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Coin production In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.

1.545 × 10 8

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Distance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.

  1. Write the number of miles in one light year in scientific notation.
  2. Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.
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Debt At the end of fiscal year 2015 the gross United States federal government debt was estimated to be approximately $18,600,000,000,000 ($18.6 trillion), according to the Federal Budget. The population of the United States was approximately 300,000,000 people at the end of fiscal year 2015.

  1. Write the debt in scientific notation.
  2. Write the population in scientific notation.
  3. Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.

1.86 × 10 13 3 × 10 8 6.2 × 10 4

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Writing exercises

  1. Explain the meaning of the exponent in the expression 2 3 .
  2. Explain the meaning of the exponent in the expression 2 −3 .
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When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

answers will vary

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “use the definition of a negative exponent,” “simplify expressions with integer exponents,” “convert from decimal notation to scientific notation,” “convert scientific notation to decimal form,” and “multiply and divide using scientific notation.” The rest of the cells are blank.

Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?

Chapter review exercises

Section 6.1 Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.


11 c 4 23 c 2 + 1
9 p 3 + 6 p 2 p 5
3 7 x + 5 14
10
2 y 12

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a 2 b 2
24 d 3
x 2 + 8 x 10
m 2 n 2 2 m n + 6
7 y 3 + y 2 2 y 4

binomial monomial trinomial trinomial other polynomial

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Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

  1. 3 x 2 + 9 x + 10
  2. 14 a 2 b c
  3. 6 y + 1
  4. n 3 4 n 2 + 2 n 8
  5. −19
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  1. 5 p 3 8 p 2 + 10 p 4
  2. −20 q 4
  3. x 2 + 6 x + 12
  4. 23 r 2 s 2 4 r s + 5
  5. 100

3 4 2 4 0

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Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

3 m 2 + 7 n 2 3 m 2

7 n 2

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6 x 2 y 4 x + 8 x y 2

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Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

( 5 x 2 + 12 x + 1 ) + ( 6 x 2 8 x + 3 )

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( 9 p 2 5 p + 3 ) + ( 4 p 2 4 )

13 p 2 5 p 1

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( 10 m 2 8 m 1 ) ( 5 m 2 + m 2 )

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( 7 y 2 8 y ) ( y 4 )

7 y 2 9 y + 4

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Subtract
( 3 s 2 + 10 ) from ( 15 s 2 2 s + 8 )

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Find the sum of ( a 2 + 6 a + 9 ) and ( 5 a 3 7 )

5 a 3 + a 2 + 6 a + 2

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Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

Evaluate 3 y 2 y + 1 when:

  1. y = 5
  2. y = −1
  3. y = 0
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Evaluate 10 12 x when:

  1. x = 3
  2. x = 0
  3. x = −1

−26 10 22

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Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial −16 t 2 + 200 gives the height of a stone t seconds after it is dropped from the cliff. Find the height after t = 3 seconds.

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A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial −4 p 2 + 460 p . Find the revenue received when p = 75 dollars.

12,000

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Questions & Answers

The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
Edi Reply
Tickets for a show are $70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled $17,200. How many adult tickets and how many child tickets were sold?
Mum Reply
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
Edi Reply
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Jesus Reply
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Ronald Reply
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Dojzae Reply
LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?
Xona Reply
5%
Michael
hey everyone how to do algebra
The Reply
Felecia answer 1.5 hours before he reaches her
Adriana Reply
I would like to solve the problem -6/2x
rachel Reply
12x
Andrew
how
Christian
Does the x represent a number or does it need to be graphed ?
latonya
-3/x
Venugopal
-3x is correct
Atul
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year?
Stephanie Reply
Tickets for the community fair cost $12 for adults and $5 for children. On the first day of the fair, 312 tickets were sold for a total of $2204. How many adult tickets and how many child tickets were sold?
Alpha Reply
220
gayla
Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
Tsimmuaj Reply
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
? Is there anything wrong with this passage I found the total sum for 2 jobs, but found why elaborate on extra If I total one week from the store *4 would = the month than the total is = x than x can't calculate 10 month of a year
candido
what would be wong
candido
87 divided by 3 then multiply that by 4. 116 people total.
Melissa
the actual number that has 3 out of 4 of a whole pie
candido
was having a hard time finding
Teddy
use Matrices for the 2nd question
Daniel
One number is 11 less than the other number. If their sum is increased by 8, the result is 71. Find the numbers.
Tsimmuaj Reply
26 + 37 = 63 + 8 = 71
gayla
26+37=63+8=71
ziad
11+52=63+8=71
Thisha
how do we know the answer is correct?
Thisha
23 is 11 less than 37. 23+37=63. 63+8=71. that is what the question asked for.
gayla
23 +11 = 37. 23+37=63 63+8=71
Gayla
by following the question. one number is 11 less than the other number 26+11=37 so 26+37=63+8=71
Gayla
your answer did not fit the guidelines of the question 11 is 41 less than 52.
gayla
71-8-11 =52 is this correct?
Ruel
let the number is 'x' and the other number is "x-11". if their sum is increased means: x+(x-11)+8 result will be 71. so x+(x-11)+8=71 2x-11+8=71 2x-3=71 2x=71+3 2x=74 1/2(2x=74)1/2 x=37 final answer
tesfu
just new
Muwanga
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?
Tsimmuaj Reply
yes math
Kenneth
company A 13 company b 5. A 17,000+13×100=29,100 B 29,000+5×20=29,100
gayla
need help with math to do tsi test
Toocute
me too
Christian
have you tried the TSI practice test ***tsipracticetest.com
gayla
Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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