Heng was trying to factor 10 x 2 + 5 x 10x 2 +5x10, x, squared, plus, 5, x. She found that the greatest common factor of these terms was 5 x 5x5, x and made an area model:

Full question:

Heng was trying to factor 10x²+5x. She found that the greatest common factor of these terms was 5x and made an area model: What is the width of Heng's area model?

The width of the area model is 2x + 1

Step-by-step explanation:

Given

Expression: 10x² + 5x

Factor: 5x

Required

Width of the Area Model

To solve this, I'll assume the area model is Length * Width

Provided that we're to solve for the width of the model.

This implies that; Length = 5x

Area = Length * Width

And

Area = 10x² + 5x

Equate these two

Length * Width = 10x² + 5x

Factorize express on the right hand side

Length * Width = 5x(2x + 1)

Substitute 5x for Length

5x * Width = 5x(2x + 1)

Divide both sides by 5x

Width = 2x + 1

Hence, the width of the area model is 2x + 1

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

step-by-step explanation: