Quadratic equations Questions and Answers

Give the center and radius of the circle represented by the equation 4x 16x 4y 4y 127 0 The center of the circle is The radius of the circle is Type an ordered pair using integers or fractions Type an integer or a simplified fraction

5 A trigonometric equation in the form a sinx b c sinx d 0 where a b c d E N has 3 solutions in 0 2 The conditions that are required are A a b c d B a b c d C a b c d D a b c d

The table contains price demand and total cost data for the production of extreme cold sleeping bags where p is the wholesale price in dollars of a sleeping bag for an annual demand of x sleeping bags and C is the total cost in dollars of producing x sleeping bags Complete parts A through C below CLOS X 950 1 150 1 900 2 050 B Find a linear regression equation for the cost data using x as the independent variable C x 46 864 x 92 868 217 Round to three decimal places as needed profit P 230 220 160 125 A Find a quadratic regression equation for the price demand data using x as the independent variable p x 0 000084 0 163134 x 148 0621 Round the constant to four decimal places as needed Round all other values to six decimal places as needed C 135 000 150 000 180 000 190 000 C What is the form of the equation for profit Write the profit function in terms of the variables from the table x p and C

According to 2010 U S census the population of Sebastian was 21 749 The 2020 U S census found that the population of Sebastian had grown to 26 186 Use the exponential growth model Y Yekt where t is the number of years after 2010 to write an exponential growth function for the city of Sebastian Round the growth constant k to four significant figures The exponential growth function that models the population of Sebastian is Use the population growth model to predict the population of Sebastian in year 2032 Round the solution to the nearest whole number The model predicts that the population of Sebastian in 2032 will be Determine the year when model predicts the population of Sebastian will be 39 032 Round the solution to the nearest whole number According to the model the population of Sebastian will be 39 032 in the year

2 Choose the correct graph on the right C Q O

For the function f x 6x 7 determine whether f x is one to one If so a write an equation for the inverse function in the form y f x b graph fand f1 on the same axes and c give the domain and the range of f and f If the function is not one to one say so G OA The domain off is and the range of fis Type your answers in interval notation c Give the domain and range of f and f1 Begin by finding the domain and range of f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice OA The domain of f is and the range of f Type your answers in interval notation OB The function is not one to one Give the domain and the range of f1 Select the correct choice below and if necessary fill in any answer boxes to complete your choice B The function is not one to one d 4

Each letter of the alphabet is assigned a numerical value according to its position in the alphabet Encode the message NEED HELP using the one to one function defined f x x 4 Give the inverse function that the decoder would need when the message is received Write the encoded message Use space to separate the numbers

Find a set of parametric equations to represent the graph of the rectangular equation using t x and t 1 x Enter your answers as comma separated lists of equations x 3y 2 a c x x 4 y 1 2 3 b 7 1 x x 1 4 y 2 t 3 Very nice

Find the partial fraction decomposition for the following rational expressic 2 2 x 18x 81

Rewrite the given expression using natural logarithms only log129 log129 Use a calculator to approximate the value of log129 Round the solution to four decimal places necessary 4 log129

g x logg 1 1 The domain of g is

f log 8 4x The domain of f is 2 00 X

Question 5 7 1 15 Part 2 of 3 Determine the remaining sides and angles of the triangle ABC What is the measure of angle B O 44 6 Simplify your answer Type an integer or a decimal What is the length of side a Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed CIL B HW Score 25 O Points 0 of 62 6 ft 20 2 115 2

Solve the logarithmic equation X 10log 6

in exponential form log 636 2 Write the equivalent exponential equation Type an equation Type your answer using exponential notation Do not sim

Solve the logarithmic equation x log 5 125

Find the area of the triangle ABC a 12 62 in b 5 16 in C 13 73 Question 12 7 1 55 What is the area of the triangle 7 8 in2 Simplify your answer Type an integer or decimal rounded to the nearest tenth as needed

ample of 400 g of radioactive lead 210 decays to polonium 210 according to the function A t 400e 0 032t where t is time in years Find the amount of radioactive lead remaining af 4 yr b 8 yr c 10 yr d Find the half life The amount of radioactive lead remaining after 4 yr will be und to the nearest integer as needed g

Find the doubling time of an investment earning 3 interest if interest is compounded continuously The doubling time of an investment earning 3 interest if interest is compounded continuously is years Round to the nearest tenth of a year

value of a large copy machine during the first 5 years of use a What is the value of the copier after 2 years and 3 months After 2 years and 3 months the copier is worth b What is the salvage value of the copier if it is replaced after 5 years After 5 years the salvage value of the copier is 500 O c State the domain of this function o 0 d Sketch the graph of this function 18000 16000 14000 12000 t 3500t 18000 where Vis value and it is time in years can be used te 10000 8000 6000 4000 2000 Clear All Draw What is the range of the function After how many years will the copier be worth only years the copier will be worth only After 1800 Round to 2 decimal place

In a mountain range of California the percent of moisture that falls as snow rather than rain can be approximated by the function p h 76 In h 602 where h is the altitude in and p h is the percent of an annual snow fall at the altitude h Use the function to approximate the amount of snow at the altitudes 5000 feet and 7000 feet The percent of annual precipitation that falls as snow at 5000 feet is approximately Round to the nearest integer

How much time will be needed for 21 000 to grow to 24 371 36 if deposited at 6 kt compounded quarterly For calculating use the formula A P 1 P 1 7 year s The amount 21 000 will grow to 24 371 36 in Do not round until the final answer Then round to the nearest tenth as neede

Solve the equation Give the solution in exact form log 3 6x 1 1 Rewrite the given equation without logarithms Do not solve for x

a Find the decibel rating of a sound d 10 log having intensity 1 000 000 000 000lo where lo is the initial intensit lo 1 b If the intensity of a sound is tripled by how much is the decibel rating increased a Find the decibel rating of a sound having intensity 1 000 000 000 0001 where lo is the initial intensity The decibel rating of this sound is 120 b If the intensity of a sound is tripled by how much is the decibel rating increased The decibel rating of the sound increases by about decibels Round to the nearest integer as needed

Use the change of base theorem to find the logarithm log 21 Use the change of base theorem to rewrite the given expression in terms of natural logarithms or common logarithms log 21 log Do not evaluate Do not simplify Evaluate the expression log 21 log21 Simplify your answer Do not round until the final answer Then round to four decimal places as needed

log 25 log25 0 Simplify your answer Do not round until the final answer Then round to four decimal places as needed

Use the parent function f x log z and transformation techniques to graph h z log x 6 2 Also indicate which transformation s is are applied Determine the domain range and vertical asymptote of h Select all transformations that apply Horizontally compress the graph of f by a factor of 6 Reflect the graph of f about the z axis Shift the graph of f 6 units to the left Shift the graph of f 2 units up Vertically compress the graph of f by a factor of 2 Vertically stretch the graph of f by a factor of 2 Reflect the graph of f about the y axis Shift the graph of f 6 units to the right Shift the graph of f 2 units down Horizontally stretch the graph of f by a factor of 6

If 0 is an acute angle and sin0 y express the other five trigonometric values As a function of y sin cos 0 1

of the pool OA S that is 4 m deep and full of water has a viewing window on one of its vertical walls Find the force on a window that is a circle with a radius of 1 5 m tangent to the bottom Using the center of the window as the origin find the width function w y for each value of y on the face of the window w y 2 2 25 Set up the integral that should be used to find the total force on the window Use the center of the window as the origin 0 0 with the y axis passing through the left side of the window Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers OB dx dy

deltamath com The function f x log x 3 4 is graphed below Plot all lattice points of the inverse Use the labeled points as your guide 10 9 8 Draw Graph Click on the graph to plot a point Click a point to delete it 10 9 8 7 6 5 4 3 2 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 Reset 1 2 3 4 5 6 7 8 9 10

10 a 5 points Solve for x and round the answer to the nearest tenth 5 11 b 5 points Evaluate the logarithm without using a calculator log4 32

10 Given find sin O B tan 0 2 3 where T 2 T and csc 2 where 0 TC 2

Distinguishing accuracy and precision Four research teams measured the speed at which signals travel down a certain type of nerve fiber and what each team wrote in its team notebook is shown in the table below Suppose a later and more reliable measurement gives 75 0 m s for the signal speed in the same type of nerve fiber Decide which of the earlier measurements was the most accurate and which was the most precise team A B C D what was written in the notebook 70 0m s 65 0m s 0 5m s 85 m s 6 0 between 70 0m s and 75 0m s Alexi most accurate measurement most precise measurement

11 21 11 21 B 2 A 21 12 D E 21

1 point The figure 6 4 y 6 4 2 EN 2 X 4 shows the graph of the function

9 8 7 5 4 3 2 1 9 8 7 6 5 4 3 2 1 H 2 n 5 6 on 9 A X 1 2 3 4 5 6 7 8 9 Write an equation for the ellipse graphed in standard form

Factor out the greatest common factor from the polynomial 2k m4 4k8m4 10k m5 2k m 4k8m4 10k m5 Simplify your answer

Rationalize the denominator Assume that the variable is positive 7 98y 7 www

Rationalize the denominator Assume that the variable is positive 5 2x 5

Rationalize the denominator Assume all variables are positive 5 7 5 m n4 7 3 4 11

Rationalize the denominator Assume that the variable is positive 63

Click here to watch the video Rationalize the denominator Simplify if possible 4 3 1 4 3 1

Rationalize the denominator and simplify Assume that all variables represent positive real numbers 5 10x 5 10x

Rationalize the denominator Simplify if possible 5 4 5 3 5 4 5 3

Rationalize the denominator Assume that the variable is positive 12 p 12

Multiply and simplify 5 8 3 3 6 3 5 8 3 3 6 3 0

Multiply and simplify 5 7 5 7

54 7 2 54 7 2

The diagram shows the stem and leaf tables of the weights of two groups 20 years olds from towns A and B town A 7 5100 642 6 5 1 7 9 9 8 7 4 0 8 6 4 2 2 2 1 6 7 8 9 10 2234 1 7 8 0 4 4 4 6 0 2 3 5 2 3 3 4 59 6679 How many people were weighed in town B What was the modal group in town B What was the modal weight in town A What was the median weight in town B kg kg kg What was the range of weights in town B On average which group was heavier A or B or are they equal E town B Key 7 5 75kg kq 1 2 1 2 2 2 Mai EN

x 11x 30 0