Rationalize Dominators Warmup

• 18

• 32

Answer explanation

The conjugate of a binomial expression of the form a + b is a - b. Here, a is 5 and b is \sqrt{7}. Therefore, the conjugate of 5 + \sqrt{7} is 5 - \sqrt{7}, which is the correct answer.

Tags

CCSS.HSN.CN.A.3

• 18

Answer explanation

The conjugate of an expression of the form a - b is a + b. Here, a is 6 and b is 3√2, so the conjugate is 6 + 3√2, which matches the first answer choice.

Tags

CCSS.HSN.CN.A.3

Multiply:

​ ​ ​ (a)   +​ ​ ​ (b)   ​ - ​ (c)   - ​ (d)  

• unnecessary blank

Answer explanation

To solve the expression, combine the terms correctly. The correct answer is 8, as it results from the proper addition and subtraction of the given values.

Tags

CCSS.HSN.RN.A.2

Definition of math Conjugate?

• The conjugate of a complex number is obtained by doubling its imaginary part.

• The conjugate of a complex number is obtained by changing the sign of its imaginary part.

• The conjugate of a complex number is the same as the original number.

• The conjugate of a complex number is obtained by changing the sign of its real part.

Answer explanation

The correct choice states that the conjugate of a complex number is obtained by changing the sign of its imaginary part. For example, for the complex number a + bi, its conjugate is a - bi.

Tags

CCSS.HSN.CN.A.3

Which Expression is a Monomial?

• A single term like 3x or 5.

• 4xy - 5y + 6

• 2x + 3

• x^2 + 7

Answer explanation

A monomial is defined as a single term, which can be a number, a variable, or a product of numbers and variables. The correct choice, 'A single term like 3x or 5,' fits this definition, while the other options contain multiple terms.

Which Expression is a Binomial?

• x - y + 1

• xy

• x^2 + y^2

• x + y

Answer explanation

A binomial is an expression with exactly two terms. The expression 'x + y' has two terms, making it a binomial. In contrast, 'x - y + 1' has three terms, 'xy' is a single term, and 'x^2 + y^2' has two terms but is not a binomial.