Algebra Questions
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Algebra
Complex numbersFind each quotient Simplify your answers 1 1 1 500 to check 4 58 2 43 55 6 5 3 2 1 121 120
Algebra
Quadratic equationsFor what value of k will the linear system below be consistent Try to do this problem with pencil and paper only 121 322 721 421 512 k 12 k 6 6
Algebra
Complex numbersWrite an equation for the polynomial graphed below 5 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 1 2 3 A Preview uit 5
Algebra
Complex numbersTo test for any significant difference in the number of hours between breakdowns for four machines the following data were obtained Machine Machine Machine 1 2 3 6 4 7 9 5 3 7 5 8 4 7 1 9 0 7 7 9 7 10 2 9 4 9 8 10 8 Ho H H H3 H4 Ha H H H3 H4 10 0 9 4 10 1 Ho H H H3 H4 Ha H H H3 H4 8 9 8 4 Machine 4 9 7 12 8 12 0 10 6 11 1 a At the x 0 05 level of significance what is the difference if any in the population mean times among the four machines State the null and alternative hypotheses 11 6 O Ho Not all the population means are equal Ha H H H3 H4 O Ho At least two of the population means are equal Ha At least two of the population means are different Ho M H H3 H4 H Not all the population means are equal Find the value of the test statistic Round your answer to two decimal places Find the p value Round your answer to three decimal places
Algebra
Complex numbersThe table of data lists input output values for a function Complete parts a through c a Is the change in the inputs x the same Select the correct choice below and if necessary fill in the answer box to complete your choice OA Yes and it is equal to OB No X 11 28 96 113
Algebra
Quadratic equationsFind all real solutions of the equation by factoring Enter your answers as a comma separated list 4x 4x3 0 X
Algebra
Matrices & DeterminantsYou may need to use the appropriate technology to answer this question Develop the analysis of variance computations for the following completely randomized design At a 0 05 is there a significant difference between the treatment means A 136 119 113 107 130 114 130 95 xj 2 s 186 29 118 Treatment B 108 113 125 104 106 110 98 113 105 88 107 C 91 82 86 101 88 116 111 119 99 97 99 95 78 164 89
Algebra
Quadratic equationsThe function g is related to one of the parent functions described in an earlier section g x x 6 a Identify the parent function f f x b Describe the sequence of transformations from f to g Select all that apply O reflection in the x axis horizontal shift of 6 units left Overtical shift of 6 units upward Overtical shrink Ohorizontal shift of 6 units right c Sketch the graph of g O y y 5 10 5 4 2 2 4 V V 5 15 10 5 10 5 4 2 15 y 15 10 5 5 2 d Use function notation to write g in terms of f g x f 4 X X 15 10 10 M y 10 5 5 10
Algebra
Quadratic equationsSolve the following system of equations graphically on the set of axes below 1 2 5 y 10 9 8 7 6 5 y x 4 Plot two lines by clicking the graph Click a line to delete it 3 2 1 7 1 N 2 co 759 2 10 7 5 1 2 9 10 x
Algebra
Quadratic equationsadditional parentheses 000000 1 5x 3 2 2 5x3 4 25 2 15 2 2x2x2 3 3 x 5 13 441 25420H 3 4 3 x 4 3 25 4 3 X 6 2x2 5 4 5 10 2 2 1 5 6 1 3 2 6 x 2 5 2 8 X7 56 8 3 2 2 17 7 5 1 5 5
Algebra
Quadratic equationsUse Gauss Jordan row reduction to solve the given system of equations system is dependent express your answer using the parameters x y ar x y z 8x y 32 0 8x y 2z 5
Algebra
Quadratic equationsMatch the graph with its function using the x intercepts 4 4 4 4 24 y x x 2 y x x 2 y x x 2 y x x 2
Algebra
Quadratic equationsA ball is projected upward from the ground Its distance in feet from the ground in t seconds is given by s t 16t 126t At what times will the ball be 223 feet from the ground
Algebra
Matrices & Determinantsnd the solution set of each linear system Identify inconsistent systems and dependent equation x 3y z 20 x 4y z 18 x 3y 4z 19
Algebra
Quadratic equationsA conical tank contains seawater to a height of 2 ft The tank measures 12 ft high and 5 ft in radius Find the work needed to pump all the water to a level 2 ft above the rim of the tank lb The specific weight of seawater is 64 ft3 Approximate the answer to three decimal figures
Algebra
Permutations and CombinationsConsider the following planes 5x y z 5 15x 3y 5z 25 e Find the engle in degrees between the two planes Round your answer to two decimal places 45 25 X b Find a set of parametric equations for the line of intersection of the planes Use t for the parameter Enter your answers as a comma separated list of equ x y 5 5z 5
Algebra
Quadratic equationsOne leg of a right triangle is 2 millimeters longer than the shorter leg and the hypotenuse is 4 millimeters longer than the shorter leg Find the lengths of the sides of the triangle The length of the shorter leg is The length of the longer leg is The length of the hypotenuse is millimeters cubic millimeters square millimeters
Algebra
Quadratic equationsThe length of a rectangle is 19 centimeters less than five times its width Its area is 30 square centimeters Find the dimensions of the rectangle The width is and the length is
Algebra
Quadratic equationsThe product of two consecutive room numbers is 306 Find the room numbers The number of the first room or the smaller room number is x 1
Algebra
Quadratic equationsPart 4 Write a real world situation for each expression below be creative A b 12
Algebra
Sequences & SeriesBONUS Bonus will be graded as noted in the rubric with the understanding that a student s grade cannot exceed 105 points Part 6 Bento boxes b are special boxed lunches in Japanese cuisine Sushi rolls r are also a popular lunch item usually made of rice seaweed vegetables and either raw or cooked fish Steven wants to buy 3 bento boxes b and 2 sushi rolls r A Write an expression that represents Steven s purchase B Each bento box is 10 yens and sushi rolls are 8 yens How much did Steven spend on his purchase Show your work
Algebra
Complex numbersEvaluate each expression show your work A 2c 4 when c 3 B 3 t 8 when t 4 C 43 x 2 when x 5
Algebra
Complex numberse From the zeros of the numerator and denominator of R x divide the x axis into intervals Determine where the graph of R is Above or Below the x axis by choosing a number in each interval and evaluating R there In short fill out the chart below and do an Interval Analysis as done in class 12 points Interval Number Chosen Value of f Location of graph Point on graph R x x 8x 12 X 9
Algebra
Complex numbersWhat is the range of the function graphed below 3543 1 y 4 D 3 y 3 379199 44 5 B x
Algebra
Quadratic equationsThe function h defined by h t 49 4 9t 10 t models the height in meters of an object seconds after it is dropped from a helicopter b C Find or approximate the time when the object hits the ground Explain or show your reasoning From what height is the object dropped Explain or show your reasoning Where is the vertex of the graph
Algebra
Quadratic equations3 A quadratic function is defined by g x x 4 7 What is the vertex of the graph of function g C a b Does the vertex represent the minimum value or the maximum value of the function Explain or show how you know If you were to shift this graph 6 units down from where it is now what would be the equation represented by the new graph
Algebra
Quadratic equationsNAME T Introduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f 1 2 a b C y 1 O 1 2 3 4 5 6 2 0 2 6 0 3 4 5 5 DATE 2 2 24 4 4 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form 2 A quadratic function is defined by p x x 1 x 3 Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex y 5 4 3 2 1 WN TO 6 5 4 3 2 10 1 2 3 T 2 3 4 PERIOD 5 X
Algebra
Quadratic equationstroduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f y 1 2 1 a b C 1 2 3 4 5 2 0 2 3 4 6 0 5 en 4 4 16 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form
Algebra
Quadratic equations2 2 3 Select Select Two numbers multiply together to equal 90 but add together to equal 9 What are the two numbers Select 4 Select 5 6 and 1 7
Algebra
Quadratic equations2 2 Two numbers multiply together to equal 90 but Select add together 9 What are the two numbers Select t Select 2 Select and 1
Algebra
Quadratic equations6 2x 2 10 When you square both sides what is the resulting O equation in the next step before you solve for x O O 2x 2 100 2x 2 10 1 2x 2 100 2x 2 10 C
Algebra
Quadratic equationsb Where are the x intercepts d Where is the y intercept e Where is the vertex f Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex X
Algebra
Quadratic equationsWhat is the quotient of 3x4 4x2 8x 1 x 2 Watch for any missing terms 3x 6x 8x 24 47 x 2 3x 6x2 8x 24 47 3x 6x 8x 24 3x 4x 8x 1 47 3x 4x 8x 1 O3x 6x 8x 24 47 X 2
Algebra
Quadratic equationsJoshua decides to use synthetic division to find the quotient of 3x 8x 2x 3x 10 x 2 What value from the divisor should he write in front of the coefficients 00 3 S S
Algebra
Quadratic equationsWhat is the quotient of x3 3x2 5x 3 x 1 Ox 2x 3 Ox 2x 3 Ox 3x 8 x 2x 7 0 0 0 0
Algebra
Matrices & DeterminantsWe can find the remainder for the quotient using either substitution or synthetic division as discussed in class Using either method explain whether or not we can conclude that x 5 is a factor of the polynomial f x x 17 15 Show your work process to find the remainder Your answer must include what that remainder value is and if it indicates x 5 is a factor or not
Algebra
Quadratic equationsdentify the graph of the function g x f x 1 2 from the transformation of the parent quadratic function f x
Algebra
Quadratic equationsSolve using the square root property m 3 12 X D Font Size 4 A Q A BIUS X x 99
Algebra
Quadratic equationsIdentify the equation of a parabola with a minimum value of 1 of x x 2 3 Of x 2 x 2 3 o f x x 4x 5 of x x 4x 7
Algebra
Complex numbersMATCH the indicated operation on the left with each simplified expression along the top Each row should contain exactly one check mark 1 7i a 2 3i 3 4 b 2 3i 3 4i c 2 3i 3 4i 2 3i 3 4i d THE 6 i O 5 1 0 24 0 68i 18 000 0 1
Algebra
Quadratic equationsThe figure shows a graph of the function f x in the xy coordinate plane 5 10 5 5 C Use the dropdown menus to indicate whether each statement is true or false f x has A a minimum of 8 B two real zeroes C a decreasing interval from 1 D a y intercept of 7 E A vertex at 1 8 F f x 0 over 0 5 Sign out
Algebra
Quadratic equationsSolve the equation by completing the square x 8x 20 Ox 8 72 O x 10 2 O x 20 4 Ox 4 72
Algebra
Sequences & SeriesA ball is thrown into the air with an upward velocity of 40 feet second Its height h after t seconds is given by the function h t 16t 40t 12 Answer the following questions by typing your answer in the box provided for each part A In how many seconds does the ball reach its maximum height Round your answer to two decimal places B What is the maximum height of the ball Round your answer to the nearest foot feet seconds