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# Basic Algebra

### A Discussion On Exponential and Logarithmic Functions

1. Convert the following equations into logarithmic form: a. 2 = 6x b. 7 = 6y c. 9 = 3y d. X = 8y 2. Convert the following equations into exponential form: a. X = log54 b. 7 = log6Y c. X= log8Y d. 90 = log4Z 3. Simplify the following expressions: a. X

### A number of algebra practice questions and solutions

Evaluate. ((-1)2 - 3)3 + 5 · (-5) Simplify the following expression: When converting from Fahrenheit degrees to Celsius degrees , a well known formula is used: . Solve for . Simplify. Simplify. Simplify. Write your answer without parentheses. Rewrite the following without an exponen

### Galois's Construction of his Fields

Let beta be the Galois imaginary associated with the irreducible polynomial x^3 + x^2 + 1 over mod2. Solve the (systems of simultaneous) equations in GF(2, x^3+x^2+1). 1) (1+ beta)x + beta = 1 + beta^2 2) x + y = beta and x + beta*y = 1

### Which of the following products is not equivalent to the others?

Which of the following products is not equivalent to the others? Explain your answer. a) (2x-4)(x+3) b) (x-2)(2x+6) c) 2(x-2)(x+3) d) (2x-4)(2x+6) Please explain (in very elementary terms) and how you calculated the answer. Thank you. I need step by step to REALLY understand.

### A number of algebra questions and solutions

A number of high school/college algebra questions and solutions including factorization and solving simulataneous equations, 11 questions in total

### Exponential and Logarithm

The number of bacteria present in a certain culture at time t (measured in hours) is given by P(t)=P0* 2^(0.2t). Time t=0 corresponds to 8.00 A.M. on a particular day and P0 = 2000 is the initial number of bacteria. Find the number of bacteria present at noon the same day. How long does it take to have 20,000 bacteria pr

### Minimum Value, Maximum Value, and Saddle Points

1) Find the local maximum and minimum values and saddle point(s). Here is the function: f(x,y) = x^3y + 12x^2 -8y 2) Use Lagrange multiplier to find the extreme values (i.e. the max and min) of: f(x,y) = 4x+6y subjected to the constraint x^2 + y^2 = 13

Application Assignment #4 (Quadratic Equations) Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. Part 1 Mrs. Thom

### Step-by-Step Solution to Algebra Problems

Please see the attachment for details. Questions 1-3: Simplify Question 4: Perform Computations/Scientific Notations Questions 5,6: Evaluate Polynomials Questions 7,8: Find Product Question 9: Divide a Polynomial by a Monomial and find the Quotients Question 10: Find Quotient and Remainder.

### How many light bulbs and switch plates were sold?

Please give detailed explanation along with the computation. Light Bright Warehouse sells boxes of high efficiency light bulbs (\$5 box) and switch plates (\$10 each). In May, total sales were \$42000. Customers bought 5 times as many boxes of light bulbs as switch plates. How many of each did Light Bright Warehouse sell?

### Algebra Problems: finding the product

Please do not send answers in PDF Format 1. Find the following product: 5x2y(-4x5y4) - 5x2y - 4x5y4 - -20x10y4 - X7 y5 - -20x7y5 2. Short Answer. Find the following product: 6z (6z3-9z2+4) 3. Find the following product: (x - 8)(x + 8) - x2 +64 - x2 - 16x -64 - x2 + 16x -64 - x2 - 64 4. Short Answer. Fi

### Toxic Pollutants Formula and Driving Marathon Expressions

1. Toxic pollutants: The annual cost in dollars for removing p% of the toxic chemicals from a town's water supply is given by the formula: C(p)= 500.000/(100 - p) a) Use the accompanying graph to estimate the cost for removing 90% and 95% of the toxic chemicals. b) Use the formula to find C(99.5) and C(99.9). c) What

### Strong Induction: Example Problem

Use strong induction to show that when a convex polygon P with consecutive vertices VI, V2, ... , Vn is triangulated into n - 2 triangles, the n - 2 triangles can be numbered 1, 2, ... , n - 2 so that Vi is a vertex of triangle i for i = 1,2, ... , n - 2.

### Solve: Rational Exponents and Radicals

What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical expression. Explain how the process of combining radicals through addition and subtraction is similar to combining polynomials. What makes two radicals like radi

### Graph the parabola using the quadratic formula

(2-(-2)^)^ - 5 x 4 -(4w + u) - 4 (6u + 4w) The surface area of a right prism is given by , where is the area of the base, is the perimeter of the base, and is the height of the prism. Solve for . Solve for . Simplify your answer as much as possible. . Write

Solve and check the following equation; Explain/demonstrate how you derived your answer. Note: the radical sign extends over the expression 3x + 2. â??3x+2 - 2â??x = 0 Answer the following questions; Define a radical. What happens to a solution if the radicand is negative? Why do simplified radicals pro

### Wind Chill

W = 91.4- (10.5 + 6.7v-0.45v)(457 - 5t), where W and t are in degrees Fahrenheit and v is in miles per hour (mph). a) Find W to the nearest whole degree when t =25°F and v =20 mph. b) Use the accompanying graph to estimate W when t =25°F and v =30 mph. Comparing wind chills. Use the formula from above to determine wh

Write down a quadratic equation and solve it using the quadratic formula or by completing the square. Write 50-100 words comparing and contrasting the two methods.

### Parabolic Equation

Your bridge design has two towers, each with height ( h) of 300 ft above the road. Two suspension cables connect the two towers. The equation modeling the shape of these cables is parabolic. The total distance (d) between the two towers must be 3500 feet. The lowest point (l) of the cable above the road must meet 8 feet. Find t

### Mathematical Induction Statement

Let p(n) be the statement that 1^3 + 2^3 + ... + n^3 = (n*(n + 1)/2)^2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step.

### How do we communicate our thoughts and ideas?

Using mathematics, how do we communicate our thoughts and ideas? How do we use math to express abstract ideas?

### Compute the firm's profit, Derive an expression for marginal

Ï?=-10-48Q+15Q^2-Q^3 a. Compute the firm's profit for the following levels of output: Q=2,8, and 14. b. Derive an expression for marginal profit. Compute marginal profit at Q=2,8, and 14. Confirm that profit is maximized at Q=8. (Why is profit not mazimized at Q=2?)

A. Why do you factor a quadratic equation before you solve? B. Why are there usually two solutions in quadratic equations? Under what conditions will a quadratic equation have only one solution? No solutions? C. How can you tell before solving the equation how many solutions to expect?

### Rational expression, Rational equation, Polynomial

A. Choose an example of a rational expression, and present a step by step solution. B. Under what situation would one or more solutions of a rational equation be unacceptable? C. Define a polynomial and a rational expression. What makes a rational expression unique? Provide two original examples of a rational expression an

### Exhibiting Rational Expressions

(1) Explain how multiplying and dividing rational expressions is similar to multiplication and division of fractions. Give an example of each and compare the process. (2) When simplifying the rational expression (x+8)/(x+2), explain why it is improper to cancel out the x's. State a general rule for canceling factors in a rati

### Determine the degree of the polynomial

For each of the following polynomials, (a) list the degree of each term; (b) determine the leading term and the leading coefficient; and (c) determine the degree of the polynomial. (1) A 10-ft wide round water trampoline is floating in a pool measuring x ft by x ft. Find a polynomial for the remaining surface area of the pool

### GCF of Monomials and Expressions

Please show all work for all problems listed. Thank you This will help me with future problems like these. Find the GCF of the monomials. 16x2z, 40xz2, 72z3 Factor the GCF of expression. 15x2y2 - 9xy2 + 6x2y a(a + 1) - 3(a + 1) Factor each polynomial completely. x3y + 2x2y2 + xy3 Use grouping to factor e

### Converting word problem to algebraic expression

1.) Write the following as an algebraic expression using x as the variable : the sum of a number and -8 2.) Write the following as an algebraic expression using x as the variable: Five more than the product of 7 and a number. 3.) Solve -3 ( -19+4 )/-5

### A method and example on how to solve 3 simultaneous equations containg 3 variables

The method shows one how to solve 3 simultaneous equations as below for x, y, z Problem is to the solve the following simultaneous equations 22x + 5y + 7z = 12 (1) 10x + 3y + 2z = 5 (2) 9x + 2y + 12z = 14 (3)

### Factoring Equations

1. Factor 2. Factor. 3. Factor completely: . 4. Factor . 5. Factor. 6. Factor completely: . 7. Factor the quadratic expression . 8. Factor. 9. Factor completely: . 10. Factor completely: . 11. Factor the quadratic expression . 12. Factor. 13