Your numbers are 2, 3, 4.
The three consecutive numbers are x, x+1, x+2
The square of the first equals the third so x^2=x+2
Solve this quadratic as x^2-x-2=0
Factor into (x+1)(x-2)=0
So your answers are x=-1 and x=2
Since the question says they’re positive integers, use x=2
So the numbers are 2, 3, 4
I'm assuming that since 87% failed, that would the remaining 13% was a success. If that assumption is correct, than we simply have to take:
.13 * 13531 = 1759.03 products were successful.
Answer:
The graph of a linear equation is a straight line. The "solution" to a system of two linear equations is the point where the two lines cross. If the two lines are parallel, they never cross; hence parallel lines have no solution. Two lines are parallel if they have the same slope (the m value in y = mx+b). One of your equations is y = -2x + (you left the y-intercept out). The slope is -2. So any line with a slope of m = -2 will be parallel to this line and will not cross it. The second line also needs a different value of b, the y-intercept. Otherwise it is the same line and every point is a solution. So if your equation is:
y = -2x + 1
Then any equation of the form y = -2x + b, b≠1 will create a system with no solution. Hence the values of m and b are m = -2, b ≠ 1.
24x^2 +25x - 47 53
----------------------- = -8x -3 - ---------------
ax-2 ax-2
add 53/ax-2 to each side
24x^2 +25x - 47+53
----------------------- = -8x -3
ax-2
24x^2 +25x +6
----------------------- = -8x -3
ax-2
multiply each side by ax-2
24x^2 +25x +6 = (ax-2) (-8x-3)
multiply out the right hand side
24x^2 +25x +6 = -8ax^2 +16x-3ax +6
24 = -8a 25 = 16 -3a
a = -3 9 = -3a
a = -3
Choice B
