The diagram below represents the blueprint of a vegetable garden. The beans and potatoes are planted in rectangular gardens. The corn is planted in an area that is represented by a composition of two rectangles. The horizontal lines will represent the lengths of each section of the garden and the vertical lines will represent the widths of each section of the garden. The diagram below represents the blueprint of a vegetable garden. The beans and potatoes are planted in rectangular gardens. The corn is planted in an area that is represented by a composition of two rectangles. The horizontal lines will represent the lengths of each section of the garden and the vertical lines will represent the widths of each section of the garden. Please use the information provided in this diagram to answer questions #1 - 4. x2 - 7x + 2

x2 + 1

Corn

m

Beans

x - 1

Potatoes

A = x3 - x2 - 30x + 72

x + 6
x2 - 9

Directions: Make sure you show all work for the following questions.
Determine & state the length of the potato garden.

Determine & state the length of m.

Determine & state the perimeter of the corn garden.

Mark said that the area of the bean garden is x3-x2+x-1. Do you agree or disagree with Mark? Explain your answer in complete sentences.

Step-by-step explanation:

1. The length of the vegetable garden is:

(x² − 7x + 2) + (x² + 1) = 2x² − 7x + 3

The length of the potato garden is therefore:

(2x² − 7x + 3) − (x² − 9) = x² − 7x + 12

2. m + x² + 1 = x² − 7x + 12

m = -7x + 11

3. The perimeter of the corn garden is:

P = (x² − 7x + 2) + (x − 1) + (-7x + 11) + (x + 6) + (x² − 9) + (x + 6) + (x − 1)

P = 2x² − 10x + 14

4. The area of the bean garden is width time length:

A = (x − 1) (x² + 1)

A = x³ − x² + x − 1

Mark is correct.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).