Complex numbers Questions and Answers

Find the measure of the side of the triangle in the proportional triangles in the diagram 8 x R 36 42 X 27 A

Use a graphing calculator to determine which of the following graphs represents the algebraic function f x 5x 4x 2 2 3 2 1 1 2

7 97 Find the inverse functions for the functions given below a f x 4x 1 b g x log7x

Match the example to the figurative language Match Term She ran like the wind Ladies like to laugh at lunch I m so hungry I could eat a horse The building rumbled and groaned before crashing down The trees danced in the wind My mom is an angel Definition A Hyperbole B Personification C Simile D Metaphor E Alliteration F Onomatopoeia

The function w x x 3x is shown in the graph The function w x has what type of symmetry 64 3 2 7 2 S 3 N 31 X M 2 3 4 5 Symmetric with respect to the x axis Symmetric with respect to the y axis Symmetric with respect to the Origin The function doesn t have any of these types of symmetry XA

98 Solve each of the following equations 2 x 1 18 a b 2 3 10

Which is statement correctly describes the symmetry of an EVEN function An EVEN function is symmetric with respect to the x axis An EVEN function is symmetric with respect to the y axis An EVEN function is symmetric with respect to the origin An EVEN function is symmetric with respect to the line y x

Find the exact values of the angles that are solutions to the equation sin 0 0 5 Express your solutions in radians

Find all of the solutions of the polynomial equation x 3x 3x 3x 2 0 x 1 x 2 x t x 1 x 2 x 1 x 2 x 1 x 2

Which of the following is NOT a factor of the polynomial function shown in the graph X x d x 3 x 3 x 5 4 3 2 1 31 2 Which of the following is NOT a factor of the polynomial graphed below 23 15

Perform the indicated operation and simplify the result 4 4 6 6 x x 1 X 1 X Simplify your answer Use a comma to separate answers as needed 1 x

Divide as indicated 12x 16 X 4 OA Select the correct choice below and fill in the answer box es to complete your choice Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as nee B 9x 12 x 16 12x 16 9x 12 x 4 x 16 12x 16 X 4 9x 12 x 16 X no numbers must be excluded

Evaluate the function f x x 4x 4x a f 2 b f x 3 1 at the given values of the independent variable and simplify c f x a f 2 Simplify your answer b f x 3 Simplify your answer c f x Simplify your answer

Add the following terms if possible 420 3 125 Select the correct choice below and if necessary fill in the answer box to complete your c OA 4 20 3 125 Type an exact answer using radicals as needed OB The radicals cannot be combined

Simplify the exponential expression 69 6x y 7x y9 6 9 6x y 7x y

e the following formula for t G W Wrt Simplify your answer

Use the FOIL method to multiply the binomials 3x 4 5x 1 3x 4 5x 1 Simplify your answer

Evaluate the expression without using a calculator 125 Rewrite the expression using a radical 2 125 3 Evaluate 125 2 3 2 3 11 Do not evaluate Simplify your answer

Solve the equation using the quadratic formula 2x2 7x 1 0 The solution set is Simplify your answer Type an exact answer using radicals and i as ne

169x 196y squares Select the correct choice below and fill in any answer boxes within your choice OA 169x 196y OB The polynomial is prime

Rationalize the denominator 6 5 6 Use sqrt to input a square root into WeBWork For example sqrt 5 represents 5 Make sure to simplify all square roots completel Make sure your fraction is completely reduced a well

True or false for all real numbers x if x 1 then 2x 3 2 is a proposition True False

Factor the following polynemial given that it has a zero at 5 with multiplicity 2 x 4 1x 3 57x 3 5x 700

An amount A is initially 13 To find next year s amount we multiply this year s amount by 6 Find a formula that gives the amount A after t years

Prove that sin 2 x 45 cos 2 x 45 sin2x

A a b c d e f g x y z B c r a z y Find the following See Example 1 a n A b n B c n ANB d n A U B

The function f is given by the graph below

A television camera is positioned 4 000 ft from the base of a rocket launching pad The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight Also the mechanism f focusing the camera has to take into account the increasing distance from the camera to the rising rocket Let s assume the rocket rises vertically and its speed is 600 ft s when it has risen 3 000 ft a How fast in ft s is the distance from the television camera to the rocket changing at that moment ft s b If the television camera is always kept aimed at the rocket how fast in rad s is the camera s angle of elevation changing at that same moment rad s

raph of a polynomial function shows the lef ing polynomials represents the function de 1 4 x 6 3x 5 4x 4 5x 3 4x 2 2x 3

a cos B tan 3 4 b sin a b 3 2 and cos B c tan x 2 13 3r 2 B 2

5 The table shows the total weight of shrimp a fisherman catches each week Time weeks Weight pounds 2 3 5 6 110 170 500 530 What is the average rate of change from Week 2 to 5 in pounds per week

Use transformations of the graph of f x x2 to determine the graph of the given function h x x 5 2

9 The graph of a function f is given Use the graph off to sketch y f x A S 9

Given the conic section polar and cartesian coordinates What kind of conic section is this O parabola O circle ellipse hyperbola O none of the above 6 5 2 sin 0 Vertex vertices Polar identify the type of conic and find the vertex vertices in both Vertex vertices Cartesian Give answers as a list of one or more ordered pairs separated by commas Enter all answers in their exact

n 2 p 5q 4 asume zero Write any variables in alphebetical order the denominator does not equal

Use your graphing calculator to graph y cos1 x in degree mode Use the graph with the appropriate command to evaluate each expression a cos 1 1 1 b cos c arccos x

A D B E Which of these graphs could be the graph of y 3x 4 Give the letter of the graph as your answer C F

Line segment bar AB has endpoints at 6 1 and 7 7 Line segment bar YZ has endpoints at 9 5 and 8 11

For the equation 1 7 cos 20 t 70 180 1 9 cos 20 t 200 180 A cos 20nt 6 find suitable A and values

Find a formula for the inverse of the Answer

Graph the trigonometric function y cosx 2 Plot all points corresponding to minima and maxima within one cycle Within that cycle also plot all points along the midline points whose y coordinates midway between the function s minimum and maximum values Then click on the graph a function button 418 3 4 3 125 3m 4 L

Evaluate the expression on a calculator Express the answer in the form a bj

Convert the quantity to the inc 7 in to cm

The density 6 of the cylinder z y 25 0 3 varies with the distance r from the z axis 8 3 rg cm Find the mass of the cylinder assuming z y z are in cm mass include units

Calculate the total length of the steel needed to form the angled support section of bridge the gray lines 5m 10m 6m 3m find perimeter and show in radical form

The current in a stream moves at a rate of 7 mph If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream what is the speed of the boat in still water

Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y In x y 0 and x 8 about the y axis 3 S C A B D O 2x In x dx 2x x 8 In x dx E 2x x 8 In x dx 2xx ln x dx F 2x In x dx 2xx ln x dx

Consider the following figure mCE A Given Find 2 B D 1 mz1 76 mz2 32 mCE and mBD in degrees C E

Find the surface area of the triangular prism 10 m 7 m 8 m 6 m sq m Enter

Given f x a b c d e 2x 1 and g x 7x 8 find the following f g 2 f g x g f x gog x X fof 2 Recall the definition of a composite function What is the order of operations in evaluating a compos the output of one function affect the input of the other function