Algebra Questions

Solve for x 1 L x d X Simplify your answer

Change the percent to a decimal equivalent 2 10 10 The decimal equivalent is

Find the following quotient 0 46 0 3 0 46 0 3 Simplify your answer Round to the nearest hundredth as needed

If the boys of a class are arrnged in rows each consistings of 24 36 and 40 boys 18 boys fall short in each case But they can be arranged in rows each containing 27 boys Find the least number of boys of the class

The equation of the graph is f x Simplify your answer 10 10

Find a polynomial function P of the lowest possible degree having real coefficients a leading coefficient of 1 and with the given zeros 2 21 2 and 1 The polynomial of lowest degree is P x

Latoya deposits the same amount of money into a bank account every month The table below shows the amount of money in the account after diffe mounts of time Time months 6 Money dollars 423 Answer the following questions 8 10 533 643 dollars a How much money was already in the account when Latoya started depositing money 12 753 b Choose the statement that best describes how the time and the amount of money in the account are related Then give the value requested As time increases the amount of money in the account decreases At what rate is the amount of money in the account decreasing dollars per month O As time increases the amount of money in the account increases At what rate is the amount of money in the account increasing dollars per month 8 08 X 5

Find the 3 degree polynomial with real coefficients depicted in the image below Note that 4i is a root of the polynomial Put your answer in the expanded form ax bx cx d 5 2 0 20 20 0 16 5

b w N 3x 81y6x4 y J3

Consider the function f z 9 12z 3x Determine without graphing whether the function has an absolute maximum or absolute minimum Determine the value and location of the maximum or minimum Use these characteristics to determine the domain and range of f Report the domain and range using interval notation The function f has an Select an answer of The domain of fis The range of f is which occurs at I

Use division to rewrite the rational expression and use translations to sketch the graph by hand Then generate an accurate depiction of the function with a graphing calculator 3x 5 X 2 Choose the corect grapi celow OA B Q G OC OD Determine an accurate depiction of f x with a graphing calculator Choose the correct graph below Use the viewing window 16 16 21x1 16 16 21 OA OD Q G o O

In this question we introduce a new definition Definition An n x n matrix is called happy if H On and H HT a Show that I is happy b Find a 2 x 2 happy matrix H I2 c Find all possible values for the determinant of a happy matrix H d Show that if H is an invertible happy matrix then H is hanni

Consider a generic quadratic function f x ax bx c with characteristics described below Determine the domain and range of f The vertex of the graph of f is 12 29 The graph of f a parabola opens downward The domain of f is The range of f is

The height in feet of a ball thrown by a child is modeled by the quadratic equation 1 12 f x 1 2x 3 where I is the horizontal distance in feet from the point at which the ball is thrown Use f to answer the following questions Round solutions to three decimal places if necessary How high is the ball when it leaves the child s hand feet How far away from the child does the ball reach its maximum height feet What is the maximum height the ball feet How far from the child does the ball strike the ground feet

Find the 3rd degree polynomial with real coefficients depicted in the image below Note that 2i is a root of the polynomial Put your answer in the expanded form ax bx cx d 5 0 0 2 1 0 5

Perform the operation below Enter your answer as a complex number in standard form 2 5i 3 7i

Find all complex roots real and or imaginary for the following polynomial Enter multiple answers separated by a comma f x x 4x 14x 20 roots

Create a 3rd degree polynomial with real coefficients and a leading coefficient of 1 which has the roots below 2 2 3i Put your answer in the expanded form ax3 bx cx d

Ise division to rewrite the rational expression and use translations to sketch the graph by hand Then generate an mccurate depiction of the function with a graphing calculator f x X 5 X 6 Which of the following transformations are used to obtain the graph of f x from the graph of y Select all that apply A Shift the graph 1 unit upward B Shift the graph 6 units to the left c Reflect the graph about the y axis D Shift the graph 6 units to the right E Stretch the graph vertically by a factor of 6 OF Reflect the graph about the x axis G Shift the graph 1 unit downward H Shrink the graph horizontally by a factor of 6 Stretch the graph horizontally by a factor of 6 Shrink the an

NASA launches a rocket at t 0 seconds Its position height in meters above sea level as a function of time t is given by s t 4 9t 67t 290 Use this position function to answer the following questions Round solutions to three decimal places if necessary Assuming that the rocket will splash down into the ocean at what time does splashdown occur The rocket splashes down after seconds How many seconds after the launch does the rocket reach its peak height The rocket reaches its peak height seconds after launch How high above sea level does the rocket get at its peak The rocket peaks at meters above sea level

Explain how the graph of the function f x can be obtained from the graph of y Then graph t and give the domain and range 1 To obtain the graph of f stretch the graph of y OA 9 Graph the function f x Choose the correct graph below Q G B x The domain of f x is Type your answer in interval notation vertically by a factor of 9 G OC Q OD o G

Explain how the graph of the function f x 2 can be obtained from the graph of y Then graph f and give domain and range To obtain the graph of 1 shift the graph of y The domain of f x is up Graph the function f x 2 Choose the correct graph below C 2 unit s G OD a a

Based on the graph find the range of y f x 7 f x 10 x if x 0 if x 0 Ay 10 5 10 0 7 5 10 OA 10 10 OB 0 U 0 00 OC 0 0 U 0 U 0 0 OD 0 00 W

Which of the graphs below have domain o 6 U 6 00 Q Q Q A 461 B L Use the letters below the graphs to answer the following question Graph s has have domain 6 U 6 00 Use a comma to separate answers as needed 10 C 1245 Q 2 16 X D

Write f x 3 5 x as the composition of two functions

A person standing close to the edge on top of a 56 foot building throws a ball vertically upward The quadratic function s t 16t 104t 56 models the ball s height above the ground in feet t seconds after it was thrown After how many seconds does the ball reach its maximum height seconds What is the maximum height of the ball feet W How many seconds does it take until the ball hits the ground seconds

Find the quadratic function that models the data in the table below 3 4 5 6 7 40 65 96 133 21 X y 2 1 0 5 16 0 1 1 2 8 8 176 9 10 280 225 The equation of the quadratic function that models the given data is y x x 0

1 point Consider the matrix 0 A Answer 7 x 368 15T 3 3 x 9 x 9 and let B be a matrix similar to A i e B is of the form SAS for some nonsingular matrix S Find all possible values of a so that det B 0 Separate multiple values by a comma

Set f x 54x6 45x5 102x69x 35x 16x 4 Plot the function on the interval 2 2 and use Newton s Method to find all five roots in the interval Determine for which roots Newton converges linearly and for which the convergence is quadratic

5 Prove that if x is rational then x is rational

A quadratic function has its vertex at the point 9 9 The function passes through the point 5 1 When written in standard form the function is f x a zh k where

Find all real solutions of the following Check your results 1 X 4 4 2 x 4x 2 Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The solution s is are and the extraneous solution s is are Type exact answers using radicals as needed Use a comma to separate answers as needed OB The solution s is are and there are no extraneous solutions Type an exact answer using radicals as needed Use a comma to separate answers as needed OC There are no real solutions but an extraneous solution of Type an exact answer using radicals as needed Use a comma to separate answers as needed D There are no real solutions

In the electric currect flow it is found that the resistance measured in the units called ohms offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire If a wire 0 01 in in diameter has a resistance of 0 427 ohm what is the resistance of a wire of the same length and material with diameter 0 0249 in to the nearest ten thousandth The resistance of a wire is sohm Round your answer to the nearest ten thousandth C

Let y f a be the piecewise defined function given below a f 2 b f 1 c For what values of r is f x 0 help numbers Domain Range help numbers help inequalities x 1 d Find the domain and range of f You may find it helpful to graph this function on your own paper to find the domain and range Your answers must be inequalities not intervals help inequalities help inequalities f x 0 x 1 if a 1 if 1 x 1 if a 1

The weight y of a fiddler crab is directly proportional to the 1 25 power of the weight x of its claws A crab with a body weight of 1 8 grams has claws weighing 1 1 grams Estimate the weight of fiddler crab with claws weighing 0 85 gram The crab weighs approximately grams Type an integer or decimal rounded to the nearest hundredth as needed

1 point Find the determinant of the matrix M and use the adjoint method to find M det M 2 2x 6 2x 4x x 1 x 2x 10 6x 20 12x M 18881 0 0 3 3x

Use a calculator to solve the equation on the interval 0 0 2n cos 0 0 52 IXE What are the solutions in the interval 0 0 2n Select the correct choice and fill in any answer boxes in choice below A The solution set is Type your answer in radians Round to two decimal places as needed Use a comma to separate answers as needed OB There is no solution

A pole 5 feet tall is used to support a guy wire for a tower which runs from the tower to a metal stake in the ground After placing the pole Camden measures the distance from the pole to the stake and from the pole to the tower as shown in the diagram below Find the length of the guy wire to the nearest foot t to scale 19 ft 5 ft 12 ft Oct 8 3 40 US 9

Part 1 of 4 Use the vertex and intercepts to sketch the graph of the quadratic function Give the equation for the parabola s axis of symmetry Use the parabola to identify the function s domain and range f x 4 x 1 2 Use the graphing tool to graph the equation Use the vertex and the y intercept when drawing the graph Click to enlarge graph CIE Ay 20 12 Q

Given f x 2x 4x 8 answer the following questions Vertex Axis of Symmetry Y Intercept Minimum Type your answer as a coordinate point without spaces Type your answer as an equation without spaces Type your answer as a coordinate point without spaces GRAPH THE QUADRATIC IN YOUR NOTEBOOK

POSSIBLE POINTS 2 A ball is thrown up in the air The function that represents the path of the ball is f t 16t2 80t 4 where f is the height in feet and t is the time in seconds What is the maximum height that the ball reaches feet

Write an equation for a parabola with x intercepts 4 0 and 3 0 which passes through the point 1 20 Write the equation

Solve the following inequality x 9x 8 0 Select the correct choice below and if necessary fill in the answer box OA The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB There is no real solution

Write an equation in factored form for a parabola with x intercepts 2 0 and 4 0 and goes through the point 1 4 f x a x b x c a b C Type your answer as a fraction

Factor the expression completely 7x 7x 84 7x 7x 84

Identify the interval s on which the function f x x 2x 3 is positive CHOOSE ALL THAT APPLY x 2 x 2 x 1 x 3 x 3 x 3 x 1 x 2 x 1 x 2 0x 1 x 3

Solve the quadratic equation by factoring 7x 8 1 Write your answer as an integer or an improper fraction X X

Factor f x 2x 92 5 f x b Type your factors without spaces

ation of the cos 20 3 2 What are the solutions to cos 20 3 in the interval 0 0 2n Select the correct choice below and if necessary fill in the answer box to complete your choice 2 OA The solution set is 0 Simplify your answer Type an exact answer using as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to separate as needed OB There is no solution

ll 2x 3 5 Determine the y intercept of a line with a slope of 2 that is a tangent to the curve y y 1 2x 4x 5