Use compatible numbers to find two estimates that the quotient is between 1045÷2

The two estimates of quotient is 522 and 523 .

Step-by-step explanation:

Compatible numbers are numbers which are close in value to the given numbers, and  make it easy to calculate the answer for any given arithmetic problem .

To find two estimates that the quotient is between in 1045÷2

We now that 1045 is greater than 1044 and less than 1046 i.e.1044<1045<1046

Dividing 2 from all sides ,we get

1044÷2<1045÷2<1046÷2

⇒522<1045÷2<523

As the quotient of 1045÷2 is lying between 522 and 523.

Therefore, the two estimates of quotient is 522 and 523

(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