2 \mbox { to factor the expression}$

$(x+8)^2+(y+2)^2=70+4$

$(x+8)^2+(y+2)^2=74$

$\mbox {The equation can be written in the form } (x-p)^2+(y-q)^2=r^2 \mbox { , so it represents a circle with the radius } r=\sqrt{74} \mbox { and the center } (-8,-2)$

Hello Guest,

$x^2+y^2=4x-12y+8$

$x^2+y^2-4x+12y=8$

$x^2-4x+y^2+12y=8$

$x^2-4x+?+y^2+12y=8+?$

$\mbox {To complete the square } {x}^{2}-4x+4=(x-2)^2 \mbox { add four}$

$x^2-4x+4+y^2+12y=8+4$

$\mbox {Use } a^2-2ab+b^2=(a-b)^2 \mbox { to factor the expression}$

$(x-2)^2+y^2+12y=8+4$

$(x-2)^2+y^2+12y=12$

$\mbox {To complete the square, the same value needs to be added to both sides}$

$(x-2)^2+y^2+12y+?=12+?$

$\mbox {To complete the square } y^2+12y+36=(y+6)^2 \mbox { add 36 to the expression}$

$(x-2)^2+y^2+12y+36=12+?$

$\mbox {Since 36 was added to the left side, also add 36 to the right side}$

$(x-2)^2+y^2+12y+36=12+36$

$\mbox {Use the first binomial } a^2+2ab+b^2=(a+b)^2 \mbox { to factor the expression}$

$(x-2)^2+(y+6)^2=12+36$

$(x-2)^2+(y+6)^2=48$

$\mbox {The equation can be written in the form } (x-p)^2+(y-q)^2=r^2 \mbox { , so it represents a circle with the radius } r=\sqrt{48} \mbox { and the center } (2,-6)$