Roxanne is going to build a rectangular prism out of 36 one- inch cubes. She wants the height of the rectangular prism to be 3 inches, and she wants the width to be shorter than the length. How many rectangular prisms with different dimensions can she build?

3

Step-by-step explanation:

Since Roxanne has 36 one inch cubes, the maximum volume of rectangular prism she can have is 36 in³ = 1 in × 1 in × 36 in.

Now, if Roxanne wants a rectangular prism with height 3 inches, this implies that the area of its base is 36 in³/3 in = 12 in².

We now find all the factors of 12 = 1 × 12, 2 × 6, 3 × 4.

So, we have 3 different areas of base of rectangular prism in which the width is shorter than its length the width being the smaller dimension.

So, the different rectangular prisms in which the volume = 36 in³ in which the width is shorter than its length and has a height of 3 in is

1 × 12 × 3, 2 × 6 × 3, 3 × 4 × 3.

So we have 3 different rectangular prisms

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!