Question

Fan+medal see pic

Answer 1

@welshfella @mathstudent55 @pooja195 @Ethan01

Answer 2

i need the answer to all of them starting with A ill give a medal for each one

Answer 3

The tomato patch is a square and each side of the square measures x.

Answer 4

what should i write for a?

Answer 5

The length of the garden exceeds three times the length of the tomato patch by 2 ft

The tomato patch has length x.

How do you write three times a length exceeded by 2?

Answer 6

times 2?

Answer 7

Exceeded by 2 means a difference of 2. It is 2 more than the other.
First you need to deal with "three times"
The tomato patch has length x.
The vegetable garden has length 2 more than three times the tomato patch.
If the tomato patch is x, then what is three times the tomato patch?

Answer 8

No.
The "3 times" part is correct.
The tomato patch has length x.
The garden is 3 times the tomato patch, then add 2.
3 times the tomato patch means 3 times x.

Answer 9

k so what about B?

Answer 10

We are not done with A yet.
The length of the garden vegetable is
3x + 2
3x means 3 times x, which accounts for three times the length of the tomato patch.
The "+2" part accounts for "exceeded by 2".

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

This is the length function of part A.

Now we need the width function for part A.

Answer 11

oh ok

Answer 12

Now we need to look in the problem to see what the width of teh vegetable garden has to be.
We see this "She also wants the garden's width to exceed the width of the tomato patch by 5 feet."

Answer 13

?

Answer 14

Since the tomato patch is a square, the length and width are equal.
Since we are using x for the length of the square tomato patch, we also use x for the width of the tomato patch.
Using x for the width of the tomato patch, how do you represent the width of the vegetable garden knowing that the width of the vegetable garden has to exceed the width of the tomato patch by 5 ft?

Answer 15

I’m not sure

Answer 16

Remember from before that "exceed" means "more", meaning add more to it, don't multiply it.

Answer 17

so what is it

Answer 18

Here are some examples with numbers:
If the tomato patch has width 3, then the vegetable garden has width 3 + 5 = 8.
More examples:

Width of Width of
tomato patch vegetable garden
6 6 + 5 = 11
1 1 + 5 = 6
10 10 + 5 = 15
x ?

Answer 19

k

Answer 20

Notice the table above.
For any width of the tomato patch, you add 5 to find the width of the vegetable garden.
If the width of the tomato patch is x, what do you do to find the width of the vegetable garden?

Answer 21

add 5

Answer 22

Correct. That is exactly it.
When we add 5 to x we get x + 5.
Since we don't know what x is, we are just stating that for any value that x may represent as the width of the tomato patch, the width of the vegetable garden is 5 more than that, or x + 5.
That is the answer to the second part of part A.

\(W_G(x) = x + 5\)

Answer 23

Now we can do part B.

Answer 24

k ty

Answer 25

In part B they want the area of the garden.
The garden is a rectangle.
How do you find the area of a rectangle?

Answer 26

i don’t know

Answer 27

okay

Answer 28

To find the area of a rectangle, you multiply the length and the width.
We have the length of our rectangle as: 3x + 2
We have the width of our rectangle as: x + 5
We need to multiply then together to find the width.

Answer 29

\(A_G(x) = LW\)

\(A_G(x) = (3x + 2)(x + 5)\)

Answer 30

okay so what about c

Answer 31

That was part B, the area.

Answer 32

yeah

Answer 33

Now let's do C.
If the tomato patch has sides of 7 ft, what is the length of the garden?
Remember that the length of the garden is 2 more than 3 times the length of the patch.

Answer 34

In part C they tell us the patch has length 7 ft.
No. x + 5 is the width. We'll do that soon.
Now we're doing the length of the garden.
The length of the garden is 3x + 2, and we are told x is 7 ft.
What is the length of the garden?

Answer 35

@mathstudent55 what is it??????

Answer 36

You're going to tell me.
The patch has length 7 ft.
The garden has length 3 times the patch plus 2.
What is the length of the garden?

Answer 37

Now you can use an actual number instead of x.
When the length of the patch was unknown and only represented as x, we stated that the length of the garden was 3x + 2.
Now we know what the actual length of the patch is.
It is 7 ft.
Replace x with 7, and calculate 3x + 2.

Answer 38

can u go on my new topic??

Answer 39

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