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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

4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
Andrew Reply
divide 3x⁴-4x³-3x-1 by x-3
Ritik Reply
how to multiply the monomial
Ceny 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 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin 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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