Hector must find the sum of 50+83+50 by using mental math. which property allows hector to simplify the equation to 50+83+50 and find an equivalent sum? associative property
commutative property
distributive property
identity property

Commutative property

Step-by-step explanation:

We know that the  commutative property of addition says that two numbers can be added in either order.

i.e. For any arbitrary number a and b,

The given sum:

Using commutative property of addition, we have

Then,

Hence, commutative property of addition allows Hector to simplify the equation to 50+83+50 and find an equivalent sum.

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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is