Determine whether the mathematical statement below will represent a rational/irrational number always, sometimes or never. The sum of a rational number and an irrational number is irrational.
The sum of two rational numbers is rational.
The product of a rational number and an irrational number is irrational.
The sum of two irrational numbers is irrational.
The product of two rational numbers is rational.
The product of two irrational numbers is irrational.
The circumference of a circle is irrational.
The diagonal of a square is irrational.
Between two rational number there is an irrational number
Between two irrational number there is an irrational number
If the circumference of a circle is rational, the area is rational.

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step-by-step explanation:

sorry no step by step

(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

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves