A rectangle has a perimeter of 20 cm . One side of the rectangle measures \( x \mathrm{~cm} \), while the other side is 2 cm shorter than the first side. Determine the lengths of both sides. Longest side \( =\square \mathrm{cm} \) and the shortest side \( =\square \mathrm{cm} \).

Consider the line \( y=\frac{5}{2} x-3 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (2,-5) \). Find the equation of the line that is parallel to this line and passes through the point (2, -5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line:

Use the properties of logarithms to rewrite the expression. Simplify the res \( \log _{3} \frac{\sqrt{x} \sqrt[3]{y}}{w} \sqrt{z} \) Choose the correct answer. A. \( -\frac{1}{2} \log _{3} x-\frac{1}{3} \log _{3} y+5 \log _{3} w+\frac{1}{2} \log _{3} z \) B. \( \frac{1}{2} \log _{3} x+\frac{1}{3} \log _{3} y-5 \log _{3} w-\frac{1}{2} \log _{3} z \) C. \( { }^{2} \log _{3} x+3 \log _{3} y-5 \log _{3} w-2 \log _{3} z \) D. This cannot be simplified.

Your answer Is Incorrect. \( 9 \times(3+4)=(\square \times 3)+(\square \times 4) \) Use the distributive property to fill in the blanks below.

1 Graph \( y-2=\frac{2}{3}(x-3) \)

1. Louls owns his own orchard. He plants 5 fruit trees for every 5 nut tiees. The equation \( f=\frac{9}{5} n \) models the relationship between the number of nut trees planted and the number of fruit trees planted. Determine the number of nut trees planted if 135 fruit trees were planted.