Explain how you would use addition to find the product of –2 and 5 using the integer tiles and the number line.

Answer with explanation:

We have to find the product of →: -2 × 5, using addition.

1. Product of -2×5 using addition →With the Help of Integer tiles

Draw two tiles of same color and same size , which can be either Square or Rectangle ,either in five rows five times by putting addition sign between two rows or after every two tiles or in the same column five times by putting addition sign after every two tiles.

If you add all these tiles , which will be equal to 10 in both the case, and put negative sign before it to obtain the result.

2. Product of -2×5 using addition on the→Number line                           →Draw a  line, mark numbers 0,2,4,6...on right side and,-2,-4,-6,-8,...on the left of number line .                                 We have to find the product of , -2 × 5 or -5 ×2

Multiplication shows commutative property, which is →A × B= B ×A

→Mark circle on 0, and move a distance of 2 units, five times on the left of 0, on the number line to get the desired result.

→→The Second way is to , mark arc on the number 0 ,  and move distance of  5 units on the left of number line twice, to get the desired result.

Image showing above procedure is shown below.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204