Quadratic equations Questions and Answers

A tube with one end closed has a second resonant frequency of 3187 5 Hz The length is increased by a factor of 4 Find the new second resonant frequency Show all work

Which two triangles are congruent b the ASA Theorem Complete the congruence statement Q A R PK J U

Given the function P x 3x 4 9x 3 6x 2 intercepts are its intercept is its

Solve the following inequality and write interval notation for the solution set Then graph the solution set 1 2 Choose the correct solution set below O A OA 2 O c 2 OE O C O E There is no solution Choose the correct graph below 2 1 2 3 3 4 2 6 3 1 0 0 2 2 O B OD 4 2 6 3 B 2 12 3 3 OD 12 1 1 0

x y 4 Symmetry x axis y axis igin none of the above 2 b x y 4 Symmetry x axis y axis origin none of the above

Question 4 Find the values of a b and c for which the quadratic equation ax bx c 0 has the given numbers as solutions b 1 i 2 a 3 and 2

Question 7 Solve each equation below a x 5 2 x 1 b 2x 5 2 x 2

Question 9 Solve the absolute value equation or inequality a 112 6x 3 9 b 2x 3x 5

Question 5 A rectangular piece of metal has length twice the width Suppose squares with sides 4 in long are cut from the four corners and the flaps are folded upward to form an open box If the volume of the box is 1536 in what were the original dimensions of the piece of metal Hint Volume of a box Length x Width x Height

Question 3 Solve for y in terms of x in the equation below Write the answer in simplified form 5x 6xy 2y 1

uestion 6 Solve the rational equation 4x 3 x 1 NIX 11 x x

p 7q p 7g p 79 7q p 7q p p 7q Drag each factored form above to the polynomial it equals below 2 1 p 14pq 49q p 14pq 49q 2 p 49q

Rationalize the denominator of the radical expression P 144 p 12 Assume the variable represents a nonnegative number P 144 p 12 Simplify your answer Type an exact answer using radicals as needed Rationalize all denominators WAN

Suppose an environmental agency decides to get rid of the impurities from the water of a polluted river The estimated cost of removing x of the impurities is given by the following formula How much will i to remove 50 of the impurities C x 2x 50 x 100 x billion dollars It will cost billion dollars to remove 50 of the inpurities Round to two decimal places as needed

Match the rational exponent expression in Column I with the equivalent radical expression in Column II Assume that x is not 0 4 x 1 a 4x b 4x 1 c 4x 3 d 4x 4x 4 1 Drag the radical expressions given above to the appropriate box so they match the expression with rational exponents to which they are equivalent C 1 4x 4 x 4x 4x 11 SEXOCR

Subtract the rational expressions 10x 4 6x 7 10x 4 6x 7 8x 17 6x 7 8x 17 6x 7 Simplify your answer

Perform the addition 9 9 9 x y x y 9 Simplify your answer

Find the product or quotient 7x 7 5 3x 3 7

Simplify the rational expression If the rational expression cannot be simplified so state x 1 X 1 Select the correct choice below and fill in any answer boxes in your choice OA 3 1 x 1 11

Find and simplify the functions fg x and f g x Are they the same function f x x 5 and g x x 2 25

f a B 1 x 8 Type an exact answer using radicals as needed CIL 6 1

For the linear equation 6x 5y 60 0 the x intercept is and the y intercept is The equation in slope intercept form is y The slope of the graph of this equation is

Let ABCD be a quadrilateral with 90 degree angles ABC and ADC Explain why ABCD is cyclic and identify the center of the circumscribing circle Let diagonals AC and BD intersect at P If AC 20 BP 7 and DP 9 determine the distance from P to the center of this circle

216 r 4n Select the correct choice below and if necessary fill in the answer box to complet choice O A 216 r 4n Simplify your answer Type your answer in factored form OB The polynomial is prime

A vehicle purchased for 29800 depreciates at a constant rate of 17 each year Its value after t years ca be modeled by the equation A P 0 83 where P is the original value of the vehicle Determine the number of years that it takes for the vehicle to depreciate to 8000 Round to the nearest tenth

A line s equation is given in point slope form y 20 7 3 x 9 1 This line s slope is 2 A point on this line that is apparent from the given equation is

a 6b a 6b 6b a 6b a a 6b a 6b Drag each factored form above to the polynomial it equals below a 12ab 36b a 12ab 36b a 36b 36b a

Factor using the common factor p 3 7 5 Assume all variables represent positive real numbers p 3 7 5 p 3 2 5 p 3 5 7 5 p 3 2 5 p 3 5 p 3 7 5 Simplify your answer

Factor the polynomial m 15m Select the correct choice below and if necessary fill in the answer box to complete yo choice OA m4 15m2 34 Type your answer in factored form Factor completely B The polynomial is prime

Factor the polynomial by grouping 8st 12t2s 3 8st 12t 2s 3 Factor completely

3 2p 9 6p 4p 2p 3 4p 6p 9 2p 3 4p 6p 9 Drag each factored form above to the polynomial it equals below 8p3 27 8p3 27 27 803

ACDE the measure of ZE 90 ED 28 CE 45 and DC 53 What rati represents the tangent of ZC

A store manager determines that the revenue from shoes when the price for a pair of shoes is t dollars will be h t t 36t dollars What price should be charged to maximize revenue What will the revenue be at this price dollars dollars

Describe the real solutions for the equation 4x 9x 7 0 OTwo distinct real solutions One real solution O No real solutions

Solve y 2 y 1 17 y Enter your answers separated by commas

Consider the graph of y 2x 4x 1 Graph by plotting the vertex and the y intercept Then graph the parabola by selecting the vertex FIRST and then the y intercept 6 5 Clear All Draw 43 2 1 6 5 4 3 2 1 1 2 3 4 5 6 1 2 3 4 5 6

9 Find the center and radius of x y 14x 20y 20 10 points

x 6 Let f x 2 pts a What are the equations of the vertical asymptote s 2 pts b What are the equations of the horizontal asymptote s 2 pts c Does the graph cross the horizontal asypmtote If so where

y x 2 9 8 9 9 5 4 3 2 1 1 3 4 1 2 3 B 5

Into which quadrant does the right most tail end behavior extend for the polynomial function f x 5x x 2

8 Function Notation Let f x x 1 and find f a 2

Find the product 5x 9y 5x 9y 2

Amplitude Period 2 Midline Based on the graph above determine the amplitude period midline and equation of the furm Use f x as the output Function 3 2 t 2 5

The volume of a rectangular solid with length L width W and height H is given by the formula V LWH Use this formula to write a polynomial in standard form that models or represents the volume of the open box 8 2x 10 2x X

2 Write the equation of the function in the form of y a sin b x c d a 0 and in the form y a cos b x c d a 0 11 2 As a sine function 6 4 2 0 As a cosine function m 2 3m 2 2m 5m 2

Find the arc length of the graph of the function over the indicated interval Round your answer to three decimal places y x3 2 2 2 754 X H 3 2 WebAssign Plot

Find the inverse of f x x f x Provide your answer below

20 Write the equation of g x if it shrink vertically by a sixth then reflect across the x axis then translate seven units left and twelve units down from f x 42 x 5 8

Find the value of x in the following equation Express your answer as exact as possible or as a decimal rounded to two decimal places Separate multiple answers with a comma Answer 2 Points log 704 6 Key Keyboard Show

D x x4 6x 7x 6x 8 Step 2 of 3 Use synthetic division to identify integer bounds of the real zeros Find the least upper bound and the greatest lower bound guaranteed by the Upper and Lower Bounds of Zeros theorem AnswerHow to enter your answer opens in new window 2 Points Keypad Keyboard Shortcu