Question 1:
For this case we must factor the following expression:
[tex]n ^ 2 + 2n-24 = 0[/tex]
We must find two numbers that when multiplied result in -24 and when added together result in 2. These numbers are: 6 and -4.
[tex]6*(-4)=-24\\6-4=2[/tex]
Thus, we factor:
[tex](x + 6) (x-4) = 0[/tex]
The roots are:
[tex]x_ {1} = - 6\\x_ {2} = 4[/tex]
Answer:
Option C
Question 2:
For this case we have that by definition, the area of a rectangle is given by:
[tex]A = w * l[/tex]
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
According to the statement we have:
[tex]A = 30 \ ft ^ 2\\l = 3w-1[/tex]
Substituting:
[tex](3w-1) w = 30\\3w ^ 2-w = 30\\3w ^ 2-w-30 = 0[/tex]
Where:
[tex]a = 3\\b = -1\\c = -30[/tex]
The solution:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}\\x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (3) (- 30)}} {2 (3)}\\x = \frac {1 \pm \sqrt {1 + 360}} {2 (3)}\\x = \frac {1 \pm \sqrt {361}} {6}\\x = \frac {1\pm19} {6}\\[/tex]
We have two roots:
[tex]x_ {1} = \frac {1-19} {6} = \frac {-18} {6} = - 3\\x_ {2} = \frac {1 + 19} {6} =\frac {20} {6} = 3,333[/tex]
We choose the second value (the positive), when rounding is [tex]3.33 \ ft[/tex]
Answer:
Option A
