The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. when you put 40 liters of water into the aquarium, it was full to 2/3 its volume. what part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter^3)

The height of aquarium is of its length

Step-by-step explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium = of length

                              = decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

of volume of aquarium = 40

multiply both side by 3

divide both side by 40

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

hence the height of aquarium is of its length

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be