Quadratic equations Questions and Answers

A triangle has side lengths of 25 and 28 and an included angle measuring 78 degrees Find the area of th triangle Round your final answer to 4 decimal places units Area

If two opposite sides of a square are increased by 5 meters and the other sides are decreased by 3 meters the area of the rectangle that is formed is 84 square meters Find the area of the original square Must use a quadratic equation to solve the problem

Find the volume of the solid formed by rotating the following region contained in the first quadrant about the y axis f x e 16 x 1 9 Volume Find exact value it will involve T

Money is transferred continuously into an account at the constant rate of 80 000 per year The account earns interest at the annual rate of 4 5 compounded continuously How much will be in the account at the end of 7 years Round to the nearest dollar

Estimating Average Rate of Change from Data Table 11 9 gives the U S gross domestic product data in billions of dollars for the years 2004 2012 Table 11 9 U S Gross Domestic Product Data Year Amount billions of dollars 2004 10 908 2005 11 631 2006 12 364 2007 13 362 2008 13 995 2009 14 297 2010 14 044 2011 14 582 2012 15 094 Source http www tradingeconomics com united states gdp a Find the average rate of change of the gross domestic product from 2006 to 2007 and then from 2010 to 2011 b Find a quadratic regression model for the data in Table 11 9 and overlay its graph on a scatter plot of the data Let x 0 stand for 2004 x 1 stand for 2005 and so forth e Use the model in part b and a calculator NDER computation to estimate the rate of change of the gross domestic product in 2006 and in 2010

Determine the distance across a river to point A to point B point C is downriver 500m from point B the angle of point C to point A is 28

A member of a collegiate track and field team recently adopted a new training regimen His times s in the 400 meter event began to improve as described by the 46 where s is his time and t is the number of months since 2 60 function s 1 e beginning the new training regimen Determine k if his times have improved 1 0 second after 6 months Substitute t 0 to determine his 400 m time before the training change Round to the nearest thousandth 0 360 month 1 0 167 month 1 0 021 month 2 946 month 1 0 339 month 1

An investment is expected to pay 8 per year compounded continuously If you want the value of the investment to be 600 000 after 25 years how much should you invest initially Round to the nearest dollar O 162 402 O 260 753 81 201 40 601

An initial investment of 1000 doubles in value in 7 3 years Assuming continuous compounding what was the interest rate Round to the nearest tenth of a percent O 4 7 100 9 5 4 1 7 3

The population P of a bacteria culture is modeled by P 3300e where t is the time in hours If the population of the culture was 5800 after 40 hours how long does it take for the population to double Round to the nearest tenth of an hour 51 0 hours 7 0 hours 43 7 hours 69 3 hours 45 5 hours

What is the half life of a radioactive substance if 2 4 g decays to 0 80 g in 65 hours Round to the nearest tenth of an hour 30 8 hours 41 0 hours O 26 4 hours O 20 5 hours O 10 3 hours

An initial investment of 2000 grows at an annual interest rate of 7 compounded continuously How long will it take to double the investment 9 90 years O 1 year 9 29 years O 10 90 years O 10 29 years

Siven that 4i is a zero factor the following polynomial function completely Use the Conjugate Roots Theorem if applicable f x x x 14x 16x Answer 480

Dolores invests 8200 in a new savings account which earns 5 9 annual interest compounded quarterly What will be the value of her investment after 3 years Round to the nearest cent Interest formu Keyp

6 65 y x 2x 8 2 y 3x 7 65 6x 4y 3z 5 3y 12 2z y 6

Tell whether each sentence below is true or false 1 Higher degree systems can have more than one pair of solutions 65 2 66 The value of a determinant can be found by cross multiplying and adding the products

me concentration C t of a certain drug in the bloodstream after t minutes is given by the formula C t 0 04 1 e 0 21 What is the oncentration after 5 minutes Round to three decimal places nswerHow to enter your answer opens in new window 2 Points K Keyboard SH

4 Given the rational function 4m2 100 2 7m 15 match each term with its appropriate value or point Hole Vertical Asymptote X intercept y intercept Horizontal Asymptote DRAG DROP THE ANSWER 5 0 x 1 5 y 2 0 6 X 5

14 a A boat that can travel fifteen miles per hour in still water can travel thirty six miles downstream in the same amount of time that it can travel twenty fo upstream Find the speed of the current in the river Hint Rate speed of the vehicle with no current wind speed of the water or wind Part A Set up the equation Part B Solve for the rate of the water current Remember to use the table Distance Rate Time

a Monique solves the equation B Step 4 15 x 5 C Step 2 155 8x x 5 x 8x X 5 15 x 8x x 5 155 x 5 0x 8x 15 0 x 5 x 3 x 5 0 x 3 0 x 5 x 3 x 8 as shown She identified 5 and 3 as solution x 5 Monique s teacher tells her that she made an error somewhere In which step did Monique first make her error A Step 1 Ste 1 Step 2 Step 3 Step 4 Step 5 Step 6

12 Select all the solutions to the following equation 4n 20 1 n 2 n 2 A 4 B 23 D 3 C 4 23 3 n 4n 3 n 3n 10

8 Which of the following best represents the graph of f x A B y 0 1 2x 4

2 Subtract the two rational expressions and write your answer in simplest form 8 x 4 x 36 22 16

Simplify the following expression 4y 24y 2y 2y y2 2y 3 y2 3y 18

3 4 The point 6 3 lies on the terminal arm of a rotation angle 0 Determine the exact value of sin in simplified terms 1 5 3 5

Simplify Do not use a calculator or round to a decimal 48 243 11

Simplify Assume all variables represent positive values Do not use a calculator or round to a decimal Write the exact most simplified form 49 7245 11

Evaluate each of the following a 125 b 216 c 343

Solve y 7x 2 10x 2 using the quadratic formula

Graph the function Compare the graph to the graph of f x xt 5 g x 3x 2 8 Transformations 1 2 Write a quadratic function in VERTEX FORM whose graph satisfies the given conditions 6 a Vertex of 5 2 and passes through 7 0 b Vertex 4 6 and passes through 2 18

Find the zeros of the function 3 y 5x x 2 x 6 9 h x 2x 20x 50x 10 y 3x 48x

Graph the function be sure to graph the axis of symmetry Compare the graph to the graph of f x x 1 g x 3x 10 2 r x x 4 3 Transformations 1 2 XemV Transformations 1 2 ONT

Find the area between y x 2 2x 1 and y 5 x 2

See your levels Write 117 200 as a decimal number Submit

quation and sketch the graph of the function 4 0 3 x 3 0

Section 12 5 Homework Write the partial fraction decomposition of the given rational expres 9 3x 2 5x 2 What is the partial fraction decomposition

Solve 17x 2 1 4x over the set of complex numbers

Between Radians and Degrees Converting degrees to radians is just as easy Here s how we get the formula 1 radian becomes T 180 180 degrees radian 1 degree In your own words explain how we created the new formula

equation of a circle with diameter endpoints of 2 5 6 3

A quadratic function y f x is plotted on a graph and the vertex of the resulting parabola is 6 5 What is the vertex of the function defined as g x f x 2

Suppose 2 adults produce 62 6lb of garbage in one week At this rate how many pounds will 40 adults prode

quadra ers must be ALL CAPS with no spaces 19 Escape Room 7 x 12x 11 M 11 1 ormula to reveal the three letter code P No Solution 20 21 6x 140 11x N 4 5 Q 5 5 2x 8x 13 O 1 11 R 4 42 4 42 2 2

Find the measure of the angle indicated 13 Find m Q 6 61 14x 6 128

Change 2x 5x 1 f x by putting the quadratic function in standard form vertex form using the method of completing the square so it has this form f x a x h k Find vertex h k

VA town has a population of 7000 and grows at 4 every year What will be the population after 13 years to the nearest whole number

on Planet B is 100 to 3 If an elephant weighs 2800 pounds on Planet A find the elephant s weight on Planet B

f x x 1 x 1 i determine f x and ii graph f x and f x on the same axe 16 y

Find the standard form of the equation of the hyperbola with the given characteristics Vertices 1 2 3 2 passes through the point 5 6 y 1 16 x 1 24 33 1

You deposit 675 in a savings account that earns 6 interest compounded monthly Write a function that represe balance after t years

32 Find the inverse of the function a f x 4x 1 d f x x 2 b f x x 8 e f x x 3 c f x 2x 6 f f x 3 x 8