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Basic Algebra

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)

Denumerable and Induction

1. Show that if A and > are denumerable disjoint sets then A u > is denumerable 2. Show that every set of cardinalty c contains a denumerable subset 3. Show by induction that 6 divides n^3 - n for all n in N

Sum of consecutive odd integers

If m and n are odd integers with n>1, given the sum of n consecutive odd integers, starting with m, is 18,079. Find all possible values of m and n.

Lebesque measurable sets in R^n.

Prove that lebesque measurable sets in R^n form sigma algebra. ( Please use basic definition when you talk about the lebesgue measurable sets in R^n). The def we have is: (k_1)^(m)={ -1/2 + m_i =< x_i =< 1/2+ m} m=(m_1,m_2,...,m_n) m belongs to z^d Now we say that A in R^n is Lebesque measurable set in R^n if

Speed and Distance

Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?

Distance and Speed

Janet drove 120 miles at x mph before 6:00 a.m. After 6:00 a.m., she increased her speed by 5 mph and drove 195 additional miles. Write a rational expression for her total traveling time. Evaluate the expression for x = 60.

Context-fee language

Thank you for taking the time to look at my problem. I cannot make math symbols, thus, I will let ^ denote "raised to the power." For example, a^2 is a squared or a "raised to the power" of 2. Also, I will use the symbol * to denote multiplication. For example, 2*7=14. Okay, here is my problem: Show that the language L={ a

Functions and Relations

A football player attempts a field goal by kicking the football. The ball follows the path modelled by the equation h=-4.9t2(means t squared)+10t+3, where h is the height of the ball above the ground in metres, and t is the time sincethe ball was kicked in seconds. 1. Describe the path of the ball. 2. After how many sec