Which of the following results in a sum or a product that is rational? choose all that apply. (3 points)

Remark

It is easier in this case to state the irrational ones and then talk about the rationals.

sqrt(2) * sqrt(3) is irrational. The square root of 6 fills your calculator's window with many numbers and there is no pattern to them. Sqrt(6) cannot be expressed as a fraction or a repeating decimal which is also a fraction.

The last one is also irrational for the same reason. 3*pi cannot be expressed as either a repeating decimal or a fraction.

All the others are rational. The one you might have trouble with is the first one.

0.12 repeating is actually found by letting x = 0.12121212121212121212...Then

100 x =  12.121212121212121212 ...

      x =    0.121212121212121212...     Subtract

99 x = 12

x = 12/99

So the mixed fraction you get is 3 12/99 which is 309/99

When you multiply that by 1.4 it does not change the fact that you still get a fraction. It turns out to be 721 / 165.  The method is similar to the one used to get 12 / 99. I don't think you need to know the exact answer. You need only need to know that the first one is rational.

Choice 2 is rational because 9 and 25 are  perfect squares. sqrt(9) = 3

Sqrt(25) = 5.

3*5 = 15.

Answer

One Two are four are all rational.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer is x<