Question

evaluate each expression for the given values of the variables. 34. length of a hypotenuse of a right triangle: $sqrt{a^{2}+b^{2}}$ when $a = 15$ and $b = 20$. 35. perimeter of a parallelogram: $2x + 2y$ when $x=\frac{5}{3}$ and $y=\frac{3}{2}$.

Explanation:

34.

Step1: Substitute values

Substitute \(a = 15\) and \(b = 20\) into \(\sqrt{a^{2}+b^{2}}\).
\(\sqrt{15^{2}+20^{2}}\)

Step2: Calculate squares

Calculate \(15^{2}=225\) and \(20^{2} = 400\).
\(\sqrt{225 + 400}\)

Step3: Add inside square - root

\(225+400=625\), so we have \(\sqrt{625}\).

Step4: Find square - root

\(\sqrt{625}=25\)

Step1: Substitute values

Substitute \(x=\frac{5}{3}\) and \(y = \frac{3}{2}\) into \(2x + 2y\).
\(2\times\frac{5}{3}+2\times\frac{3}{2}\)

Step2: Calculate multiplications

\(2\times\frac{5}{3}=\frac{10}{3}\) and \(2\times\frac{3}{2}=3\).
\(\frac{10}{3}+3\)

Step3: Make common denominator

Rewrite \(3\) as \(\frac{9}{3}\). Then we have \(\frac{10}{3}+\frac{9}{3}\).

Step4: Add fractions

\(\frac{10 + 9}{3}=\frac{19}{3}=6\frac{1}{3}\)

Answer:

25

35.