Write each of the following statements in Exercises 1\u201312 as a mathematical expression. State whether or not the expression is linear or nonlinear. If it is nonlinear, then explain why.<\/p>\n
Exercise 1.
\nThe sum of a number and four times the number
\nAnswer:
\nLet x be a number; then, x+4x is a linear expression.<\/p>\n
Exercise 2.
\nThe product of five and a number
\nAnswer:
\nLet x be a number; then, 5x is a linear expression.<\/p>\n
Exercise 3. Exercise 4. Exercise 5. Exercise 6. Exercise 7. Exercise 8. Exercise 9. Exercise 10. Exercise 11. Exercise 12. Students practice writing expressions and identifying them as linear or nonlinear.<\/p>\n Write each of the following statements as a mathematical expression. State whether the expression is linear or nonlinear. If it is nonlinear, then explain why.<\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Write each of the following statements as a mathematical expression. State whether the expression is a linear or nonlinear expression in x.<\/p>\n Question 1. Question 2. Question 3. Engage NY Eureka Math 8th Grade Module 4 Lesson 2 Answer Key Eureka Math Grade 8 Module 4 Lesson 2 Exercise Answer Key Write each of the following statements in Exercises 1\u201312 as a mathematical expression. State whether or not the expression is linear or nonlinear. If it is nonlinear, then explain why. Exercise 1. … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84914"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=84914"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84914\/revisions"}],"predecessor-version":[{"id":137266,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84914\/revisions\/137266"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=84914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=84914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=84914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nMultiply six and the reciprocal of the quotient of a number and seven.
\nAnswer:
\nLet x be a number; then, 6\u2219\\(\\frac{7}{x}\\) is a nonlinear expression. The expression is nonlinear because the number
\n\\(\\frac{7}{x}\\)=7\u2219\\(\\frac{1}{x}\\)=7\u2219x-1<\/sup>. The exponent of the x is the reason it is not a linear expression.<\/p>\n
\nTwice a number subtracted from four times a number, added to 15
\nAnswer:
\nLet x be a number; then, 15+(4x-2x) is a linear expression.<\/p>\n
\nThe square of the sum of six and a number
\nAnswer:
\nLet x be a number; then,(x+6)2<\/sup> is a nonlinear expression. When you multiply(x+6)2<\/sup>, you get x2<\/sup>+12x+36. The x2<\/sup> is the reason it is not a linear expression.<\/p>\n
\nThe cube of a positive number divided by the square of the same positive number
\nAnswer:
\nLet x be a number; then, \\(\\frac{x^{3}}{x^{2}}\\) is a nonlinear expression. However, if you simplify the expression to x, then it is linear.<\/p>\n
\nThe sum of four consecutive numbers
\nAnswer:
\nLet x be the first number; then, x+(x+1)+(x+2)+(x+3) is a linear expression.<\/p>\n
\nFour subtracted from the reciprocal of a number
\nAnswer:
\nLet x be a number; then, \\(\\frac{1}{x}\\)-4 is a nonlinear expression. The term \\(\\frac{1}{x}\\) is the same as x-1<\/sup>, which is why this expression is not linear. It is possible that a student may let x be the reciprocal of a number, \\(\\frac{1}{x}\\), which would make the expression linear.<\/p>\n
\nHalf of the product of a number multiplied by itself three times
\nAnswer:
\nLet x be a number; then, \\(\\frac{1}{2}\\)\u2219x\u2219x\u2219x is a nonlinear expression. The term \\(\\frac{1}{2}\\)\u2219x\u2219x\u2219x is the same as\\(\\frac{1}{2}\\) x3<\/sup>, which is why this expression is not linear.<\/p>\n
\nThe sum that shows how many pages Maria read if she read 45 pages of a book yesterday and \\(\\frac{2}{3}\\) of the remaining pages today
\nAnswer:
\nLet x be the number of remaining pages of the book; then, 45+\\(\\frac{2}{3}\\) x is a linear expression.<\/p>\n
\nAn admission fee of $10 plus an additional $2 per game
\nAnswer:
\nLet x be the number of games; then, 10+2x is a linear expression.<\/p>\n
\nFive more than four times a number and then twice that sum
\nAnswer:
\nLet x be the number; then, 2(4x+5) is a linear expression.<\/p>\nEureka Math Grade 8 Module 4 Lesson 2 Problem Set Answer Key<\/h3>\n
\nA number decreased by three squared
\nAnswer:
\nLet x be a number; then, x-32<\/sup> is a linear expression.<\/p>\n
\nThe quotient of two and a number, subtracted from seventeen
\nAnswer:
\nLet x be a number; then, 17-\\(\\frac{2}{x}\\) is a nonlinear expression. The term \\(\\frac{2}{x}\\) is the same as 2\u2219\\(\\frac{1}{x}\\) and \\(\\frac{1}{x}\\)=x-1<\/sup>, which is why it is not linear.<\/p>\n
\nThe sum of thirteen and twice a number
\nAnswer:
\nLet x be a number; then, 13+2x is a linear expression.<\/p>\n
\n5.2 more than the product of seven and a number
\nAnswer:
\nLet x be a number; then, 5.2+7x is a linear expression.<\/p>\n
\nThe sum that represents the number of tickets sold if 35 tickets were sold Monday, half of the remaining tickets were sold on Tuesday, and 14 tickets were sold on Wednesday
\nAnswer:
\nLet x be the remaining number of tickets; then, 35+\\(\\frac{1}{2}\\) x+14 is a linear expression.<\/p>\n
\nThe product of 19 and a number, subtracted from the reciprocal of the number cubed
\nAnswer:
\nLet x be a number; then, \\(\\frac{1}{x^{3}}\\) -19x is a nonlinear expression. The term \\(\\frac{1}{x^{3}}\\) is the same as x-3<\/sup>, which is why it is not linear.<\/p>\n
\nThe product of 15 and a number, and then the product multiplied by itself four times
\nAnswer:
\nLet x be a number; then,(15x)4<\/sup> is a nonlinear expression. The expression can be written as 154<\/sup>\u2219x4<\/sup>. The exponent of 4 with a base of x is the reason it is not linear.<\/p>\n
\nA number increased by five and then divided by two
\nAnswer:
\nLet x be a number; then, \\(\\frac{x+5}{2}\\) is a linear expression.<\/p>\n
\nEight times the result of subtracting three from a number
\nAnswer:
\nLet x be a number; then, 8(x-3) is a linear expression.<\/p>\n
\nThe sum of twice a number and four times a number subtracted from the number squared
\nAnswer:
\nLet x be a number; then, x2<\/sup>-(2x+4x) is a nonlinear expression. The term x2<\/sup> is the reason it is not linear.<\/p>\n
\nOne-third of the result of three times a number that is increased by 12
\nAnswer:
\nLet x be a number; then, \\(\\frac{1}{3}\\) (3x+12) is a linear expression.<\/p>\n
\nFive times the sum of one-half and a number
\nAnswer:
\nLet x be a number; then, 5(\\(\\frac{1}{2}\\)+x) is a linear expression.<\/p>\n
\nThree-fourths of a number multiplied by seven
\nAnswer:
\nLet x be a number; then, \\(\\frac{3}{4}\\)x\u22197 is a linear expression.<\/p>\n
\nThe sum of a number and negative three, multiplied by the number
\nAnswer:
\nLet x be a number; then, (x+(-3))x is a nonlinear expression because (x+(-3))x=x2<\/sup>-3x after using the distributive property. It is nonlinear because the power of x in the term x2<\/sup> is greater than 1.<\/p>\n
\nThe square of the difference between a number and 10
\nAnswer:
\nLet x be a number; then, (x-10)2<\/sup> is a nonlinear expression because (x-10)2<\/sup>=x2<\/sup>-20x+100. The term x2<\/sup> is a positive power of x>1; therefore, this is not a linear expression.<\/p>\nEureka Math Grade 8 Module 4 Lesson 2 Exit Ticket Answer Key<\/h3>\n
\nSeven subtracted from five times a number, and then the difference added to nine times a number
\nAnswer:
\nLet x be a number; then, (5x-7)+9x. The expression is a linear expression.<\/p>\n
\nThree times a number subtracted from the product of fifteen and the reciprocal of a number
\nAnswer:
\nLet x be a number; then, 15\u2219\\(\\frac{1}{x}\\)-3x. The expression is a nonlinear expression.<\/p>\n
\nHalf of the sum of two and a number multiplied by itself three times
\nAnswer:
\nLet x be a number; then, \\(\\frac{1}{2}\\) (2+x3<\/sup>). The expression is a nonlinear expression.<\/p>\n","protected":false},"excerpt":{"rendered":"