hectictar

Maybe you have mis-typed the question?

What you have said in the question is basically just like saying:

2 + 2  =  5

What is the slope?

number of 1 by 1 squares  =  21

number of 2 by 2 squares  =  12

number of 3 by 3 squares  =  5

number of 4 by 4 squares  =  0

21 + 12 + 5   =   38

Just remember that the slope-intercept form of the equation of a line is

y  =  mx + b

where  m  is the slope

and  b  is the y-intercept

Read this equation...

12  =  \(\frac12\) + 8

12   is equal to   \(\frac12\) + 8

12   is equal to   8.5

Does that make sense to you??  

As long as  b5   means  b times 5   then...

1465  =  b5 + 5

                               we can just rewrite  b5  as  5b

1465  =  5b + 5

                               Subtract  5  from both sides of the equation

1460  =  5b

                               Divide both sides of the equation by  5

292  =  b

                               That is the same as...

b  =  292

Glad to help!!!

I got the same thing as you 👍👍

area of tabletop  =  area of rectangle + area of triangle

Given that the area of the tabletop is  150 ft² ,  we can make the equation

150 ft²   =   area of rectangle + area of triangle

150 ft²   =   6x ft²  +  \(\frac12\)(4)(6) ft²

                                                     At this point we can cancel the  ft²  on every term

150   =   6x  +  \(\frac12\)(4)(6)

                                                     Simplify  \(\frac12\)(4)(6)  to get  12

150   =   6x  +  12

                                  Subtract  12  from both sides.

138  =  6x

                                  Divide both sides by  6

23  =  x

x² + y   =   4

                            Square both sides of the equation.

(x² + y)²  =  4²

                                       Expand the left side.

(x² + y)(x² + y)  =  16

x⁴ + 2x²y + y²  =  16

                                       Rearrange the terms on the left side.

2x²y + x⁴ + y²  =  16

                                       Since  x⁴ + y² = 10  we can substitute  10  in for  x⁴ + y²

2x²y + 10  =  16

                            Subtract  10  from both sides.

2x²y  =  6

                            Divide both sides by  2

x²y  =  3

\(\text{3.499 dollars per gallon}\,\times\,\frac{\text{350 miles per day}}{\text{21 miles per gallon}}\,\times\,\text{20 days}\ =\ \frac{3.499\,\times\,350\,\times\,20}{21}\ \text{dollars}\ \approx\ 1166.33\ \text{dollars} \)_