Quadratic equations Questions and Answers

Find the solution of the logarithmic equation logo x 20 log 15

5 2 x 1 3 x 2 6 x 3x 8

Extended Practice Variables on both sides Solve for the unknown in the equations shown below 1 5x 10 6x 12 2 12x 2 10x 8

5 2x 4 4x 10 6 4 2x 4x 10

1 2x 4 10 Guided Examples 2 3x 4 11

2x 20 3x 15 2x 15 3x 20

5 If 3 2 r 10 2 r 10 19 what is 4r 6 Solve for s if 10 2 s 10 4 2s 5

Scaffolded Problems 1 Given the equation 3 4 2x 5x 27 what its the value of x Distribute Combine Like Terms Constant Term Coefficient 12 6x 5x 27 12 11x 27 12 39 divided 11 x 3 5 Check Did I solve for the unknown

Find w 12w 3w 4 77 4 Solve for t 6 21 3 2 12 t 16

Practice No Calculator Solve for y 2 y 3 y 42 12 2 Solve for a 10 9 3a 2 36

5 If 6x 4 4 7 14 what is the value of x 3 6 What is the value of x 12 8x 24 12

3 What is the value of x 3 2x 7 3 4 Given 5 3x 5 4 4 find 3x 10

5 Given the equation 3 2 x 7 3 4 x find the value of 4x

Practice Calculator

Solve for x 2 x 5 4 6 Partner Practice 2 Solve for x 20 4 5 2n 8

4 x 1 3 2x 4 14 4x 4 6x 12 14 10x 16 14 X 2 16 16

Learning Target I can solve equations that require distribution and combining like terms Example Problems

15 4 points For f x 2 3x and g x x 4 find and simplify the function fog x

22 3 points The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium 137 into the atmosphere The function f x 1000 0 5 30 describes the amount f x in kilograms of cesium 137 remaining in Chernobyl x years after 1986 If even 100 kilograms of cesium 137 remain in Chernobyl s atmosphere the area is considered unsafe for human habitation Find f 80 for the function f x 1000 0 5 30 in order to determine if Chernobyl will be safe for human habitation by 2066 Round your answer to the nearest whole number

23 5 points Using the compound interest formula A P 1 2 fit A P n find accumulated value of an investment of 5000 for 10 years at an interest rate is 5 1 compounded quarterly Round your answer to the nearest cent

20 3 points Condense the logarithm expression as much as possible Be sure the final answer has coefficient of 1 log 17 log x 6log 2

13 5 points Find an equation for the line perpendicular to the line 2x 3y 6 having a y intercept of 4

For problem 14 An arrow is fired into the air the height in feet of the arrow 1 seconds after it was shot into the air is given by the function h t 161 641 5 14 4 points Find the maximum height of the arrow

21 5 points Solve for x log x log x 4 log 12

5 points Solve for x x 4 x 2

1 5 points Solve for x x 9 19 x 3 6 15 5

2 3 points Factor completely 3x 9x 30

Write the function in the form f x x k q x r for the given value of k f x x 4x 8x 12 k 2 Demonstrate that f k r f 2

5 SECURITY An important bridge crosses a river at a key location Because it is so important robotic security cameras are placed at the locations of the dots in the figure Each robot can scan x degrees On the lower bank it takes 4 robots to cover the full angle from the edge of the river to the bridge On the upper bank it takes 5 robots to cover the full angle from the edge of the river to the bridge Bridge upper bank lower bank a How are the angles that are covered by the robots at the lower and upper banks related Derive an equation that x satisfies based on this relationship b How wide is the scanning angle for each robot What are the angles that the bridge makes with the

A car rental agency rent compact midsize and luxury cars Its goal is to purchase 64 cars for a total of 1 552 000 and to earn a daily rental of 1896 from all the cars The compact cars cost 16 000 each earn 20 per day in rental the midsize cars cost 22 000 each earn 30 per day and the luxury cars cost 38 000 each and earn 42 per day Solve the system algebraically or use the rref in your graphing calculator to find how many Compact and Midsize cars the agency should purchase to meet its goal O 23 Compact and 22 Midsize 30 Compact and 22 Midsize 24 Compact and 22 Midsize O 24 Compact and 23 Midsize

10 Simplify logo b by by first applying the property for the logarithm of a product Then simplify logo b by by first applying the exponent rule for a product Explain the relationship between exponent properties and logarithm properties 3

Calculate 4 1i Give your answer in a bi form In polar form use the angle 0 0 2TT a b

What is the solution of this system of equations x 2y 6 2 2 None of the above 0 3 There are an infinite number of solutions 0 0

Consider the following 70 F Sunny Y 2 In 2 In x 1 y In 4 x 1 a Use graphing utility to graph the two equations in the same viewing window x y Y Y 15 10 15 10 Q Search 15 10 15 y 10 10 13h b Use the table feature of the graphing utility to create a table of values for each equation Round your answers to two decimal places If an answer does 0 3 G L

The graph shown below approximates the number of children in a country who lived with only their grandparents in the years from 1991 through 2009 The number of children is a function f of the year x Approximate the number of children living with only grandparents in 1991 That is find f 1991 Number of children in millions 2 5 2 4 2 3 2 2 2 1 2 04 1 9 1 8 1 74 1 6 1 5 1 4 1 3 1 2 1 1 91 93 95 97 99 01 03 05 07 09 Q 57 C The number of children living with only grandparents in 1991 is approximate million Type an integer or a decimal

For the function f x 2x 8 construct and simplify the difference quotient The difference quotient is f x h f x h

In the sequence below what term is the number 121 6 11 16 n Type a whole number

Name the integers from the list below 1 3 7 5 20 0 42 6 39 15 16 6 67 What are the integers Select all that apply A 1 4646646664 OD 15 1 4646646664 G 16 B E 3 5 1 67 H 42 C 6 39 OF 20 01 0

the product property of logarithms to write the logarithm as a sum of logarithms Then simplify if possible Assume that the variable represents a positive number log 25s Olog

g x 1 if 2 x 0 if 1 x 0 1 2 if 0 if 1 x 2 Find g 1 g 0 75 and g 1 g 1 g 0 75 g 1 2 as follows

11 7n 1 n 2n 6 A 7n 53n 27n 24 B 7n 15n 44n 6 C 16n 58n 72n 18 D 32n 28n 22n 5 12 12 x 4 7x 8x 3 A 32x 68x 37x 6 B 7x 20x 35x 12 C 21x 52x 35x 4 D 49x 28x 40x 24

3 24K 16k 3 1 274 184 274 98 4 7m 4 49 28 14m 28 12m 24

7 8k 8 k 5 A 8k 32k 40 B 8k 48k 40 C 8k 48k 40 D 8k 40 8 8 7x 1 5x 7 A 35x 54x 7 B 35x 7 C 35x 44x 7 D 35x 54x 7

Find each product 5 7p 3X6p 1 A 16p 6 p 64 B 42p 25p 3 C 16p 64p 64 D 16p 64 6 6 6k 1X72 2 A 42 19 2 B 4 16 12 C 42 52 2 D 42 2

Determine the GCF of 6x y 12xy 9x y A B C D 3r y 36xy 36x y 3xy

Factor the polynomial by grouping 4a 7a 4a 7 A 7a 9 a 4 B C 4a 7 a 1 7a 9 a 5 D 4a 7 a 2

9 96n 84n 112n 98 11 4v 12v 5v 15

2 12p 21p 28p 49 4 6v 16v 21v 56 6 214 844 154

A person purchased a used Chevrolet Cavalier for 4500 The car is expected to decrease in value by 22 each year over the next several years What would be the decay factor of a model that would represent the value of the car 0 78 0 990 0 22 1 22

7 8k 8 k 5 A 8k 32k 40 B 8k2 48k 40 C 8k 48k 40 D 8k 40 9 2a 2 3a 5a 6 A 28a 63a 19a 20 B 6a 16a 22a 12 C 10a 27a 32a 14 D 56a 29a 8a 20 11 7n 1 n 2n 6 A 7n 53n 27n 24 B 7n 15n 44n 6 C 16n 58n 72n 18 D 32n 28n 22n 5 8 10 12 8 7x 1 5x 7 A 35x 54x 7 B 35x 7 C 35x 44x 7 D 35x 54x 7 10 8n 7 7n 5n 3 A 12n 46n 14n 42 B 8n 32n 8n 48 C 15n 17n 22n 24 D 56n 89n 59n 21 12 x 4 7x 8x 3 A 32x 68x 37x 6 B 7x 20x 35x 12 C 21x 52x 35x 4 D 49x 28x 40x 24