1. Divide, then write the result as a division statement. a) (x3-3x2+5x-4)/(x-2) X not equal to 2 ___________ x-2)x3-3x2+5x-4 x3-2x2 -x2+5x -x2+2x 3x-4 3x b) (x3-3x-2)/(x+3) 2. Use the Remainder Theorem to determine the remainders ( do not divide). a) (x3-7x2+2x-4)/(x+2)
Solve the quadratic equations in questions 1 - 5 by factoring. 1. x2 - 49 = 0 2. 3x3 - 12x = 0 3. 12x2 + 14x + 12 = 18 4. -x3 + 22x2 - 121x = 0 5. x2 - 4x = 5 In questions 6 - 10, solve the quadratic equation by graphing. 11. Write a quadratic equation that will have solutions of x = 3 and x = -7. 12. Write a quadr
See attached file for full problem description.
Please discuss the following equation: Determine the domain and range of y = -2x + 1. Show all work that is required.
For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
A company uses the formula C(x) = 0.02x^2 - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2 + 300x - 200. What is the profit if 500 are sold? For what value of x will the profit be at a maximum?
Find the complex solution to this quadratic equation: x^2 + 6x + 10 = 0. keywords: imaginary solutions
For the equation y = x^2 - 6x + 3, what is the domain and the range?
For problems #5 and #6, solve each inequality without graphing 5. x^2 + 3x < 18 6. 2/(a - 2) < 3/(a + 1)
The formula h(s) = -32s2 + 400s + 8 models a rocket's height, h, in feet, s seconds after launching. Find the height, h(s), five seconds after launch.
Solve by any method: x - 2 - 8√(x - 2) + 15 = 0.
The rule-of-70 provides a simple way to calculate the approximate number of years it takes for the level of a variable growing at a constant rate to double. The rule states that if the constant growth rate is r, the variable will double after approximately n years when n = 70/ r. a) Explain how this rule can be derived. b)
12x^(5/3)(4x^(2)-9)^-1 +2x^(-1/3) -3(2x^(1/3)+3x^(-2/3))^-1 = (7x-6) / (x^(1/3)(2x-3))
15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below. a). Use the two points reporting data for 9 hours of study
1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function
Math Puzzle. See attached file for full problem description. 3 - 4(2 - 1)=? For y = -2x - 6 slope = ? y-intercept = ? Solve this system of equations: x + y=5 and 3x - 5y= -9 X=? Y = ? For x/3 - y/6 = 5, what is the Lowest Common Multiple, that is, what do you multiply all terms by to eliminate the denominators?
9x4 + 4x3 - 27x2 + 12x <------ Factor by finding the GCF x2 + 2x - 15 <--------Factor by grouping For these problems, identify which of the methods from this lesson (GCF, grouping, difference of squares, or perfect squares) could be used to factor the polynomial. 17. x2 + 2x + 1 A This polynomial could b
A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magma activity within the earth in an area of New Zealand known for its volcanic activity. One of the shortcuts they apply when doing calculations in the field is to use synthetic division. After the
4 (i) Let C be a linear code in IF. Explain what is meant when we say that C is cyclic. Give also the algebraic characterisation of cyclic codes using the ring .... (ii) Explain why the cyclic codes in R are in 1-1 correspondence with the monic polynomials in IFq[xJ that divide ? 1. Give the definition of the generator polynom
Solve by the method of your choice: (5x - 1)^2 = 24
Solving rational exponents a) √ x-2= 1 b) √ x^3 =27 c) 3√x^2 = 3
The 7th degree polynomial x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 has a factor (x - 3) (a) Divide x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 by x - 3 and thus: (b) Express it in the form (x - 3)(ax^6 + bx^3 + c) (c) By putting Z = x^3, find all the factors, real or complex of the 6th degree polynomial and thus: (d) Expres
Please see attached PDF file; I'm trying to derive a couple of results involving Lagrange multipliers and a linear algebra equivalence. This makes use of the extension to Lagrange multipliers whereby the constraint is an inequality (see, e.g., section 5.1 of http://www.cs.berkeley.edu/~klein/papers/lagrange-multipliers.pdf ).
Can you reduce this rational expression any further? 6 + 2b / (x - w)(b - 3)
1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35... 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number Multiply the number by 12 Add 12 to the product Divide the sum by 4 Subtract
Make a field of 4 elements, and the addition and multiplication table for this field.
Using the following numbers, how can you come up with a sum of 24? Use the number only once. 3 3 12 20
Solve the quadratic equation: x^4 + x^3 = 100x^2 + 100x
Simplify: (3.4 x 10^-4)(4.1 x 10^5)
Divide: (6x^3 + x^2 - 3x + 2) / (2x - 3)