## Algebra 2 Textbooks : : Free Homework Help And Answers

Step-by-step solutions to all your Algebra 2 homework questions – Slader Free step-by-step solutions to all your questions … Algebra 2 Textbook answers Questions Review. x. Go. 1. … and Transformations 5.2 Quadratic Models 5.3 Factoring Quadratic Expressions 5.4 Quadratic Equations 5.5 Complex Numbers 5.6 Completing the Square 5.7 The …

## Sequences And Series Cumulative Assessment

Question 1.The frequencies of the notes on a piano form a geometric sequence. The frequencies of G and A are shown in the diagram. What is the approximate frequency of E at ?Answer:

Question 2.You take out a loan for $16,000 with an interest rate of 0.75% per month. At the end of each month, you make a payment of $300.a. Write a recursive rule for the balance an of the loan at the beginning of the nth month.b. How much do you owe at the beginning of the 18th month?c. How long will it take to pay off the loan?d. If you pay $350 instead of $300 each month, how long will it take to pay off the loan? How much money will you save? Explain.Answer:

Question 3.The table shows that the force F needed to loosen a certain bolt with a wrench depends on the length of the wrenchs handle. Write an equation that relates and F. Describe the relationship.Answer:

Question 4.Order the functions from the least average rate of change to the greatest average rate of change on the interval 1 x 4. Justify your answers.Answer:

Question 6.The diagram shows the bounce heights of a basketball and a baseball dropped from a height of 10 feet. On each bounce, the basketball bounces to 36% of its previous height, and the baseball bounces to 30% of its previous height. About how much greater is the total distance traveled by the basketball than the total distance traveled by the baseball?A. 1.34 feet

## Lesson 84 Finding Sums Of Infinite Geometric Series

**Essential Question** How can you find the sum of an infinite geometric series?

**EXPLORATION 1**

Finding Sums of Infinite Geometric SeriesWork with a partner. Enter each geometric series in a spreadsheet. Then use the spreadsheet to determine whether the infinite geometric series has a finite sum. If it does, find the sum. Explain your reasoning. .)

**EXPLORATION 2**

Writing a ConjectureWork with a partner. Look back at the infinite geometric series in Exploration 1. Write a conjecture about how you can determine whether the infinite geometric seriesa1 + a1r + a1r2 + a1r3 +. . .has a finite sum.

**EXPLORATION 3**

Writing a FormulaWork with a partner. In Lesson 8.3, you learned that the sum of the first n terms of a geometric series with first term a1 and common ratio r 1 isSn = a1\\)When an infinite geometric series has a finite sum, what happens to r n as n increases? Explain your reasoning. Write a formula to find the sum of an infinite geometric series. Then verify your formula by checking the sums you obtained in Exploration 1.

**Communicate Your Answer**

How can you find the sum of an infinite geometric series?Answer:

Find the sum of each infinite geometric series, if it exists.a. 1 + 0.1 + 0.01 + 0.001 + 0.0001 +. . .b. \Answer:

Question 1.Consider the infinite geometric series\Find and graph the partial sums Sn for n = 1, 2, 3, 4, and 5. Then describe what happens to Sn as n increases.Answer:

**Find the sum of the infinite geometric series, if it exists.**Question 2.\^\)Answer:

\Answer:

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## Big Ideas Math Algebra 2 Answers

Students who are in search of Big Ideas Math Algebra 2 Solutions can get them on this page. Free answers for Big Ideas Math Algebra 2 Common Core High School is available here. Get the answers to the homework questions from the math experts. Big Ideas Math encourages the growth mindset in students and also it helps the teachers to teach the students in a simple way. We have provided user-friendly solutions for all the questions in Big Ideas Math Answers Algebra 2.

## Lesson 83 Analyzing Geometric Sequences And Series

**Essential Question** How can you recognize a geometric sequence from its graph?In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. For example, in the geometric sequence 1, 2, 4, 8, . . . , the common ratio is 2.

**EXPLORATION 1**

Recognizing Graphs of Geometric SequencesWork with a partner. Determine whether each graph shows a geometric sequence. If it does, then write a rule for the nth term of the sequence and use a spreadsheet to find the sum of the first 20 terms. What do you notice about the graph of a geometric sequence?

**EXPLORATION 2**

Finding the Sum of a Geometric SequenceWork with a partner. You can write the nth term of a geometric sequence with first term a1 and common ratio r asan = a1rn-1.So, you can write the sum Sn of the first n terms of a geometric sequence asSn = a1 + a1r + a1r2 + a1r3 + . . . +a1rn-1.Rewrite this formula by finding the difference Sn rSn and solve for Sn. Then verify your rewritten formula by funding the sums of the first 20 terms of the geometric sequences inExploration 1. Compare your answers to those you obtained using a spreadsheet.

**Communicate Your Answer**

How can you recognize a geometric sequence from its graph?Answer:

Find the sum of the terms of each geometric sequence.a. 1, 2, 4, 8, . . . , 8192b. 0.1, 0.01, 0.001, 0.0001, . . . , 10-10Answer:

**Tell whether the sequence is geometric. Explain your reasoning.**Question 1.27, 9, 3, 1, \, . . .Answer:

2, 6, 24, 120, 720, . . .Answer:

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## Sequences And Series Mathematical Practices

Mathematically proficient students consider the available tools when solving a mathematical problem.

**Monitoring Progress**

**Use a spreadsheet to help you answer the question.**Question 1.A pilot flies a plane at a speed of 500 miles per hour for 4 hours. Find the total distance flown at 30-minute intervals. Describe the pattern.Answer:

Question 2.A population of 60 rabbits increases by 25% each year for 8 years. Find the population at the end of each year. Describe the type of growth.Answer:

Question 3.An endangered population has 500 members. The population declines by 10% each decade for 80 years. Find the population at the end of each decade. Describe the type of decline.Answer:

Question 4.The top eight runners finishing a race receive cash prizes. First place receives $200, second place receives $175, third place receives $150, and so on. Find the fifth through eighth place prizes. Describe the type of decline.Answer:

## Chapter : Quadratic Functions : 52 Solving Quadratic

5.3 Solving Quadratic Equations by Finding Square Roots 5.4 Complex Numbers … Home > Algebra 2 > Chapter 5 > 5.2 Solving Quadratic Equations by Factoring Chapter 5 : Quadratic Functions 5.2 Solving Quadratic Equations by Factoring. Click below for lesson resources. Make your selection below 5.2 Extra Challenges 5.2 Extra Examples …

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## Puzzle Time Did You Hear About The Trees Birthday

Solving puzzles is a way of improving the ability to solve problems

The riddle solution is **IT WAS A SAPPY ONE**

The above solution to the riddle is correct due to the following **reason**:

*Question: The parts of the question missing involves solving a equations with the result giving the values of the letters required to solve the puzzle*

1) m + 7 = 9

12) -144· = -12··k

k **= 12**

The length of a banner is 2 and a half times its width

The length of the banner is 20 ft.

Therefore, the width is **8** ft.

Part C

27 out of the 32 members in are decorating for a dance

**5** members are not decorating

**Listing **the the letters to which the **above values point to** in the matrix from the **puzzle **question gives

ITWASASAPPYONE, which reads

**IT WAS A SAPPY ONE**

Learn more about **puzzles and algebraic equations **here:

## Lesson 82 Analyzing Arithmetic Sequences And Series

**Essential Question** How can you recognize an arithmetic sequence from its graph?In an arithmetic sequence, the difference of consecutive terms, called the common difference, is constant. For example, in the arithmetic sequence 1, 4, 7, 10, . . . , the common difference is 3.

**EXPLORATION 1**

Recognizing Graphs of Arithmetic SequencesWork with a partner. Determine whether each graph shows an arithmetic sequence. If it does, then write a rule for the nth term of the sequence, and use a spreadsheet to fond the sum of the first 20 terms. What do you notice about the graph of an arithmetic sequence?

**EXPLORATION 2**

Finding the Sum of an Arithmetic SequenceWork with a partner. A teacher of German mathematician Carl Friedrich Gauss asked him to find the sum of all the whole numbers from 1 through 100. To the astonishment of his teacher, Gauss came up with the answer after only a few moments. Here is what Gauss did:Explain Gausss thought process. Then write a formula for the sum Sn of the first n terms of an arithmetic sequence. Verify your formula by finding the sums of the first 20 terms of the arithmetic sequences in Exploration 1. Compare your answers to those you obtained using a spreadsheet.

**Communicate Your Answer**

How can you recognize an arithmetic sequence from its graph?Answer:

Find the sum of the terms of each arithmetic sequence.a. 1, 4, 7, 10, . . . , 301b. 1, 2, 3, 4, . . . , 1000c. 2, 4, 6, 8, . . . , 800Answer:

Which is different? Find both answers.Answer:

\Answer:

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## Puzzle Time Answer Key Algebra 2

1, 2 5. 0.27,0 and 3.7,0 6. 0, 6 and 2, 2 7. 1, 2 and 1, 2 8. 1, 0 9. no solution 10. 3, 2 and 2, 3 11. no solution 12. 8, 32 and 2, 2 13. 4, 24 and 2,12 14. 7 3, 8 and , 8 3 15. The horizontal line is tangent to the circle either at the top or the bottom. 3.5 Enrichment and Extension …

## Pdf Alg1 Rbc Answers A

2 36 3,62 3 yx V=+ 9.4 Puzzle Time A HARE RESTORER 9.5 Start Thinking When a = 0, the Quadratic Formula is undefined because you cannot divide by zero. In this case, the function has no x2 term, and is therefore not quadratic but linear. The other situation that ma kes the Quadratic Formula undefined is when bac2 < 40. Note …

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## Sequences And Series Chapter Review

**8.1 Defining and Using Sequences and Series **

Question 1.Describe the pattern shown in the figure. Then write a rule for the nth layer of the figure, where n = 1 represents the top layer.Answer:

**Write the series using summation notation.**Question 2.

Question 12.Find the sum [la

You take a job with a starting salary of $37,000. Your employer offers you an annual raise of $1500 for the next 6 years. Write a rule for your salary in the nth year. What are your total earnings in 6 years?Answer:

**8.3 Analyzing Geometric Sequences and Series **

Question 14.Tell whether the sequence 7, 14, 28, 56, 112, . . . is geometric. Explain your reasoning.Answer:

Write a rule for the nth term of the geometric sequence. Then graph the first six terms of the sequence.Question 15.25, 10, 4, \ , . . .Answer:

Find the sum \5i1 .Answer:

**8.4 Finding Sums of Infinite Geometric Series **

Question 19.Consider the infinite geometric series 1, \ Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. Then describe what happens to Sn as n increases.Answer:

Question 20.Find the sum of the infinite geometric series 2 + \, if it exists.Answer:

Write the repeating decimal 0.1212 . . . as a fraction in simplest form.Answer:

**8.5 Using Recursive Rules with Sequences **

**Write the first six terms of the sequence.**Question 22.a1 = 7, an = an-1 + 11Answer:

a1 = 26, an = \an-1.Answer:

## Lesson 85 Using Recursive Rules With Sequences

**Essential Question** How can you define a sequence recursively?A recursive rule gives the beginning term of a sequence and a recursive equation that tells how an is related to one or more preceding terms.

**EXPLORATION 1**

Evaluating a Recursive RuleWork with a partner. Use each recursive rule and a spreadsheet to write the first six terms of the sequence. Classify the sequence as arithmetic, geometric, or neither. Explain your reasoning. .)

**EXPLORATION 2**

Work with a partner. Write a recursive rule for the sequence. Explain your reasoning.a. 3, 6, 9, 12, 15, 18, . . .b. 18, 14, 10, 6, 2, 2, . . .c. 3, 6, 12, 24, 48, 96, . . .d. 128, 64, 32, 16, 8, 4, . . .e. 5, 5, 5, 5, 5, 5, . . .f. 1, 1, 2, 3, 5, 8, . . .

**EXPLORATION 3**

Writing a Recursive RuleWork with a partner. Write a recursive rule for the sequence whose graph is shown.

**Communicate Your Answer**

How can you define a sequence recursively?Answer:

Question 5.Write a recursive rule that is different from those in Explorations 13. Write the first six terms of the sequence. Then graph the sequence and classify it as arithmetic, geometric, or neither.Answer:

**Write the first six terms of the sequence.**Question 1.a1 = 3, an = an-1 7Answer:

an= \^\)Answer:

an = \n-1Answer:

Question 39.**REWRITING A FORMULA**You have saved $82 to buy a bicycle. You save an additional $30 each month. The explicit rule an= 30n+ 82 gives the amount saved after n months. Write are cursive rule for the amount you have saved n months from now.Answer:

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## Lesson 81 Defining And Using Sequences And Series

**Essential Question** How can you write a rule for the nth term of a sequence?A sequence is an ordered list of numbers. There can be a limited number or an infinite number of terms of a sequence.a1, a2, a3, a4, . . . , an, . . .Terms of a sequenceHere is an example. 1, 4, 7, 10, . . . , 3n-2, . . .

**EXPLORATION 1**

Writing Rules for SequencesWork with a partner. Match each sequence with its graph. The horizontal axes represent n, the position of each term in the sequence. Then write a rule for the nth term of the sequence, and use the rule to find a10.a. 1, 2.5, 4, 5.5, 7, . . .b. 8, 6.5, 5, 3.5, 2, . . .c. \d. \e. \, 1, 2, 4, 8, . . .f. 8, 4, 2, 1, \, . . .

**Communicate Your Answer**

How can you write a rule for the nth term of a sequence?Answer:nth term of a sequencean = a1 + Question 3.What do you notice about the relationship between the terms in an arithmetic sequence and a geometric sequence? Justify yourAnswer:An **arithmetic sequence** has a constant **difference between** each consecutive pair of terms. This is similar to the linear functions that have the form y=mx +b. A **geometric sequence** has a constant ratio **between** each pair of consecutive terms.

**Monitoring Progress**

**Write the first six terms of the sequence.**Question 1.

Question 27.**FINDING A PATTERN**Which rule gives the total number of squares in the nth figure of the pattern shown? Justify your answer.Answer:

**In Exercises 3138, write the series using summation notation.**Question 31.7 + 10 + 13 + 16 + 19Answer:

\Answer:

\Answer:

## Big Ideas Math Book Algebra 2 Answer Key Chapter 8 Sequences And Series

Check out Big Ideas Math Algebra 2 Answers Chapter 8 Sequences and Series aligned as per the Big Ideas Math Textbooks. Use the below available links for learning the Topics of BIM Algebra 2 Chapter 8 Sequences and Series easily and quickly. You just need to tap on them and avail the underlying concepts in it and score better grades in your exams. The Solutions covered here include Questions from Chapter Tests, Review Tests, Cumulative Practice, Cumulative Assessments, Exercise Questions, etc.

\x 8 = 17Answer:8)x = \Answer:Question 10.**ABSTRACT REASONING**The graph of the exponential decay function f = bx has an asymptote y = 0. How is the graph of f different from a scatter plot consisting of the points , , , . . .? How is the graph of f similar?Answer:

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## Solutions To Big Ideas Math: Algebra 1 9781608404520

YES! Now is the time to redefine your true self using Slader’s free Big Ideas Math: Algebra 1 answers. Shed the societal and cultural narratives holding you back and let free step-by-step Big Ideas Math: Algebra 1 textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life.

## Finding Sums Of Infinite Geometric Series 84 Exercises

**Vocabulary and Core Concept Check**Question 1.The sum Sn of the first n terms of an infinite series is called a ________.Answer:

Question 2.**WRITING**Explain how to tell whether the series \a1ri1 has a sum.Answer:

**Monitoring Progress and Modeling with Mathematics**

In Exercises 36, consider the infinite geometric series. Find and graph the partial sums Sn for n= 1, 2, 3, 4, and 5. Then describe what happens to Sn as n increases.Question 3.\Answer:

Question 4.\Answer:

4 + \Answer:

2 + \Answer:

**In Exercises 714, find the sum of the infinite geometric series, if it exists.**Question 7.\^\)Answer:

\^\)Answer:

\^\)Answer:

\^\)Answer:

2 + \Answer:

-5 2 \Answer:

3 + \Answer:

\Answer:

**ERROR ANALYSIS** In Exercises 15 and 16, describe and correct the error in finding the sum of the infinite geometric series.Question 15.

Question 17.**MODELING WITH MATHEMATICS**You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet. On each successive swing, your cousin travels 75% of the distance of the previous swing. What is the total distance your cousin swings?Answer:

Question 18.**MODELING WITH MATHEMATICS**A company had a profit of $350,000 in its first year. Since then, the companys profit has decreased by 12% per year. Assuming this trend continues, what is the total profit the company can make over the course of its lifetime? Justify your answer.Answer:

Answer:

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