( 2 , 6 ) , ( 3 , 12 ) , ( 4 , 15 ) , ( 5 , 21 ) We want to find the line t = m s + q , with slope m and y-intercept q , that best fits this data. Namely, we go ahead and try to solve the system A x = b with A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 2 1 3 1 4 1 5 1 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ , b = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 6 12 15 21 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ and x = [ m q ] However, this system is very likely to be inconsistent. So instead we write down the normal equation A T A x = A T b and solve it to get the least squares solution x = [ m , q ] T .

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or  

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

6 cm

step-by-step explanation:

could you provide figure.