Question 1:
For this case we must solve the following expression:
[tex]\frac {k} {3} + 4-2k = -9k[/tex]
Adding 9k to both sides of the equation we have:
[tex]\frac {k} {3} + 4-2k + 9k = -9k + 9k\\\frac {k} {3} + 4 + 7k = 0[/tex]
Subtracting 4 from both sides of the equation:
[tex]\frac {k} {3} + 4-4 + 7k = -4\\\frac {k} {3} + 7k = -4\\\frac {k + 21k} {3} = - 4\\\frac {22k} {3} = - 4\\[/tex]
Multiplying by 3 on both sides:
[tex]22k = -12[/tex]
Dividing between 22 on both sides:
[tex]k = \frac {-12} {22}\\k = - \frac {6} {11}[/tex]
Answer:
[tex]k = - \frac {6} {11}[/tex]
Question 2:
For this case we have that by definition, the area of the rectangle is given by:
[tex]A = a * b[/tex]
Where a and b are the sides of the rectangle.
If the area is at least[tex]246ft ^ 2[/tex] we have:
[tex]A \geq246[/tex]
That is to say:
[tex]8 (2x + 4) \geq246\\16x + 32 \geq246\\16x \geq246-32\\16x \geq214\\x \geq \frac {214} {16}\\x \geq13.375[/tex]
Answer:
[tex]x \geq13.375[/tex]
