The diagram below shows 5 identical bowls stacked one inside the other. the height of 1 bowl is 2 inches. the height of 5 bowls is 5 inches.

part a: write an equation using x and y to find the height of a stack of bowls based on any number of bowls.

part b: describe what the x and y variable represent.

part c: use the equation from part a to find the number of bowls if the height of the stacked bowls is 12.5 inches.

(Bowls, Height) (1, 2)  (5,5)

Slope is (5-2)/(5-1) = 3/4 inch
y = (3/4)x + b
(2) = (3/4)(1) + b
(2)-(3/4) = b

B=1.25.  Y= 0.75*x + 1.25. 

Part B
X is the number of bowls in the stack and Y is the corresponding height of the stack.

f

step-by-step explanation:

f

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.