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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

Ivan has $8.75 in nickels and quarters in his desk drawer. The number of nickels is twice the number of quarters. How many coins of each type does he have?
mikayla Reply
2q=n ((2q).05) + ((q).25) = 8.75 .1q + .25q = 8.75 .35q = 8.75 q = 25 quarters 2(q) 2 (25) = 50 nickles Answer check 25 x .25 = 6.25 50 x .05 = 2.50 6.25 + 2.50 = 8.75
Melissa
John has $175 in $5 and $10 bills in his drawer. The number of $5 bills is three times the number of $10 bills. How many of each are in the drawer?
mikayla Reply
7-$10 21-$5
Robert
Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? (Round your answer to the nearest tenth of a percent.)
Parker Reply
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Markeice Reply
8mph
michele
16mph
Robert
3.8 mph
Ped
16 goes into 80 5times while 20 goes into 80 4times and is 4mph faster
Robert
what is the answer for this 3×9+28÷4-8
What Reply
315
lashonna
how do you do xsquard+7x+10=0
What
(x + 2)(x + 5), then set each factor to zero and solve for x. so, x = -2 and x = -5.
bruce
I skipped it
What
In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.
Jenise Reply
how do i set this up
Jenise
25%
Melissa
25 percent
Muzamil
950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25%
Melissa
I've tried several times it won't let me post the breakdown of how you get 25%.
Melissa
Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25%
Melissa
Finally 👍
Melissa
one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%.
bruce
twenty five percent...
Jeorge
thanks melissa
Jeorge
950000-713500 *100 and then divide by 950000 = 25
Muzamil
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
jamie Reply
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary?
Iris Reply
let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is $500.
Simply
28.50
Toi
thanks
Jeorge
How many pounds of nuts selling for $6 per pound and raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound?
Valeria Reply
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that code $20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be $10 per square foot?
Nia Reply
I need help with maths can someone help me plz.. is there a wats app group?
Cindy Reply
WY need
Fernando
How did you get $750?
Laura Reply
if y= 2x+sinx what is dy÷dx
formon25 Reply
does it teach you how to do algebra if you don't know how
Kate Reply
Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)
Lara Reply
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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