What do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.

answer: a rational.

b. irrational.

step-by-step explanation:

a.   the 2 numbers are rational so we can write them as a/b and c/d where a, b c and d are integers (not = 0.)

a/b * c/d = ac / bd.

by the   closure property of integers , the product of 2 integers must also be an integer   so we can   write ac/bd = e/f where e and f are integers so the product is rational.

thus the product of 2 rational numbers is rational,

b. the product of a nonzero rational and an irrational is irrational.

let a/b be the rational number and x the irrational.

let us assume that a rational times an irrational number gives a rational number.

so we assume multiplying   a/b * x = m/n where m and n are integers.

making x the subject my multiplying both sides by b/a we get:

x = mb/an   which is   rational. because m, b , a and n are integers

but we assumed x   is irrational but we have proved it rational. so that is our contradiction.

so our assumption was wrong and rational * irrational must be irrational.

c. the rational cannot be zero because when we multiply by zero the answer is zero.   it gives a different result to b.

dwe

step-by-step explanation:

ewd

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w