Quadratic equations Questions and Answers

roblem 2 Let u v and w be vectors in R Determine which of the following statements are always true i If u 4 v 5 and u v 8 then u v 4 ii If u 2 and v 3 then u v 5 iii The expression vw u is both meaningful and defined A none of them B all of them C i and ii only D i only E i and iii only F ii only G iii only H ii and iii only

Problem 1 Let P be the point 1 3 3 Suppose that the point Po 3 3 3 is of the way from P to Q Find the point Q Problem 1 Enter the point Q a b c as a b c

2 Which of the following is equivalent to 3x 2x 4 a x b 5x 4 c 6x 4 d 1

7 Determine the interest rate necessary for 1500 to amount to 2075 in 6 years with interest compounded semi annually

5 Evaluate 3 x 4 2 4x 2 for the value x 10

3 Simplify the expression 2 4x 6y 3 2x 5y by distributing and combining like

2 Simplify the expression 2 x 4 10 y 10 by distributing and combining like terms

Homework 1 Simplify the expression 2 3x 3 3 x 10 by distributing and combining like terms

Independent Practice 1 Simplify the expression 2 3x 2 3x 8

3 b 3b 32b 28 b 7 3 6 7 2 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 b 7 4 4 k 13k 33k 30 k 10 1 k 10 A k 3k 4 B k 3k 3 C k 3k 5 D k 3k 6 5 k 10

7 Simplify the following expression 2 3x 4y 3 x 8y

4 Simplify the expression 2 x 4 x 2 5 Simplify the expression 2 3x 4 2 5x 2

5 3 Simplify the expression x 4 2x 3 10

d 2 Simplify the expression 4 2x 4 2 x 5

3 A sum of 5000 is invested at 8 p a compounded annually a Determine the amount of the investment after 3 years n b Determine the time for the investment to amount to 6211 48 at the same rate p

11 5x3 24x 61x 30 5x 4 6 A x 4x 9 B x 4x 9 C x 4x 9 D x 4x 7 5x 4 8 51 4 1 5x 4 5 5x 4

Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a D a a 10 5 a 10 a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 4 2 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10

10 224x49x 90 14x 14x 7 8 14x 7 1 2x 1 4 A x 4x 14 B x 4x 15 C x 4x 11 D x 4x 13 14x 7 10 14x 7

8 12v 153v 48v 45 12v 9 4 3 4v 3 2 3 4v 3 1 4v 3 A v 12v 8 B v 12v 4 C v 12v 7 D v 12v 5 X

7 99x 119x 76x 96 11x 2 A 9x x 6 11x 12 3 11x 12 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12

9 21 154p 104p 172p 2 14 A 11p 9p 12 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 1 7p 5 2 14p 1 2 14p 1 2 14p

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 B n 9n 8 C n 9n 10 D n 9n 8 1 n 13 3 n 13 1 n 13

Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 3 b 3b 32b 28 b 7 2 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 4 b 7

The selling price for a classic car is 14 000 which is 1000 more than two times its original price What was the original price of the car Answer

On average the number of electronic keyboards sold in Florida each year is equivalent to seven times the average number sold yearly in Alaska It on average there are 98 854 electronic keyboards sold each year in Florida how many are sold in Alaska Answer Keypad Keyboard Shortcuts

The sum of two consecutive odd integers is 180 Find the two integers Answer

The total cost of a pair of pants and a jacket was 59 01 If the price of the pair of pants was 1 49 less than the jacket what was the price of the pair of pants Express your answer as a simplified fraction or a decimal rounded to two places

The sum of two consecutive integers is 1 Find the two integers Answer

If 1 4 plus 7 1 times a number equals the sum of the number and 30 7 what is the number Express your answer as a simplified fraction or a decimal rounded to two places

Simplify the expression Write the final form with no fractions tan x 4 tanx 4 sinx tanx 2 sinx sin cos

K Find the exact value of the real number y if it exists Do not use a calculator y cos O A Select the correct answer below and if necessary fill in the answer box to complete your choice OB 2 COS y cos 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 3 2 COLLE does not exist

Is 33 52 a factor of 34 52 Explain why or why not Choose the correct answer below O A No because the exponents on the 5 terms are the same B Yes because 34 52 3 33 52 OC No because 33 52 cannot be written as a number times 34 5 D Yes because the two terms have the same factors P

Find the following for the function f x a f 0 e f x b f 1 f f x 3 4x 5 6x 7 c f 1 g f 7x a f 0 Simplify your answer Type an integer or a simplified fraction b 1 1 Simplify your answer Type an integer or a simplified fraction c 1 1 Simplify your answer Type an integer or a simplified fraction d f x h f x h d 1 x Simplify your answer Use integers or fractions for any numbers in the expression e 1 x Simplify your answer Use integers or fractions for any numbers in the expression f 1 x 3 Simplify your answer Use integers or fractions for any numbers in the expression 0 1 7x Simplity your answer Use intogors or tractions for any numbers in the expression

Assignment 1 point Calculate the acute angles rounded to the nearest degree formed by the plane z 2y z 14 and a the zz plane Answer b the z axis Answer Note You can earn partial credit on this problem 4

If possible find the measure of angle X A Not enough information to solve B 2X 52 C X 128 X 32 20 32

Find an nth degree polynomial function with real coefficients a leading coefficient of 1 and satisfying the given conditions n 3 3 and 4i are zeros f x Simplify your answer

A polynomial function P x with rational coefficients has the given roots Find two additional roots of P x 0 13 7 and 8i Two additional roots of P x 0 are Express complex numbers in terms of i Type exact answers using radicals as needed Use a comma to separate answers as needed

Is 4 a root of the polynomial f z 2z4 11z 14z 9z 18 4 va root of f x because We can also confirm this because 4 a possible rational solution

Mr Smith is opening up a new business selling bell bottom jeans One of his employees who understands math determined that the weekly profit for the company would be modeled by the equation P z r 50 z 10 z 90 If Mr Smith wants to make a positive profit and not go out of business how many jeans should he sell per week He should sell between and jeans

Which of the following are possible rational roots for the given polynomial f x 2 82 2 146 15 000 05 2 3 15 3 73 8 146 146 000 2 5 000 73 4 15 000 8 1

Find all of the real solutions to the following equation Write your answers in order from least to greatest 5x x 4x X X X

2 Sketch the graph of f x 9x 4x 1 4 2x x 1 8 On the graph show the zeros and the behavior of the function near by as well as the long run behavior

Let P 1 3 5 6 u 4 2 1 0 V 1 W W 43 U3 2 W3 3 5 V2 a Find a basis U U U3 for R such that P is the change of coordinates matrix from u U U3 to the basis V V2 V3 Hint What do the columns of P C B 6 1 6 4 and V3 U b Find a basis w W W3 for R such that P is the change of coordinates matrix from V V2 V3 to W W W3 1 3 Complete parts a and b 6 Con repr

1 point Simplify the rational expression 2x 1 2x 3

Use technology to find points and graph the line 4y 5x 8 following instructions below Plot at least two points that fit on the axes below Click a point to delete it 10 9 15 done plotting points 4 3 10 25 9 9 10

Suppose that G is a finite Abelian group that has exactly one subgroup for each divisor of IGI Show that G is cyclic

A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain cable car is to be installed running to the top of the mountain from a point 800 ft out in the plain from the base of the mountain Find the shortest length of cable needed Your answer is 3271 Preview ft

Determine which of the rational functions given below has the following feature There is a hole in its graph at x 5 OA f x OC f x X 9 x 5 OB f x OD f x x 5 x 9 x 5 x 5 5x 1 x 9 x 5 x 9 x 5

Find all complex zeros of the polynomial function Give exact values List multiple zeros as necessary f x 3x4 20x3 44x 80x 128 8 OA 4 i i 8 OB 4 2i 2i 3 OC 13 4 4 4i 4i 8 D 3 4 21 2i

Use the factor theorem to decide whether or not the second polynomial is a factor of the first 7x4 13x 2x2 x 4 x 2 Yes O No