Let A be a rational number and B be an irrational number. which of the following are true statements?

A.) the sum of a and b is never rational.

This is a true statement. Since an irrational umber has a decimal part that is infinite and non-periodical, when you add a rational number to an irrational number, the result will have the same infinite non periodical decimal part, so the new number will be irrational as well.

B.) The product of a and b is rational

This one is false. Zero is a rational number, and when you multiply an irrational number by zero, the result is always zero.

C.) b^2 is sometimes rational

This one is true. When you square an irrational number that comes from a square root like , you will end with a rational number: , but, if you square rationals from different roots than square root like , you will end with an irrational number: . 

D.) a^2 is always rational

This one is false. If you square a rational number, you will always end with another rational number.

E.) square root of a is never rational

This one is false. The square root of perfect squares are always rational numbers: , ,...

F.) square root of b is never rational

This one is true. Since the square root of any non-perfect square number is irrational, and all the irrational numbers are non-perfect squares, the square root of an irrational number is always irrational.

We can tell that given that a is a rational number and b be an irrational number, A, C, D, and F are true statements.

Step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92