Algebra 1 RCT 5: IM Unit 7 SY 24-25

Hey math detectives! Samuel and Isla are on a mission to find all the expressions that are squares of linear expressions. Can you help them crack the code?

• (2d + 8)(2d - 8)

Tags

CCSS.HSA.APR.C.4

Tags

CCSS.HSA-REI.B.4B

• x = 10, x = 2

• x = 6, x = -2

• x = 8, x = 4

• x = 2, x = -10

Tags

CCSS.HSA-REI.B.4B

• x = -1/3 or x = -5/3

• x = 1/3 or x = 5/3

• x = -1 or x = -5

• x = 1 or x = 5

Tags

CCSS.HSA-REI.B.4B

• x = 2, x = -0.75

• x = 3, x = -2

• x = 1.5, x = -4

• x = 6, x = -1

Tags

CCSS.HSA-REI.B.4B

Priya is on a mathematical adventure and discovers a mysterious solution to an equation: -2 + √3. She's curious to find out if this solution is rational or irrational. To unravel the mystery, she decides to add 2 (a rational number) to her discovery of -2 + √3. What magical sum does Priya find? Is this sum rational or irrational?

To solve this, consider the expression: (-2 + √3) + 2. Simplifying this, we get:

= -2 + √3 + 2

= (2 - 2) + √3

= 0 + √3

= √3

Since √3 is a well-known irrational number, the sum is irrational.

• The sum is √3 and it is rational.

• The sum is √3 and it is irrational.

• The sum is 0 and it is rational.

• The sum is 0 and it is irrational.

Tags

CCSS.7.NS.A.1D

Liam and Luna are having a debate about numbers. Liam claims that -2 + √3 is a rational number. Luna, being the math whiz, disagrees. Can you help them settle the argument by explaining why -2 + √3 cannot be rational?

• Because √3 is irrational, so -2 + √3 is also irrational. The square root of 3 cannot be expressed as a fraction of two integers, making it an irrational number. When you add an irrational number to a rational number (-2), the result is always irrational.

• Because -2 is irrational, so -2 + √3 is irrational. This statement is incorrect because -2 is actually a rational number. It can be expressed as a fraction (-2/1), so this option does not explain why -2 + √3 is irrational.

• Because the sum of two rational numbers is always irrational. This statement is false. The sum of two rational numbers is always rational. This option does not apply to the given problem.

• Because -2 + √3 is always an integer. This statement is incorrect. An integer is a whole number, and -2 + √3 is not a whole number, as √3 is irrational and cannot be simplified to make the entire expression an integer.

Tags

CCSS.HSN.RN.B.3

• $5 and $75

• $10 and $40

• $15 and $25

• $20 and $30

• f(x) = -(x + 2)(x + 6)

• f(x) = -(x - 2)(x - 6)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A