Chapter 6 Review Exercises

Chapter 6 Review Exercises

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.

Exercise (PageIndex{1})

  1. (11 c^{4}-23 c^{2}+1)
  2. (9 p^{3}+6 p^{2}-p-5)
  3. (frac{3}{7} x+frac{5}{14})
  4. 10
  5. 2y−12

Exercise (PageIndex{2})

  1. (a^{2}-b^{2})
  2. 24(d^{3})
  3. (x^{2}+8 x-10)
  4. (m^{2} n^{2}-2 m n+6)
  5. (7 y^{3}+y^{2}-2 y-4)
  1. binomial
  2. monomial
  3. trinomial
  4. trinomial
  5. other polynomial

Determine the Degree of Polynomials

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

Exercise (PageIndex{3})

  1. (3 x^{2}+9 x+10)
  2. 14(a^{2} b c)
  3. 6y+1
  4. (n^{3}-4 n^{2}+2 n-8)
  5. −19

Exercise (PageIndex{4})

  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
  1. 3
  2. 4
  3. 2
  4. 4
  5. 0

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Exercise (PageIndex{5})

(5 y^{3}+8 y^{3})

Exercise (PageIndex{6})

(-14 k+19 k)



Exercise (PageIndex{7})


Exercise (PageIndex{8})




Exercise (PageIndex{9})


Exercise (PageIndex{2})

(3 m^{2}+7 n^{2}-3 m^{2})



Exercise (PageIndex{3})

(6 x^{2} y-4 x+8 x y^{2})

Exercise (PageIndex{4})




Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Exercise (PageIndex{5})

(left(5 x^{2}+12 x+1 ight)+left(6 x^{2}-8 x+3 ight))

Exercise (PageIndex{6})

(left(9 p^{2}-5 p+3 ight)+left(4 p^{2}-4 ight))


(13 p^{2}-5 p-1)

Exercise (PageIndex{7})

(left(10 m^{2}-8 m-1 ight)-left(5 m^{2}+m-2 ight))

Exercise (PageIndex{8})

(left(7 y^{2}-8 y ight)-(y-4))


(7 y^{2}-9 y+4)

Exercise (PageIndex{9})

(left(3 s^{2}+10 ight)) from (left(15 s^{2}-2 s+8 ight))

Exercise (PageIndex{10})

Find the sum of (left(a^{2}+6 a+9 ight)) and (left(5 a^{3}-7 ight))


(5 a^{3}+a^{2}+6 a+2)

Evaluate a Polynomial for a Given Value of the Variable

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

Exercise (PageIndex{11})

Evaluate (3 y^{2}-y+1) when:

  1. y=5
  2. y=−1
  3. y=0

Exercise (PageIndex{12})

Evaluate 10−12x when:

  1. x=3
  2. x=0
  3. x=−1
  1. −26
  2. 10
  3. 22

Exercise (PageIndex{13})

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.

Exercise (PageIndex{14})

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.



Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

Exercise (PageIndex{15})


Exercise (PageIndex{16})




Exercise (PageIndex{17})

(left(frac{2}{9} ight)^{2})

Exercise (PageIndex{18})




Exercise (PageIndex{19})


Exercise (PageIndex{20})




Simplify Expressions Using the Product Property for Exponents

In the following exercises, simplify each expression.

Exercise (PageIndex{21})

(x^{4} cdot x^{3})

Exercise (PageIndex{22})

(p^{15} cdot p^{16})



Exercise (PageIndex{23})

(4^{10} cdot 4^{6})

Exercise (PageIndex{24})

8(cdot 8^{5})



Exercise (PageIndex{25})

(n cdot n^{2} cdot n^{4})

Exercise (PageIndex{26})

(y^{c} cdot y^{3})



Simplify Expressions Using the Power Property for Exponents

In the following exercises, simplify each expression.

Exercise (PageIndex{27})

(left(m^{3} ight)^{5})

Exercise (PageIndex{28})

(left(5^{3} ight)^{2})



Exercise (PageIndex{29})

(left(y^{4} ight)^{x})

Exercise (PageIndex{30})

(left(3^{r} ight)^{s})


(3^{r s})

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

Exercise (PageIndex{31})

((4 a)^{2})

Exercise (PageIndex{32})

((-5 y)^{3})


(-125 y^{3})

Exercise (PageIndex{33})

((2 m n)^{5})

Exercise (PageIndex{34})

((10 x y z)^{3})


1000(x^{3} y^{3} z^{3})

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

Exercise (PageIndex{35})

(left(p^{2} ight)^{5} cdotleft(p^{3} ight)^{6})

Exercise (PageIndex{36})

(left(4 a^{3} b^{2} ight)^{3})


64(a^{9} b^{6})

Exercise (PageIndex{37})

((5 x)^{2}(7 x))

Exercise (PageIndex{38})

(left(2 q^{3} ight)^{4}(3 q)^{2})



Exercise (PageIndex{39})

(left(frac{1}{3} x^{2} ight)^{2}left(frac{1}{2} x ight)^{3})

Exercise (PageIndex{40})

(left(frac{2}{5} m^{2} n ight)^{3})


(frac{8}{125} m^{6} n^{3})

Multiply Monomials

In the following exercises 8, multiply the monomials.

Exercise (PageIndex{41})

(left(-15 x^{2} ight)left(6 x^{4} ight))

Exercise (PageIndex{42})

(left(-9 n^{7} ight)(-16 n))



Exercise (PageIndex{43})

(left(7 p^{5} q^{3} ight)left(8 p q^{9} ight))

Exercise (PageIndex{44})

(left(frac{5}{9} a b^{2} ight)left(27 a b^{3} ight))


15(a^{2} b^{5})

Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

Exercise (PageIndex{45})


Exercise (PageIndex{46})




Exercise (PageIndex{47})


Exercise (PageIndex{48})



(p^{2}+3 p)

Exercise (PageIndex{49})


Exercise (PageIndex{50})



(-12 u^{2}-42 u)

Exercise (PageIndex{51})

9(left(b^{2}+6 b+8 ight))

Exercise (PageIndex{52})

3(q^{2}left(q^{2}-7 q+6 ight) 3)


(3 q^{4}-21 q^{3}+18 q^{2})

Exercise (PageIndex{53})

((5 z-1) z)

Exercise (PageIndex{54})

((b-4) cdot 11)



Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using:

  1. the Distributive Property,
  2. the FOIL method,
  3. the Vertical Method.

Exercise (PageIndex{55})


Exercise (PageIndex{56})


  1. (12 y^{2}-44y+35)
  2. (12 y^{2}-44y+35)
  3. (12 y^{2}-44y+35)

In the following exercises, multiply the binomials. Use any method.

Exercise (PageIndex{57})


Exercise (PageIndex{58})



(y^{2}-12 y+32)

Exercise (PageIndex{59})


Exercise (PageIndex{60})



(q^{2}+13 q-48)

Exercise (PageIndex{61})


Exercise (PageIndex{62})

(left(u^{2}+6 ight)left(u^{2}-5 ight))



Exercise (PageIndex{63})


Exercise (PageIndex{64})



(16 m^{2} n^{2}-2 m n-3)

Multiply a Trinomial by a Binomial

In the following exercises, multiply using

  1. the Distributive Property,
  2. the Vertical Method.

Exercise (PageIndex{65})

((n+1)left(n^{2}+5 n-2 ight))

Exercise (PageIndex{66})

((3 x-4)left(6 x^{2}+x-10 ight))

  1. (18 x^{3}-21 x^{2}-34 x+40)
  2. (18 x^{3}-21 x^{2}-34 x+40)

In the following exercises, multiply. Use either method.

Exercise (PageIndex{67})

((y-2)left(y^{2}-8 y+9 ight))

Exercise (PageIndex{68})

((7 m+1)left(m^{2}-10 m-3 ight))


(7 m^{3}-69 m^{2}-31 m-3)

Special Products

Square a Binomial Using the Binomial Squares Pattern

In the following exercises, square each binomial using the Binomial Squares Pattern.

Exercise (PageIndex{69})


Exercise (PageIndex{70})



(q^{2}-30 q+225)

Exercise (PageIndex{71})

(left(x+frac{1}{3} ight)^{2})

Exercise (PageIndex{72})

((8 u+1)^{2})


(64 u^{2}+16 u+1)

Exercise (PageIndex{73})

(left(3 n^{3}-2 ight)^{2})

Exercise (PageIndex{74})

((4 a-3 b)^{2})


(16 a^{2}-24 a b+9 b^{2})

Multiply Conjugates Using the Product of Conjugates Pattern

In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.

Exercise (PageIndex{75})


Exercise (PageIndex{76})

(left(y+frac{2}{5} ight)left(y-frac{2}{5} ight))



Exercise (PageIndex{77})

((12 c+13)(12 c-13))

Exercise (PageIndex{78})




Exercise (PageIndex{79})

(left(u+frac{3}{4} v ight)left(u-frac{3}{4} v ight))

Exercise (PageIndex{80})

(left(5 p^{4}-4 q^{3} ight)left(5 p^{4}+4 q^{3} ight))


(25 p^{8}-16 q^{6})

Recognize and Use the Appropriate Special Product Pattern

In the following exercises, find each product.

Exercise (PageIndex{81})

((3 m+10)^{2})

Exercise (PageIndex{82})



(36 a^{2}-121)

Exercise (PageIndex{83})


Exercise (PageIndex{84})

(left(c^{4}+9 d ight)^{2})


(c^{8}+18 c^{4} d+81 d^{2})

Exercise (PageIndex{85})

(left(p^{5}+q^{5} ight)left(p^{5}-q^{5} ight))

Exercise (PageIndex{86})

(left(a^{2}+4 b ight)left(4 a-b^{2} ight))


(4 a^{3}+3 a^{2} b-4 b^{3})

Divide Monomials

Simplify Expressions Using the Quotient Property for Exponents

In the following exercises, simplify.

Exercise (PageIndex{87})


Exercise (PageIndex{88})




Exercise (PageIndex{89})


Exercise (PageIndex{90})




Exercise (PageIndex{91})


Exercise (PageIndex{92})




Simplify Expressions with Zero Exponents

In the following exercises, simplify.

Exercise (PageIndex{93})


Exercise (PageIndex{94})




Exercise (PageIndex{95})


Exercise (PageIndex{96})

(left(-12^{0} ight)(-12)^{0})



Exercise (PageIndex{97})


Exercise (PageIndex{98})

((25 x)^{0})



Exercise (PageIndex{99})

(19 n^{0}-25 m^{0})

Exercise (PageIndex{100})

((19 n)^{0}-(25 m)^{0})



Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

Exercise (PageIndex{101})

(left(frac{2}{5} ight)^{3})

Exercise (PageIndex{102})

(left(frac{m}{3} ight)^{4})



Exercise (PageIndex{103})

(left(frac{r}{s} ight)^{8})

Exercise (PageIndex{104})

(left(frac{x}{2 y} ight)^{6})


(frac{x^{6}}{64 y^{6}})

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

Exercise (PageIndex{105})

(frac{left(x^{3} ight)^{5}}{x^{9}})

Exercise (PageIndex{106})

(frac{n^{10}}{left(n^{5} ight)^{2}})



Exercise (PageIndex{107})

(left(frac{q^{6}}{q^{8}} ight)^{3})

Exercise (PageIndex{108})

(left(frac{r^{8}}{r^{3}} ight)^{4})



Exercise (PageIndex{109})

(left(frac{c^{2}}{d^{5}} ight)^{9})

Exercise (PageIndex{110})

(left(frac{3 x^{4}}{2 y^{2}} ight)^{5})


(frac{343 x^{20}}{32 y^{10}})

Exercise (PageIndex{111})

(left(frac{v^{3} v^{9}}{v^{6}} ight)^{4})

Exercise (PageIndex{112})

(frac{left(3 n^{2} ight)^{4}left(-5 n^{4} ight)^{3}}{left(-2 n^{5} ight)^{2}})


(-frac{10,125 n^{10}}{4})

Divide Monomials

In the following exercises, divide the monomials.

Exercise (PageIndex{113})

(-65 y^{14} div 5 y^{2})

Exercise (PageIndex{114})

(frac{64 a^{5} b^{9}}{-16 a^{10} b^{3}})


(-frac{4 b^{6}}{a^{5}})

Exercise (PageIndex{115})

(frac{144 x^{15} y^{8} z^{3}}{18 x^{10} y^{2} z^{12}})

Exercise (PageIndex{116})

(frac{left(8 p^{6} q^{2} ight)left(9 p^{3} q^{5} ight)}{16 p^{8} q^{7}})


(frac{9 p}{2})

Divide Polynomials

Divide a Polynomial by a Monomial

In the following exercises, divide each polynomial by the monomial.

Exercise (PageIndex{117})

(frac{42 z^{2}-18 z}{6})

Exercise (PageIndex{118})

(left(35 x^{2}-75 x ight) div 5 x)



Exercise (PageIndex{119})

(frac{81 n^{4}+105 n^{2}}{-3})

Exercise (PageIndex{120})

(frac{550 p^{6}-300 p^{4}}{10 p^{3}})


(55 p^{3}-30 p)

Exercise (PageIndex{121})

(left(63 x y^{3}+56 x^{2} y^{4} ight) div(7 x y))

Exercise (PageIndex{122})

(frac{96 a^{5} b^{2}-48 a^{4} b^{3}-56 a^{2} b^{4}}{8 a b^{2}})


(12 a^{4}-6 a^{3} b-7 a b^{2})

Exercise (PageIndex{123})

(frac{57 m^{2}-12 m+1}{-3 m})

Exercise (PageIndex{124})

(frac{105 y^{5}+50 y^{3}-5 y}{5 y^{3}})


(21 y^{2}+10-frac{1}{y^{2}})

Divide a Polynomial by a Binomial

In the following exercises, divide each polynomial by the binomial.

Exercise (PageIndex{125})

(left(k^{2}-2 k-99 ight) div(k+9))

Exercise (PageIndex{126})

(left(v^{2}-16 v+64 ight) div(v-8))



Exercise (PageIndex{127})

(left(3 x^{2}-8 x-35 ight) div(x-5))

Exercise (PageIndex{128})

(left(n^{2}-3 n-14 ight) div(n+3))



Exercise (PageIndex{129})

(left(4 m^{3}+m-5 ight) div(m-1))

Exercise (PageIndex{130})

(left(u^{3}-8 ight) div(u-2))


(u^{2}+2 u+4)

Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

Exercise (PageIndex{131})


Exercise (PageIndex{132})




Exercise (PageIndex{133})

3(cdot 4^{-3})

Exercise (PageIndex{134})

((6 u)^{-3})


(frac{1}{216 u^{3}})

Exercise (PageIndex{135})

(left(frac{2}{5} ight)^{-1})

Exercise (PageIndex{136})

(left(frac{3}{4} ight)^{-2})



Simplify Expressions with Integer Exponents

In the following exercises, simplify.

Exercise (PageIndex{137})

(p^{-2} cdot p^{8})

Exercise (PageIndex{138})

(q^{-6} cdot q^{-5})



Exercise (PageIndex{139})

(left(c^{-2} d ight)left(c^{-3} d^{-2} ight))

Exercise (PageIndex{140})

(left(y^{8} ight)^{-1})



Exercise (PageIndex{141})

(left(q^{-4} ight)^{-3})

Exercise (PageIndex{142})




Exercise (PageIndex{143})


Exercise (PageIndex{144})




Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

Exercise (PageIndex{145})


Exercise (PageIndex{146})



(4.29 imes 10^{-3})

Exercise (PageIndex{147})

The thickness of a dime is about 0.053 inches.

Exercise (PageIndex{148})

In 2015, the population of the world was about 7,200,000,000 people.


(7.2 imes 10^{9})

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

Exercise (PageIndex{149})

(3.8 imes 10^{5})

Exercise (PageIndex{150})

(1.5 imes 10^{10})



Exercise (PageIndex{151})

(9.1 imes 10^{-7})

Exercise (PageIndex{152})

(5.5 imes 10^{-1})



Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

Exercise (PageIndex{153})

(left(2 imes 10^{5} ight)left(4 imes 10^{-3} ight))

Exercise (PageIndex{154})

(left(3.5 imes 10^{-2} ight)left(6.2 imes 10^{-1} ight))



In the following exercises, divide and write your answer in decimal form.

Exercise (PageIndex{155})

(frac{8 imes 10^{5}}{4 imes 10^{-1}})

Exercise (PageIndex{156})

(frac{9 imes 10^{-5}}{3 imes 10^{2}})



Chapter Practice Test

Exercise (PageIndex{1})

For the polynomial (10 x^{4}+9 y^{2}-1)
ⓐ Is it a monomial, binomial, or trinomial?
ⓑ What is its degree?

In the following exercises, simplify each expression.

Exercise (PageIndex{2})

(left(12 a^{2}-7 a+4 ight)+left(3 a^{2}+8 a-10 ight))


(15 a^{2}+a-6)

Exercise (PageIndex{3})

(left(9 p^{2}-5 p+1 ight)-left(2 p^{2}-6 ight))

Exercise (PageIndex{4})

(left(-frac{2}{5} ight)^{3})



Exercise (PageIndex{5})

(u cdot u^{4})

Exercise (PageIndex{6})

(left(4 a^{3} b^{5} ight)^{2})


16(a^{6} b^{10})

Exercise (PageIndex{7})

(left(-9 r^{4} s^{5} ight)left(4 r s^{7} ight))

Exercise (PageIndex{8})

3(kleft(k^{2}-7 k+13 ight))


(3 k^{3}-21 k^{2}+39 k)

Exercise (PageIndex{9})


Exercise (PageIndex{10})



(9 v^{2}-86 v+45)

Exercise (PageIndex{11})


Exercise (PageIndex{12})

((n-6)left(n^{2}-5 n+4 ight))


(n^{3}-11 n^{2}+34 n-24)

Exercise (PageIndex{13})

((2 x-15 y)(5 x+7 y))

Exercise (PageIndex{14})

((7 p-5)(7 p+5))


(49 p^{2}-25)

Exercise (PageIndex{15})

((9 v-2)^{2})

Exercise (PageIndex{16})




Exercise (PageIndex{17})

(left(frac{m^{4} cdot m}{m^{3}} ight)^{6})

Exercise (PageIndex{18})

(left(87 x^{15} y^{3} z^{22} ight)^{0})



Exercise (PageIndex{19})

(frac{80 c^{8} d^{2}}{16 c d^{10}})

Exercise (PageIndex{20})

(frac{12 x^{2}+42 x-6}{2 x})


(6 x+21-frac{3}{x})

Exercise (PageIndex{21})

(left(70 x y^{4}+95 x^{3} y ight) div 5 x y)

Exercise (PageIndex{22})

(frac{64 x^{3}-1}{4 x-1})


(16 x^{2}+4 x+1)

Exercise (PageIndex{23})

(left(y^{2}-5 y-18 ight) div(y+3))

Exercise (PageIndex{24})




Exercise (PageIndex{25})

((4 m)^{-3})

Exercise (PageIndex{26})

(q^{-4} cdot q^{-5})



Exercise (PageIndex{27})


Exercise (PageIndex{28})

Convert 83,000,000 to scientific notation.


(8.3 imes 10^{7})

Exercise (PageIndex{29})

Convert (6.91 imes 10^{-5}) to decimal form.

In the following exercises, simplify, and write your answer in decimal form.

Exercise (PageIndex{30})

(left(3.4 imes 10^{9} ight)left(2.2 imes 10^{-5} ight))



Exercise (PageIndex{31})

(frac{8.4 imes 10^{-3}}{4 imes 10^{3}})

Exercise (PageIndex{32})

A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial (-16 t^{2}+1000) gives the height of the package t seconds a after it was dropped. Find the height when t=6 seconds.


424 feet

Chapter 6, Review Exercises, Question 041 |Incorrect. The values in the table below are values of an exponential function y = ab. Find the function. 0 | 3 12 15 25 3.125 y 50 1.5625 Enter the exact answer. Note that "y =" is already provided. Do not include this in your submitted response to this question. 50 (0.793700526)* Edit Open Show Work Click if you would like to Show Work for this question:


Image Transcriptionclose

Chapter 6, Review Exercises, Question 041 |Incorrect. The values in the table below are values of an exponential function y = ab. Find the function. 0 | 3 12 15 25 3.125 y 50 1.5625 Enter the exact answer. Note that "y =" is already provided. Do not include this in your submitted response to this question. 50 (0.793700526)* Edit Open Show Work Click if you would like to Show Work for this question:

Exercise 6 Dangerous Shopping Book Review

In this example, your teacher has asked you to write a book review for the school magazine. Below you can find an example of this task.

More exercises available:

Shopping Exercises and Puzzles

Here you can find more ways to practice this topic with various activities.

Exercise 3 - Make brief notes related to a piece of text.

Exercise 5 - Write an informal email.

Exercise 6 - Write a report, review or article.

Exercise 2 - (Question 5) Gap-filled exercises

Exercise 3 - Matching

Exercise 4 - Multiple Choice

Exercise 5 - Gap Fill Part A

Exercise 5 - Gap Fill Part B

Here are videos to help you with the reading and wrting sections.

Speaking Test Examples:

We provide free resources across the full range of levels to provide the tools to communicate in English well.

11.6 Writing from Research: End-of-Chapter Exercises

1. In this chapter, you learned strategies for generating and narrowing a topic for a research paper. Review the following list of five general topics. Use freewriting and preliminary research to narrow three of these topics to manageable size for a five- to seven-page research paper. Save your list of topics in a print or electronic file, and add to it periodically as you identify additional areas of interest.

  • Illegal immigration in the United States
  • Bias in the media
  • The role of religion in educational systems
  • The possibility of life in outer space
  • Modern-day slavery around the world

2. Working with one of the topics you have identified, use the research skills you learned in this chapter to locate three to five potentially useful print or electronic sources of information about the topic. Create a list that includes the following:

  • One subject-specific periodicals database likely to include relevant articles on your topic
  • Two articles about your topic written for an educated general audience
  • At least one article about your topic written for an audience with specialized knowledge

3. Organize your list of resources into primary and secondary sources. What makes them such? Pick one primary source and one secondary source and write a sentence or two summarizing the information that they provide. Then answer these questions:

Chapter 6 Review Exercises

∠N ≅ ∠Z and ∠MYN ≅ ∠XYZ (vertical angles), so △MYN ∼ △XYZ.

Verify that △ABC ∼ △DEF. Find the scale factor of △ABC to △DEF.

The polygons are similar. The area of one polygon is given. Find the area of the other polygon.

The polygons are similar. Find the values of x and y.

Show that the two triangles are similar.

∠Q ≅ ∠MPN (corresponding angles) and ∠N ≅ ∠N, so △LNQ ∼ △MNP.

Sow that the triangles are similar and write a similarity statement. Explain our reasoning.

∠ACB ≅ ∠DCE and CE/CB = DC/AC, so △ABC ∼ △DEC.

Find the value of the variable.

The polygons are similar. The area of one polygon is given. Find the area of the other polygon.

In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.

no Corresponding side lengths are not proportional.

A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is 5 feet 4 inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot?

You can use a proportion to fi nd the height x. Write 5 feet 4 inches as 64 inches so that you can form two ratios of feet to inches.

x ft / 64 in. = 50 ft / 40 in.

Write proportion of side lengths.

40x = 3200 Cross Products Property

The flagpole is 80 feet tall.

Certain sections of stained glass are sold in triangular, beveled pieces. Which of the three beveled pieces, if any, are similar?

The pieces with side lengths of 5.25 inches and 7 inches (blue and red)

In a perspective drawing, lines that are parallel in real life must
meet at a vanishing point on the horizon. To make the train cars
in the drawing appear equal in length, they are drawn so that the
lines connecting the opposite corners of each car are parallel.
Find the length of the bottom edge of the drawing of Car 2.

The length of car 2 is approximately 4.3 cm in the drawing.

Primary level of prevention: Nurses have to prevent disease before happen such as immunization programs. Nurses have to provide practice advice about exercis.

Orem viewed her clients as “biopsychosocial beings, capable and willing to provide care for themselves and dependent others” (Comley, 1994, p. 756). The self.

A Nurse and Dietitian need to collaborate between each other for instance if a patient came into hospital and was malnourished, a nurse would then refer them.

According to American Holistic Nursing Association (AHNA), the goal of holistic nursing is to heal the person as whole being (what is holistic nursing, 2016).

Prenatal care will screen the women for her own personal health issues and for those that may affect the unborn fetus. In addition, it will allow the healthc.

Introduction Holism defined by the American Holistic Nurses Association as a “state of harmony among body, mind, emotions and spirit within an ever-changing.

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C. Reconsideration and Appeals

Where researchers do not receive ethics approval, or receive approval conditional on revisions that they find compromise the feasibility or integrity of the proposed research, they are entitled to reconsideration by the REB. If that is not successful, they may appeal using the established appeal mechanism in accordance with the institution’s procedures.

Reconsideration of Research Ethics Board Decisions

Article 6.18

Researchers have the right to request, and REBs have an obligation to provide, prompt reconsideration of decisions affecting a research project.


Researchers and REBs should make every effort to resolve disagreements they may have through deliberation, consultation or advice. If a disagreement between the researcher and the REB cannot be resolved through reconsideration, the researcher shall have the option of appealing the REB decisions through the established appeal mechanism (Article 6.19). REBs should establish timelines to promptly conduct reconsiderations and issue their decisions.

The onus is on researchers to justify the grounds on which they request reconsideration by the REB and to indicate any alleged breaches to the established research ethics review process, or any elements of the REB decision that are not supported by this Policy.

Appeal of Research Ethics Board Decisions

Article 6.19

Institutions shall have an established mechanism and a procedure in place for promptly handling appeals from researchers when, after reconsideration, the REB has refused ethics approval of the research.


In cases when researchers and REBs cannot reach agreement through reconsideration, the institution shall provide access to an established appeal process for the review of an REB decision. The researcher and the REB must have fully exhausted the reconsideration process, and the REB must have issued a final decision before the researcher initiates an appeal.

Based on its written institutional policies, the same authority that established the REB shall establish or appoint an appeal committee that reflects a range of expertise and knowledge similar to that of the REB, and that meets the procedural requirements of this Policy. An appeal committee may be an ad hoc or a permanent committee. Members of the REB whose decision is under appeal shall not serve on that appeal committee.

It should be stressed that the appeal process is not a substitute for REBs and researchers working closely together to ensure high quality ethical research, nor is it a forum to merely seek a second opinion.

Institutions may wish to explore regional cooperation or alliances, including the sharing of appeal boards. If two institutions decide to use each other’s REB as an appeal board, a formal letter of agreement between institutions is required (Chapter 8).

It is not the role of the three federal research agencies that are responsible for this Policy to consider any appeals of REB decisions.

Article 6.20

The appeal committee shall have the authority to review negative decisions made by an REB. In so doing, it may approve, reject or request modifications to the research proposal. Its decision on behalf of the institution shall be final.


Researchers have the right to request an appeal of an REB decision. An appeal can be launched for procedural or substantive reasons. The onus is on the researchers to justify the grounds on which they request an appeal and to indicate any breaches to the research ethics review process or any elements of the REB decision that are not supported by this Policy.

The appeal committee shall function impartially, provide a fair hearing to those involved, and provide reasoned and appropriately documented opinions and decisions. Both the researcher and a representative of the REB shall be granted the opportunity to address the appeal committee, but neither shall be present when the appeal committee deliberates and makes a decision. Appeal committee decisions on behalf of the institution shall be final and should be communicated in writing (in print or by electronic means) to researchers and to the REB whose decision was appealed. Recourse to judicial review may be available to the researcher.

NCERT Solutions for Class 10 Science Chapter 6 Life Processes (Hindi Medium)

Class 10 Science Life Processes Mind Map

Nutrition is the process by which source of energy (food) is transferred from outside the body of the organism to the inside. Most of the food sources are also carbon-based on Earth and depending on the complexity of these carbon sources different organisms use different kinds of nutritional processes.
Autotrophic Nutrition: Carbon and energy requirements of the autotrophic organism are fulfilled by photosynthesis.

  • It is the process by which autotrophs convert carbon dioxide & water into carbohydrate in the presence of sunlight and chlorophyll. Oxygen is the byproduct.
  • The following events occur during this process:
  • Absorption of light energy by chlorophyll.
  • Conversion of light energy to chemical energy and splitting of water molecules into hydrogen and oxygen.
  • Reduction of carbon dioxide to carbohydrates.

Heterotrophic Nutrition: Heterotrophs depend on other organisms for their nutrition.

  • Saprophytes: They break-down the food material outside the body and then absorb it, also termed as extra-cellular digestion. E.g. fungi like bread moulds, yeast, mushrooms etc.
  • Parasites: Derive nutrition from plants or animals without killing them. E.g. cuscuta (amar-bel), ticks, lice, leeches, tape-worms etc.
  • Holozoic nutrition: These organisms take in whole material & break it down inside their bodies. E.g. cow, deer, lion, tiger, humans etc. What can be taken in and broken down depends on body design and functioning

It is the process by which organism uses the food material to produce energy. Diverse organisms do this in different ways:

Energy released during cellular respiration is immediately used to synthesise ATP which is used to fuel all other activities in the cell. Aerobic organisms need to ensure that there is sufficient intake of oxygen:
• Plants: Exchange of gases takes place through stomata by simple diffusion. Large inter-cellular spaces ensure that all cells are in contact with air. Direction of diffusion depends upon the environmental conditions and the requirements of the plant. For e.g. CO2 elimination majorly takes place at night while oxygen release is the major event of the day time.
• Aquatic animals such as fishes take in water through their mouths & force it past the gills where the dissolved oxygen is taken up by blood.
• In human beings, the passage of air can be written as nostril → trachea → bronchi → bronchioles → alveolar sac. The alveoli provide a surface where the exchange of gases can take place. Blood releases the dissolved CO2 into the alveoli & carries O2 from alveolar air. Haemoglobin in RBC of blood transport O2 from lungs to various tissues of the body.

Life Process
The processes which maintain the body functions and are required for the survival of living being are called life processes. Some of the important life processes are nutrition, respiration, transportation, excretion etc.

Nutrition In Human Beings
The alimentary canal is a long tube extending from the mouth to the anus. The nutrition in human being is divided into five steps:
• Ingestion: Intake of food from outside source. Teeth & saliva crush the food to generate the particles of same size & texture. The food is then passed to stomach via oesophagus. The peristaltic movements occur all along the gut which helps in pushing the food forward.
• Digestion: In mouth, salivary amylase helps in carbohydrates digestion. In stomach, pepsin helps in protein digestion. However, small intestine is the main site of complete digestion of carbohydrates, proteins & fats. It receives pancreas and liver secretions. Bile juice emulsifies fats and pancreatic enzymes, trypsin & lipases digest proteins & emulsified fats. It finally converts proteins to amino acids, complex carbohydrates into glucose & fats into fatty acids & glycerol.
• Absorption: The digested food is taken up by the walls of the intestine. The inner lining of the small intestine has numerous finger-like projections called villi which increase the surface area for absorption. Large intestine absorbs water from the unabsorbed food.
• Assimilation: The villi are richly supplied with blood vessels which take the absorbed food to each & every cell of the body, where it is required either for energy, build up or repair.
• Excretion: The waste material is removed from the body via anus which is regulated by anal sphincter.

Transportation in Human Beings

  • Blood consists of fluid medium called plasma in which
    the cells are suspended. Plasma transports food, CO2 & nitrogenous wastes in dissolved form. Oxygen is carried by RBC.
  • Heart: Heart is the muscular organ made up of cardiac muscles and is as big as our fist. It is composed of four chambers (2 atria & 2 ventricles) to prevent the mixing of oxygenated & deoxygenated blood.
  • Ventricles are thick wailed as they have to pump the blood to various organs of the body. In addition, valves are also present in heart and veins to prevent the backflow of the blood.

Circulation of blood: Oxygenated blood is carried out from lungs to the left atrium with the help of pulmonary’ veins.

  • Left atrium contracts to release blood into the left ventricle which relaxes while collecting it. It then pumped out the blood to whole body via aorta.
    a Deoxygenated blood from whole body then enters the right atrium via vena cava vein.
  • Right atrium contracts to pump the blood in right ventricle. It then pumps the blood towards lungs via pulmonary’ artery for oxygenation.

Oxygenation of blood: Invertebrates such as birds, mammals etc which constantly use energy to maintain their body temperature, blood goes through heart twice during each cycle which is known as double circulation.

  • In contrast, animals like amphibians or many reptiles have three-chambered hearts as they can tolerate some mixing of the oxygenated & de-oxygenated blood streams. They do not use energy for thermoregulation and body temperature depends on the temperature in the environment.
  • Fishes, on other hand, have only two chambered heart. Blood is pumped to the gills for oxygenation and passes directly to the rest of the body.

Transportation In Plants
There are two main pathways present in plants: xylem pathway- moves water & minerals from the soil & phloem transports products of photosynthesis from leaves (where they are synthesized) to other parts of the plant.
Transport of Water

  • In xylem tissue, vessels and tracheids of roots, stems & leaves are interconnected to form a continuous system of water-conducting channels reaching all parts of the plant.
  • At root site, cells actively take up ions from soil which creates concentration gradient. Water then diffuses into the root cells in order to eliminate this gradient.
  • It provides steady movement of water into root xylem, creating a column of water that is steadily pushed upwards.
  • However, it is not efficient enough to push water over the heights of tall plants.
  • So, plants use other method which is known as transpiration to push water upwards. The loss of water in the form of vapour from aerial parts of plant is known as transpiration.
  • Evaporation of water molecules from the cells of a leaf creates a suction which pulls water from the xylem cells of roots. It also aids in thermoregulation.
  • Transport of food and other substances
  • Transport of soluble products of photosynthesis is called translocation.
  • The translocation takes place in sieve tubes with the help of adjacent companion cells both in upward & downward directions.
  • It utilizes energy (ATP) in contrast to xylem transport.
  • Material like sucrose is transferred into phloem tissue using energy from ATP.
  • It increases osmotic pressure of tissue causing water to move into it.
  • This pressure moves the material in phloem to tissues which have less pressure.
  • It allows phloem to move material according to plant’s needs.

The biological process involved in removal of harmful metabolic wastes from body is called excretion.
Many unicellular organisms remove these wastes by simple diffusion from body surface into surrounding water. However, complex multi-cellular organisms use specialised organs to perform this function.
Excretion in Human Beings: The excretory system includes pair of kidneys, pair of ureters, urinary bladder & urethra.

  • Nephrons are the functional units of kidneys. They are the clusters of thin-walled capillaries. Each cluster is associated with cup-shaped end (Bowmans capsule) of a tube that collects the filtered urine.
  • Substance such as glucose, amino acids, salts & a major amount of water are selectively re-absorbed as the urine flows along the tube. The amount of water depends up on amount of excess water & dissolved waste in the body.
  • The urine formed in each kidney is carried to urinary bladder by ureter. Urine is stored in urinary bladder until the pressure of the expanded bladder leads to the urge to pass it out through the urethra.
  • Excretion in Plants: They get rid of excess water by transpiration.
  • Many plant waste products are stored in cellular vacuoles.
  • Waste products may be stored in leaves that fall off.
  • In addition, some waste products are stored as resins & gums, especially in old xylem.
  • Lastly, plants excrete some waste substances into the soil around them.

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