For # 3 and 5 you need to use the quadratic formula:
<span>(-b +/- srt(b^2 - 4ac))/2a </span>
<span>a, b, and c are representative of this formula: ax^2 +bx + c </span>
<span>1) 2x^2+3x-9=0 </span>
<span>(2x - 3)(x + 3) = 0 </span>
<span>2x - 3 = 0, x + 3 = 0 </span>
<span>+3 +3, -3 -3 </span>
<span>2x = 3, ***x = -3*** </span>
<span>/2 /2 </span>
<span>***x = 3/2*** </span>
<span>2) 5x^2+2x=0 </span>
<span>(x)(5x + 2) = 0 </span>
<span>5x +2 = 0, ***x = 0*** </span>
<span>-2 -2 </span>
<span>5x = -2 </span>
<span>/5 /5 </span>
<span>***x = -2/5*** </span>
<span>4) 4x^2+7x-2=0 </span>
<span>(4x - 1)(x + 2) = 0 </span>
<span>4x - 1 = 0, x + 2 = 0 </span>
<span>+1 +1, -2 -2 </span>
<span>4x = 1, ***x = -2*** </span>
<span>/4 /4 </span>
<span>***x = 1/4***</span>
Correct! This one is 'none' because the lines are parallel. Also, they have the same slope and y-intercept, but they differ after the equal sign, which means that their would be NO solutions to this.
Answer: None
For a better understanding of the solution provided here please find the diagram attached.
Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.
Thus, if, for example, the end coordinates of a line segment are 
and 
then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be:
Thus for our question the endpoints are 
and 
and hence the midpoint will be:
Thus, Option C is the correct option.
So the left side has a common denominator of 3. The 6x, -2x, and 8 can all go over a single 3. (6x-2x+8/3). Simplify the x's to get 4x. Now both sides have to be multiplied by 3 to get rid of that fraction. Then you just have 4x+8=24. Subtract 8 from both sides to get the x's alone, then divide both sides by 4 to get x alone. I have a picture to help.
