91Ó°ÊÓ

Answer true or false given that \(a>0, b<0, c>0,\) and \(d<0\). $$\text { If } a

Antonio and Jeremy work for a plumbing company that was recently awarded a contract to install the plumbing fixtures in a new office complex. There are 12 bathrooms in the building. It takes Jeremy 4 hr longer than Antonio to complete one bathroom. If they work together it takes \(8 \mathrm{hr}\) to complete a bathroom. Find the rate at which each individual can complete a bathroom working alone.

For each given number, (a) identify the complex conjugate and (b) determine the product of the number and its conjugate. $$4-5 i$$

Solve the equation by using any method. \(n^{2}+8 n=-3\)

Solve the inequality and write the solution set in interval notation. \(|x|-x>10\)

For each given number, (a) identify the complex conjugate and (b) determine the product of the number and its conjugate. $$8 i$$

Pam is in a canoe on a lake \(400 \mathrm{ft}\) from the closest point on a straight shoreline. Her house is \(800 \mathrm{ft}\) up the road along the shoreline. She can row \(2.5 \mathrm{ft} / \mathrm{sec}\) and she can walk \(5 \mathrm{ft} / \mathrm{sec}\). If the total time it takes for her to get home is \(5 \mathrm{~min}(300 \mathrm{sec})\), determine the point along the shoreline at which she landed her canoe.

Solve the equation by using any method. \(\frac{x^{2}-4 x}{6}-\frac{5 x}{3}=1\)

Martha is in a boat in the ocean \(48 \mathrm{mi}\) from point \(A\), the closest point along a straight shoreline. She needs to dock the boat at a marina \(x\) miles farther up the coast, and then drive along the coast to point \(B, 96 \mathrm{mi}\) from point \(A\). Her boat travels \(20 \mathrm{mph}\), and she drives \(60 \mathrm{mph}\). If the total trip took \(4 \mathrm{hr}\), determine the distance \(x\) along the shoreline.

Write the set as a single interval. $$(-\infty, 5) \cap(-1, \infty) \cap[0,3)$$