If p and q are non-zero rational numbers, and s and t are irrational numbers, select all of the statements that are always false. answer choices are
The product pq is irrational.

The product pt is irrational.

The quotient pq is irrational.

The product st is irrational.

The quotient st is rational.

The false statements are:

The product pq is irrational.

The quotient pq is irrational.

The quotient st is rational.

A rational number is a number can be expressed as a fraction of two whole numbers. While, an irrational number is a number that cannot be expressed as the fraction of two whole numbers.

Examples of rational numbers are: 6, 2,3

Examples of irrational numbers are: √2, √3

Let p and q be represented with 2 and 6 respectively.

The product of 2 and 3 = 2 x 6 = . The number is a rational number

Let p and t be represented with 2 and √2 respectively.

The product of 2 and √2 = 2 x√2 = 2√2. The product is irrational

The quotient of pq = 6 /2 = 3.

The quotient is rational.

Let s and t be represented with √2, √3. The product is √2 x √3 = √6. The product is irrational.

The quotient of s and t = √2 /√3.

The number is irrational.

To learn more about rational numbers, please check: link

The false choices are A, C, and E

Step-by-step explanation:

Let's make an example:

p=1

q=2

s=sqrt(3)

t=sqrt(6)

Since pq=1*2=2, the answer is rational and A is false.

Since pt=1*sqrt(6)=sqrt(6), the answer is irrational and B is true.

Since p/q=1/2=0.5, the answer is rational and C is false.

Since st=sqrt(3)*sqrt(6)=sqrt(18), the answer is irrational and D is true.

Since s/t=sqrt(3)/sqrt(6)=sqrt(1/2), the answer is irrational and E is false.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d