Equations, Expressions, and Inequalities Q&A: Get Expert Help and Learn from Real-World Examples

Evaluate the expression ans write the result in theform a + bi
$\frac{1-<!--\; -\; -->\sqrt{-<!--\; -\; -->1}}{1+\sqrt{-<!--\; -\; -->1}}$

f(x)=1/sqrt(6x-2), find domain algebrically

Farris Billiard Supply sells all types of billiard equipment, and is considering manufacturing their own brand of pool cues. Mysti Farris, the production manager, is currently investigating the production of a standard house pool cue that should be very popular. Upon analyzing the costs, Mysti determines that the materials and labor cost for each cue is $25, and the fixed cost that must be coveblack is $2,400 per week. With a selling price of $40 each, how many pool cues must be sold to break even? What would the total revenue be at this break-even point?

Find all solutions of the equation and express them in the form a +bi. (Enter your answers as a comma-separated list. Simplify your answer completely.)
x^2 + 36 = 0
x =

Is 3(x + y) equal to 3x + y? Why or why not? What is the name ofthe rule that defines this operation (commutative, associative,distributive)?
If a=18, b=2, and c=7, Does the expression a/b+c evaluate to 16 or to 2?Why (explain your answer)?
Is this relationship correct? Why or why not?

4x^2 - 12xy + 8y^2 in the form (ax - by)^2 + cy^2

Which of the following statements is FALSE?
Select one:
a. The rationing function of prices is not allowed to freely operate when the government imposes price controls.
b. Price controls may take the form of price ceilings or price floors.
c. Rent controls are examples of price floors.
d. Price ceilings below the equilibrium price can cause black markets to develop.

The selling price of a scientific calculator is $15. If the markup is 25% of the dealer;s cost, what is the dealer's cost of the calculator?

Find the solution to the following system. x+y=-7x-y=5. Write your anwer in coordinate format such as "(x,y)"

Chris and Bob have a painting business. Chris has less experience and it takes him 4 hours longer than Bob to paint a fence. Working together they can paint a fence in 6 hours. How long does it take Chris to paint the fence by himself? Round your answer to the nearest tenth of an hour if necessary

Use the deductions of Social Security 7.5%, Medicare 2.5%, State tax 6.8%, Federal tax 16.5%, and a fixed health insurance payment of $100 a week, and calculate the net pay for the following employees:
A: 64 hours @ $9.75/hr Net pay ...
B: 57 hours @ $8.25/hr Net pay ...
C: 42 hours @ $9.75/hr Net pay ...
D: 72 hours @ $10.50/hr Net pay ...

A 60-gallon bathtub is to be filled with water that is exactly 100?F. Unfortunately, the two sources of water available are 125?F and 60?F.When mixed, the temperaturewill be aweighted average based on the amount of each water source in the mix. How much of each should be used to fill the tub as specified?

Write the inequality using interval notation and illustrate the inequality using the real number line.
$-<!--\; -\; -->7\le <!--\; \le \; -->x<-<!--\; -\; -->2$
Write the inequality using interval notation and illustrate the inequality using the real number line.
$x\ge <!--\; \ge \; -->-<!--\; -\; -->3$
Write the given interval as an inequality involving x, and illustrate the interval using the real number line.
[-1,9]
Use an inequality involving x to to express the interval. What is the resulting inequality?
Write the given interval as an inequality involving x, and illustrate the interval using the real number line.
$[-<!--\; -\; -->\mathrm{\infty <!--\; \infty \; -->},-<!--\; -\; -->1]$
Express the given interval as an inequality in terms of x, and select the graph of the interval.
$(-<!--\; -\; -->\mathrm{\infty <!--\; \infty \; -->},6)$

A 12-ft. board is cut into 2pieces so that one piece is 4feet longer than 3times the shorter piece. Find the lengths of both pieces.

2x+y=14, solve for y

Simplify the expression: $\frac{-<!--\; -\; -->3^2-<!--\; -\; -->5(3^2-<!--\; -\; -->2^4)}{2-<!--\; -\; -->|5-<!--\; -\; -->8|}$

The price p and the quantity x sold of a certain product obey the demand equation: P=-1/8X+100, {X/0 </ X </ 800}
What is the revenue, R(x) = x . p(x) ,to the nearest dollar when 700 units are sold?

Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: $5-<!--\; -\; -->7x>9-<!--\; -\; -->12$

A pizzeria will bake and deliver a round pizza with a 20-inch diameter. Find the exact area of the top of the pizza and an approximation. Use 3.14 as an approximation for pi.
The exact area is... (Simplify your answer. Type an exact answer in terms of x.)
The approximate area is.... (Type a whole number or decimal rounded to two decimal places as needed.)

Solve the inequality and graph the solution:
$-<!--\; -\; -->3r\le <!--\; \le \; -->18$