Problem 1:Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours . How long would it take the two painters together to paint the house? Problem 2: Two trains leave the same train station at the same time , but in opposite direction. The faster train travels at an average ra
For problems 1 -3, use the algebraic definition of the logarithm to evaluate (simplify) the expression by hand and state the property number used. All work must be shown. 1. log8 (8^(x-1) 2. log4 ((1/16)^7) 3. log (0.0001) For problems 4 - 6, solve for x exactly by hand. 4. log5 (x - 1) = 1 5. log2 (1/8) = x 6. lo
Draw the real line and label from about -5 to 5 in increments of 1. There are an infinite amount of integers on the real line. Based on your sketch you'll also agree with me that there are twice as many total integers as there are positive integers, right? But how many positive integers are there? That's it... an infinite am
1. It takes a passenger 5 hours less time than it takes a cargo plane to make the trip from Los Angeles to London. If the passenger plane averages 700 miles per hour on the trip while the cargo plane averages 450 miles per hour, how far is it from Los Angeles to London? 2. The molecular formula for Acetone. How many hydro
If the inequality involves only x, then graph the vertical line x = k. x > k is the region to the right of the line. x = k is the line itself. x < k is the region to the left of the line. Could there be a horizontal line? What would be it's equation/inequality? How do you decide on a so
1. Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers. 2. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108in2. What are the dimensions of the photo?
Why must there always be at least one real root if the degree of a polynomial is odd?
Abstract Algebra II - Modules. This is for the second problem #11 Find all similarity classes of 6x6 matrices over C with caracteristic polynomial (x^4 - 1)(x^2 - 1).
Campus Print Shop is thinking of purchasing a new, modern copier that automatically collates pages. The machine would cost $22,000 cash. A service contract on the machine, considered a must because of its complexity, would be an additional $200 per month. The machine is expected to last eight years and have a resale value of $4,
-7m^4 - 4m^3 / -5m^3
The edges of a triangular homesite have lengths of 2x - 1, x, and x + 2. Write an expression for the perimeter of the property.
5th root of z^20
A) Solve the equation: log3 (2 - 3x) = log9 (6x2 - 19x + 2) b) Prove that if a^x = b^y = (ab)^xy, then: x + y = 1
Find the sum of the roots of the equation 4x^2 + 5 - 8x = 0
Find the greatest common factor for 9, 48.
The floor plan of a house is rectangular. The house's length is 2x-10 and its width is x+3. Write an expression for the area of the house
Given the pay structures for two different babysitters, determine the number of hours of babysitting at which the two babysitters charge the same amount of money.
A parent is deciding which babysitter to use in the neighborhood. Babysitter A charges $20 per hour and a base rate of $60 per day. Babysitter B charges a base rate of $50 per day and $25 per hour. For how many hours of babysitting do the two babysitters charge the same amount?
If R is a unique factorization domain and if a,b are in R, then a and b have a greatest common divisor (a,b) in R.
If R is a unique factorization domain and if a,b are in R, then a and b have a greatest common divisor (a,b) in R. See attached file for full problem description.
Is it possible to use the inclusive brackets [ or ] with -infinity or infinity? Why or why not?
The owner of a hobby store bought a case of 9-volt batteries for $26.00. He marked the price up such that his profit was $1.74 per battery. After selling 13 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?
The height h in feet of an object after t seconds is given by the function: h = -16t^2 +60t + 9. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Problem: Find the x-intercept, given that y = x^2 - 5x - 10
Y = x^2 - 2x
Let f(x) = x^4 − 8x^3 + 12x^2 − 6x + 2. Show that f(x) is irreducible over the field of rational numbers. I know that it can't be factored... but how do I show its irreducible?
1/3 ÷ (-4/7)(-1/6) + (-1/18)
Explain in detail.
I know that the two bars | | around the expression 2-x and x-2 stand for 'absolute value'. But how does using | | differ from using simple brackets such as: ( ) or [ ] ?
See attached file for full problem description.
What's the 'English' meaning of the word 'consecutive'?
Various Algebra Questions. See attached file for full problem description.