2015-16 Lesson 2: Linear and Non-Linear Expressions in 8β’4 G8-M4-Lesson 2: Linear and Non-Linear Expressions in 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. 1. A number added to five cubed Let be a number; then, + is a linear expression. 2. The quotient of seven and a number, added to twenty-five Let be a number; then, + is a nonlinear expression. The term is the same as β
and = β , which is why it is not linear. 3. The sum that represents the number of hotdogs sold if 148 hotdogs were sold Thursday, half of the remaining hotdogs were sold on Friday, and 203 hotdogs were sold on Saturday Let be the remaining number of hotdogs; then, + + is a linear expression. 4. The product of 46 and a number, added to the reciprocal of the number squared Let be a number; then, + is a nonlinear expression. The term is the same as β , which is why it is not linear. 5. The product of 12 and a number and then the product multiplied by itself seven times Let be a number; then, () is a nonlinear expression. The expression can be written as β
. The exponent of with a base of is the reason it is not linear. 6. The sum of seven and a number, multiplied by the number Let be a number; then,( + ) is a nonlinear expression because ( + ) = + after using the distributive property. It is nonlinear because the power of in the term is greater than . I remember that 1 = β1 from the beginning of the year. It is linear because it a sum of constants and to the 1 st power. I need to use parentheses around the sum of seven and a number. I could write the expression as 1 2 + 46 by applying the commutative property of addition. 2 Β© 2015 Great Minds eureka-math.org G8-M4-HWH-1.3.0-10.2015 Homework Helper A Story of Ratios
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2015-16
Lesson 2: Linear and Non-Linear Expressions in π₯π₯
8β’4
G8-M4-Lesson 2: Linear and Non-Linear Expressions in ππ
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.
1. A number added to five cubed
Let ππ be a number; then, ππππ + ππ is a linear expression.
2. The quotient of seven and a number, added to twenty-five
Let ππ be a number; then, ππππ
+ ππππ is a nonlinear expression.
The term ππππ
is the same as ππ β ππππ and ππππ
= ππβππ, which is why it
is not linear.
3. The sum that represents the number of hotdogs sold if 148 hotdogs were sold Thursday, half of the remaining hotdogs were sold on Friday, and 203 hotdogs were sold on Saturday
Let ππ be the remaining number of hotdogs; then, ππππππ + ππππ ππ + ππππππ is a linear expression.
4. The product of 46 and a number, added to the reciprocal of the number squared
Let ππ be a number; then, ππππππ + ππππππ is a nonlinear expression.
The term ππππππ is the same as ππβππ, which is why it is not linear.
5. The product of 12 and a number and then the product multiplied by itself seven times
Let ππ be a number; then, (ππππππ)ππ is a nonlinear expression. The expression can be written as ππππππ β ππππ. The exponent of ππ with a base of ππ is the reason it is not linear.
6. The sum of seven and a number, multiplied by the number
Let ππ be a number; then,(ππ + ππ)ππ is a nonlinear expression because (ππ + ππ)ππ = ππππ + ππππ after using the distributive property. It is nonlinear because the power of ππ in the term ππππ is greater than ππ.
I remember that 1π₯π₯
= π₯π₯β1 from
the beginning of the year.
It is linear because it a sum of constants and π₯π₯ to the 1st power.
I need to use parentheses around the sum of seven and a number.
I could write the
expression as 1π₯π₯2
+ 46π₯π₯
by applying the commutative property of addition.
2
Β© 2015 Great Minds eureka-math.org G8-M4-HWH-1.3.0-10.2015
Homework Helper A Story of Ratios
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