Question

1. Simplify the Expression √36x^2/y^7


2. Simplify the Expression (1-3i)(2+5i)-(3-12i)


3. The formula c= √a^2+b^2 represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for a. Show your work. That means get "a" all by itself on one side of the equation.

Answer 1

Answer:

See below

Step-by-step explanation:

1.

$\sqrt{\frac{36x^{2}}{y^{7}}} \\= \sqrt{\frac{6^{2}x^{2}}{y^{6}y}} \\=\frac{6x}{y^{3}\sqrt{y} } \\=\frac{6x\sqrt{y}}{y^{4} }$

2.

$(1-3i)(2+5i)-(3-12i)\\=2+5i-6i-15i^{2}-3+12i\\=14+11i$

** i^2=-1, -15i^2 = 15

3.

$c=\sqrt{a^{2}+b^{2}} \\c^{2}=a^{2}+b^{2}\\a^{2}=c^{2}-b^{2}\\a=\sqrt{c^{2}-b^{2}}$