A rectangular planter that is 4 feet long, 4 feet wide, and 2 feet deep uses three bags of potting soil. The amount of potting soil needed depends on the volume of the planter. How many bags of soil would be used in a planter that had a base area of 40 square feet and a depth of 4 feet? Fill in the blanks to complete the explanation. The first planter has a volume of cubic feet and uses 3 bags of potting soil. The second planter has a volume of cubic feet. The volume of the second planter is times ad much as the volume of the first planter. Multiply the 3 bags of potting soil used in the first planter by to find that bags of potting soil would be used in the second planter.

The answers to the five blanks are as follows;

1. 32,

2. 160,

3. 5,

4. 5, and

5. 15.

Step-by-step explanation:

Step 1; The volume of a rectangular box is given by multiplying the length, width and height of the box.

The volume of the first planter = length × width × height.

Length = 4 feet, Width = 4 feet and height = 2 feet.

The volume of the first planter = 4 × 4 × 2 = 32 cubic feet. This is the answer to the first blank.

Step 2; The volume can also be calculated by multiplying the area of the rectangle by its height.

The volume of the second planter = Area × height = 40 × 4 = 160 cubic feet. This is the answer to the second blank.

Step 3; = = 5. So the second planter is 5 times bigger than the first planter. This is the answer to the third blank.

Step 4; So if the first planter needs 3 bags of soil, the second planter will need 5 times more than the first planter. This is the answer to the fourth blank.

So if the first planter needs 3 bags and the second planter is five times bigger it needs = 3 × 5 = 15 bags of potting soil. This is the answer to the fifth blank.

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

the answer will be b x² +x-1

step-by-step explanation: