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# Algebra

### Business Math : Revenue and Total Cost

The Revenue and Total Cost eqations for a glove company are R(x)=35x and C(x)=0.25x^2 + 30.5x + 10, where x is in hundreds of gloves and R(x) and C(x) are in thousands of dollars. What is the Revenue and production Cost for 700 gloves, the profit for this problem, the number of gloves that will produce the maximum profit, the

### Solve the Equation BrainMass Expert explains

Solve the following equation: X = 1 + (2x + 1)^1/2

### Solving Inequality Functions

Solve: -4 (x+6) < -4 -4x Is the answer, x< -10; x> -10; all real numbers or no solution? Please show step by step how to solve the inequality. Also, I came up with "x<0" but I do not know if this means "no solution" or "all real numbers" Can you please explain step by step h

### Equation: GCD and Mod

Find the least number N such that 1024N-11529=15625x where N and x are non-negative integers

### Algorithms : Finding integer values of x and y

A store offers 2 models of scooter, a \$29 model and a \$33 one. An order was placed with a warehouse which totalled \$2490 but the details had been lost. Can you tell the order clerk howl many of each model to send to the store? I have been applying algorithm to equations and am trying to solve integer values for this problem.

### Combinations : Problem Solving With Dice

Please see the attached file for the fully formatted problems. Question1: How many dots at the outer sides of the dice. Given view is from the top of these four dice? Question2: In the newly formed shaped below do you think answer is the same or different from above? What does your intuition say without investigating? Q

### Find a nontrivial central extension

Find a nontrivial central extension 1 --> Z_2 --> G --> A_4 --> 1 meaning determine a group G. Is it unique? (You may use the fact that A_4 has a normal series Z_2 x Z_2/Z3)

### Inequality: Proof using Unit Vectors

Prove that (a1b1+a2b2+...+anbn)^2<=(a1^2+a2^2+...+an^2)(b1^2+b2^2+...+bn^2) where ai, bi are real numbers, i=1,2,...,n

### Summation Equality: Prove by Induction

I would be grateful if someone could show me how to prove by induction the attached formula.

### Explanation of Letter Equation

Please explain: ABCDE X 4 = EDCBA

### Discriminant and graphs

PART ONE: ATTACHED PART TWO: what type of graph is: x^2 + 3y^2 - 4x + 6y = -1 A) parabola B) circle C) ellipse D) hyperbola PART THREE: Find the value of the discriminant of the equation. Describe the roots completely. Do not solve. 3x^2 + 4x - 5 = 0 A) 31; 2 real, irrational root

### Value of a Discriminant Equation

Find the vaule of the discriminant of the equation. Describe the roots completely. Do not solve. A) 31; 2 real, irrational roots B) -44; 2 imaginary roots C) 76; 2 real, rational roots D) 76; 2 real., irrational roots

### Logarithmic Equatations.

(a). SOLVE FOR X:LOG2X=8 (b). WRITE AS A SINGLE LOGARITHM:5LNX-1N(X+1)

### Finding the vertices of a hyperbola.

Find the vertices of the hyperbola with the following equation: (x-3)^2/25 - (y+4)^2/4 =1 EITHER: A) (8,-4) and (-2,-4) B) (5,-4) and (1,-4) C) (3,-2) and (3,-6) D) (3,1) and (3,-9)

### Find the equation of the parabola using focus and directrix

Find the equation of the parabola with focus (3, -1) and directrix y = 5. A) x=-1/4(y+1)^2+3 B) x=-1/4(y+1)^2+4 C) y=-1/12(x-3)^2+2 D) y=-1/12(x-3)^2-1

### Real-World Problem

In a real-world problem, what are some typical action items that you may need to do in order to get to the point having an equation to solve?

### mathematical model and extrapolating it find other information

The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet?

### Choosing the correct statements about an equation.

This question concerns the equation 3x^2- 4x- 5=0 Choose the two correct statements about this equation Options. A. The equation has no real-number solutions. B. The equation has one real-number solution. C. The equation has two solutions x= - 0.7863 and x= 2.120 correct to 4 significant figures. D. The e

### Finding the solutions for x and y for the simultaneous equations

Choose the two options that give the solution for x and for y, for the simultaneous equations. 5x+2y=2 2x+y=0.3. Options A. X= -2 B. X=0 C. X= 1.4 D. X= 1.7 E. Y= -2.5 F Y= -5 G. Y= 1.7 H. Y= 4.3

### Congruence Functions Solved

Solve the congruence 42x 12 (mod 90). Problem: Solve the congruence 42x 12 (mod 90). Solution: We have gcd (42, 90) = 6, so by Theorem Given below, there is a solution since 6 is a factor of 12. The congruence ax b (mod n) has a solution if and only if b is divisible by d, where d = (a, n). If d | b, then there a

### Examples showing how to solve for a variable.

I can't remember how to solve for x. What are some problems where I have to solve for x?

### How to get the formula for Sn of an arithmetic series?

Tn = a+(n -1)d sn = n/2(a + n) 4. For the series 3 + 9 + 15 + 21... Find: a) an expression for tn b) an expression for sn c) the answer if s = 20 d) the answer if t = 115 5. Find the # of terms in the sequencece 2,6,10... 626 I need a step by step procedure for solving these problems.

### Proof of the Irrationality using Euler's phi-function

2. Apply the proof of the irrationality of sqrt(2) to a) sqrt(3) and b) sqrt(4). If the proof breaks down, indicate precisely why. 3. Euler's phi-function is defined such that for n > 0, phi(n) = |{m < n: gcd(m,n)=1}|. So, e.g., phi(4) = |{1,3}| = 2; phi(5) = |{1,2,3,4}| = 4. a. Show that for prime p, phi(p) = p-1.

### Calculating the intersection point between two light beams.

One lighthouse is 60 ft hgt. An opposing lighthouse is 176.5 ft high. The distance between them is 3281 ft. The 60 ft lighthouse beam is 3281.54 ft. The 176.5 ft lighthouse beam is 3285.74 ft. At what point do they cross?

### Word problem in regards to geometric sequences.

A college student humorously asks his parents to charge him room and board according to this geometric sequence: \$0.01 for the first day of the month, \$0.02 for the second day, \$0.04 on the third day and so on. Find the total room and board he would pay for 30 days.

### Word problem in regards to arithmetic sums.

The game of pool uses 15 balls numbered 1 to 15. In a variety called rotations, a player who sinks a ball receives as many points as the number on the ball. What is the score of a player who sinks all 15 balls?

### Find vertex and intercepts for the equation and sketch a graph

Find the vertex and intercepts for the Quadratic function, and sketch its graph, SHOW ALL THE STEPS IN SOLVING THE PROBLEM. y = x^2 -4x -12

### Sequential Ambiguity Elements

On Monday, May 26th/03, I posted the following question to which a solution was provided by Remus Nicoara, PhD (IP). I thank Remus for his assistance and solution. I'm interested in knowing what the solution would look like if for each term, the y elements are randomly determined. Original Question In a specific sequence t

### Finding the roots of an equation.

Find to the nearest tenth, the positive real roots of f(x) ~= x^2+x-1.

### Solving for one variable in a multiple variable equation.

Solve for y: 2x - 5y = -1