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Basic Algebra

Polynomial Proof

Consider the cubic polynomial: See attached file for full problem description. Prove that if all 3 zeros are real, then all 3 coefficients are real.

Story problem

This is a intermediate algebra problem: A company that manufactures hospital beds has fixed monthly costs of $225,000. The average cost per bed, C, for the company to manufacture x beds per month is modeled by the formula C = 550x + 225,000 ------------------- x How many hospital beds can be m

Index Numbers, Ratios and Price Index

In 1990, a price index based on 1980 = 100 had a value of z. During 1990, it was rebased at 1990 = 100, and in 1998 the new index stood at 112. If the total price movement between 1980 and 1998 was an increase of 40%, was was the value of z in 1990, that is, before rebasing? The answer given was, Using ratios, 1.12 x

Pre-Algebra : Writing Equations from Word Problems and Solving Equations

Write an algebraic equation that you can use to solve for the answer. Scared of older kids, Alex pays Mr Simon some protection money. If any kid harasses Alex, Mr Simon will take care of the problem. For his services, Mr Simon asks for $90. Alex pays Mr Simon $15 and promises to pay the rest in six equal payments. How much w

Normal subgroups and product of two right cosets

Modern Algebra Group Theory (XXXV) Cosets of Subgroups of a Group Normal Subgroups of a Group A subgroup N of G is a normal subgroup of G if and only if the product of two right cosets of N in G is again a right coset of N in G.

The Order of an Element of a group

Modern Algebra Group Theory (XXXIII) Subgroups of a Group The Order of an Element of a group If in the group G, a^5 = e, aba^(-1) = b^2 for a,b belongs to

Finding value of variable

I am practicing for CLEP exam. Can't work problem backwards. Multiple choice. What is the remainder when x to the 3rd + 5x to the 2nd - 6x + 10 is divided by x + 3 ? I know the answer is 46, I just don't know why. Can some one walk me through it?

College Algebra: Writing Equations from Word Problems (4 Problems)

Please help with the following attached questions: 2,8,12,20 2. If 40L of an acid solution is 75% acid, how much pure acid is there in the mixture? 8. Unknown Numbers: Consider the following problem. The difference between six times a number and 9 is equal to five times the sum of the number and 2. Find the number.

College Algebra

Please help with the attached questions: 4, 8, 10, 14, 18, 24, 30, 38, 42, 54, 62, 78, 82, and 92 (See attached file for full problem description)

30 Logarithm Problems : Change of Base, Graphing and Solving for X

Find the exact values: 1) log (base 10) 1000 2) ln e^-100 3) log (base 5) (1/25) 4) log (base10) (0.1) 5) log (base 12) 3 + log (base 12) 48 6) 2^(log(base 2) 3 + log(base 2) 5) 7) e^(ln 15) 8) e^(3ln2) 9) log(base 8)320 - log(base8)5 -------------------------------------------------------------------------------

Putting a function in a form y=

Y = x^2 - 4x - 5 = x^2 - 2*2*x - 5 = ( x^2 - 2*2*x +2^2 ) - 2^2 - 5 = (x-2)^2 - 2^2 - 5 = (x-2)^2 - 4 - 5 = (x-2)^2 -9 y = (x-2)^2 -9 How do I put this in the form y=a(x-H)^2+K, how do I graph this function, and why is it not necessary to plot points to graph when using y=a(x-h)^2+K?

Algebra word problem

If John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be? How do I set up this equation?

Quadratic equation

Using the Quadratic equation: x2 - 4x - 5 = 0. How do I solve this by factoring? by completing the square? & solve by Quadratic formula?

Math Problems

I need the answers to these last six questions. (See attached file for full problem description)

Problem 12

Select the point which is in the feasible region of the system of inequalities: 4x + y < 8 2x + 5y < 18 x > 0, y > 0 A. (2,4) B. (-1,2) C. (1,3) D. (4,1)