# Algebra Questions

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Algebra
Complex numbers
To 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 numbers
The 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
Find all real solutions of the equation by factoring Enter your answers as a comma separated list 4x 4x3 0 X
Algebra
Matrices & Determinants
You 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
7w 3 2w 4 11
Algebra
22 5 6v 1 63
Algebra
The 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
Solve 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
additional 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
6 2 2 8 4 V 10 2 2 1 6 V6 13 26X2 5 28 VR 36 8 3 2X2 17 V8 7x4 3X6 5 1 50
Algebra
Use 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
Match 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
A 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 & Determinants
nd 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
A 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 Combinations
Consider 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
One 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
The 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
The 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
Part 4 Write a real world situation for each expression below be creative A b 12
Algebra
Sequences & Series
BONUS 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 numbers
Evaluate 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 numbers
e 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 numbers
What is the range of the function graphed below 3543 1 y 4 D 3 y 3 379199 44 5 B x
Algebra
The 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
3 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
NAME 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
troduction 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
2 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
2 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
6 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
b 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
Matrices & Determinants
Reduce the matrix to reduced row echelon form A 1 0 1 1 0
Algebra
Convert the degree measure to exact radian masuro 170 dog
Algebra
What 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
Joshua 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
Solve for x 6x 3 1 10x 5 2 3 que molecinc
Algebra
What 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 & Determinants
We 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
dentify the graph of the function g x f x 1 2 from the transformation of the parent quadratic function f x
Algebra
Solve using the square root property m 3 12 X D Font Size 4 A Q A BIUS X x 99
Algebra
Identify 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 numbers
MATCH 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
The 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
Solve 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 & Series
A 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
Algebra