Question

fan + medal see pic

Answer 1

i need help with c and the rest

Answer 2

@mathstudent55

Answer 3

@Mehek14

Answer 4

okay so d?

Answer 5

Part c.
The length of the garden is 3x + 2, where x is the length of the patch.
Now we are told the length of the patch is 7 ft.
Use 7 for x, and evaluate 3x + 2.

\(L_G(x) = 3x + 2\)

\(L_G(\color{red}{7}) = 3 \times \color{red}{7} + 2\)

Answer 6

Here are questions e-h

Answer 7

What do you get for the length of the garden?

Answer 8

what u just wrote

Answer 9

You need a number.
I wrote the expression that you need to calculate.

Answer 10

What is 3 * 7 + 2?

Answer 11

23?

Answer 12

Good.
That is the length of the garden.
Now we need the width of the garden.
the width is x + 5.
Since x is 7, what is 7 + 5?

Answer 13

12

Answer 14

Yes. Now multiply 23 and 12 to find the answer to part c.
That is the area of the vegetable garden when the tomato patch is 7 ft by 7 ft.

Answer 15

Ok, now part d.

Answer 16

Part d.
The tomato patch measures x by x.
The length of the bell pepper patch is half the length of the tomato patch.
The length is half of x.
How do you write half of x as an expression? (Hint: use a fraction.)

Answer 17

x/2

Answer 18

When you need half, you divide by 2.
Use a fraction with denominator 2 to mean divided by 2, or half.

Answer 19

Correct.

Answer 20

The length of the bell pepper patch is x/2.

Answer 21

Now we need its width.

Answer 22

k

Answer 23

Sorry. We just did the width of the bell pepper patch.
The width is x/2.
Now we need to do the length.

Answer 24

The length of the bell pepper patch must exceed the length of the tomato patch by 2 ft.

Answer 25

okay

Answer 26

When you deal with "exceed", you need an inequality.
The length of the bell pepper patch must be 2 ft or more greater than the length of the tomato patch.

Answer 27

k

Answer 28

The tomato patch has length x
The bell pepper patch must have length x + 2 or more.

Answer 29

\(W_B(x) = \dfrac{x}{2} \)

\(L_B(x) \ge x + 2\)

Answer 30

okay what about questions e - h

Answer 31

Wait.

Answer 32

The problem states "exceed by 2 ft", not "exceed by at least 2 ft."
For get the inequality.

This is the corrected length of the bell pepper patch.

\(L_G(x) = x + 2\)

Answer 33

k

Answer 34

Once again, here is the correct answer to part d.

\(W_G(x) = \dfrac{x}{2} \)

\(L_G(x) = x + 2\)

Answer 35

yeah i got that

Answer 36

I only see up to part d in the figure.

Answer 37

e. is the area of the bell pepper patch.
Multiply its length by its width.
What do you get?

Answer 38

@mathstudent55 what is it?????

Answer 39

idk

Answer 40

@mathstudent55 pls help i rly need to finish this

Answer 41

We did part d above.
You have the length and the width.
Just multiply them together to find the area.

Answer 42

\(A_B(x) = \dfrac{x}{2}(x + 2) \)

Answer 43

ok what about f

Answer 44

For f:
The area of the tomato patch is x * x = x^2.
Add that to the answer of part e.

Answer 45

ok g?

Answer 46

Part f.
\(A_{TB} = x^2 + \dfrac{x}{2} (x + 2) \)

Answer 47

okok

Answer 48

g?

Answer 49

The remaining area is the area of the vegetable garden minus the combined area of the tomato patch and the bell pepper patch.
Subtract the answer of part f. from the answer of part b.

Answer 50

ok what is the correct answer?

Answer 51

\(A_R(x) = (x + 5)(3x + 2) - [x^2 + \dfrac{x}{2}(x + 2)] \)

Answer 52

k just h left!

Answer 53

For h you need to solve a quadratic equation.

Answer 54

how do i do that

Answer 55

\(A_B(x) = \dfrac{x}{2}(x + 2)\)

That area has to equal 31.5 ft^2.

\(\dfrac{x}{2}(x + 2) =31.5\)

Multiply both sides by 2:

\(x(x + 2) = 63\)

Multiply out the left side, and subtract 63 from both sides.

\(x^2 + 2x - 63 = 0\)

In order to factor the left side,
we need 2 numbers that add to -2 and multiply to -63.
They are -9 and 7.

\(x - 9)(x + 7) = 0\)

\(x = 9\) or \(x = -7\)

A length can;t be negative, so we discard -9.

The length id the tomato patch is 9 ft.

Now we use 9 ft for x in the remainder area function above.

\(A_R(x) = (x + 5)(3x + 2) - [x^2 + \dfrac{x}{2}(x + 2)]\)

\(A_R(9) = (9 + 5)(3\times 9 + 2) - [9^2 + \dfrac{9}{2}(9 + 2)]\)

Now you need to evaluate the expression on the right side.

Answer 56

wut is that

Answer 57

I don't know, and I have to go.
Just do all the operations, and find and answer.
Remember to follow the order of operations.