1. The school band sells carnations on Valentine's Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge.

a. Write a system of equations to describe the situation.

A: y = 2x; y = 0.50x + 16.

b. Graph the system. What does the solution represent?

(Which x-values should I choose to graph the equations above so that they intersect?)

c. Explain whether the solution shown on the graph makes sense in this situation. If not, give a reasonable solution.

2. 6(x + 2) = -2(x + 10)
Can you explain how you solved this equation for the answer to be -4?

I'mgonna answer the question,

But first I need some advice sooo,

We're no strangers to love
You know the rules and so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guy

I just want to tell you how I'm feeling
Gotta make you understand

Never gonna give you up, never gonna let you down
Never gonna run around and desert you
Never gonna make you cry, never gonna say goodbye
Never gonna tell a lie and hurt you

We've known each other for so long
Your heart's been aching but you're too shy to say it
Inside we both know what's been going on
We know the game and we're gonna play it

And if you ask me how I'm feeling
Don't tell me you're too blind to see

Never gonna give you up, never gonna let you down
Never gonna run around and desert you
Never gonna make you cry, never gonna say goodbye
Never gonna tell a lie and hurt you

Never gonna give you up, never gonna let you down
Never gonna run around and desert you
Never gonna make you cry, never gonna say goodbye
Never gonna tell a lie and hurt you

(Ooh give you up)
(Ooh give you up)
(Ooh) Never gonna give, never gonna give (give you up)
(Ooh) Never gonna give, never gonna give (give you up)

We've known each other for so long
Your heart's been aching but you're too shy to say it
Inside we both know what's been going on
We know the game and we're gonna play it

I just want to tell you how I'm feeling
Gotta make you understand

Never gonna give you up, never gonna let you down
Never gonna run around and desert you
Never gonna make you cry, never gonna say goodbye
Never gonna tell a lie and hurt you

1. b. It represents, how many carnations needed to be carnations: 11

y = 2x

x = 0
y = 0
x = 1
y = 2
x = 3
y = 6
x = 4
y = 8

(0,0); (1,2);

y = .50x + 16
x = 0
y = 16
y = 0
x = -32

(0, 16); (-32,0)

Intersect (10.67, 21.33)

c . No because the solution is not a sold to break even. Whole number of carnations.

2. 6x + 12 = -2x -20
6x +2x + 12 = -2x + 2x -20
8x +12 = -20
8x + 12-12 = -20-12
8x =-32
x = -4

check if -4 is solution?
6 (-4 +2) = -2(-4+10)

6(-2) = -2(6)
-12 = -12
True
Yes -4 is a solution for this equation.

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I ain't the sharpest tool in the shed
She was looking kind of dumb with her finger and her thumb
In the shape of an "L" on her forehead

Well the years start coming and they don't stop coming
Fed to the rules and I hit the ground running
Didn't make sense not to live for fun
Your brain gets smart but your head gets dumb
So much to do so much to see
So what's wrong with taking the back streets
You'll never know if you don't go
You'll never shine if you don't glow

Hey now you're an All Star get your game on, go play
Hey now you're a Rock Star get the show on get paid
And all that glitters is gold
Only shooting stars break the mold

It's a cool place and they say it gets colder
You're bundled up now but wait 'til you get older
But the meteor men beg to differ
Judging by the hole in the satellite picture
The ice we skate is getting pretty thin
The water's getting warm so you might as well swim
My world's on fire how about yours
That's the way I like it and I never get bored

Somebody once asked could I spare some change for gas
I need to get myself away from this place
I said yep what a concept
I could use a little fuel myself
And we could all use a little change

Well, the years start coming and they don't stop coming
Fed to the rules and I hit the ground running
Didn't make sense not to live for fun
Your brain gets smart but your head gets dumb
So much to do, so much to see
So what's wrong with taking the back streets
You'll never know if you don't go
You'll never shine if you don't glow

a. To write a system of equations to describe the situation, we need to define two equations.

The first equation represents the revenue generated by selling the carnations, which is given by the product of the number of carnations sold (x) and the selling price ($2). Therefore, the first equation is: y = 2x.
The second equation represents the cost incurred by purchasing the carnations, which consists of two components: the cost of the carnations themselves ($0.50 per carnation) and the delivery charge ($16). Therefore, the second equation is: y = 0.50x + 16.

b. To graph the system of equations, we need to choose specific x-values and calculate the corresponding y-values for each equation. Let's choose the following x-values: 0, 5, and 10.

For the first equation (y = 2x):
When x = 0, y = 2 × 0 = 0.
When x = 5, y = 2 × 5 = 10.
When x = 10, y = 2 × 10 = 20.

For the second equation (y = 0.50x + 16):
When x = 0, y = 0.50 × 0 + 16 = 16.
When x = 5, y = 0.50 × 5 + 16 = 18.5.
When x = 10, y = 0.50 × 10 + 16 = 21.

Now, we plot these points on a graph and connect them to visualize the two equations.

c. The solution to the system of equations represents the point where the two lines intersect. In this case, it represents the number of carnations (x) and the corresponding revenue (y) that will result in the same cost and revenue for the school band.

To determine whether the solution shown on the graph makes sense, we can compare the costs and revenues at this point. If the revenue from selling the carnations equals the cost of purchasing them, then the solution is valid.

Let's substitute the x-value of the solution (point of intersection) into the equations:
For y = 2x, if x = [value of solution], y should also equal [value of solution].
For y = 0.50x + 16, if x = [value of solution], y should also equal [value of solution].

If both equations yield the same value of y at the solution, then the solution makes sense in this situation. If not, we need to find a new reasonable solution where the revenue matches the cost.

----------------------------------------------------------------------

To solve the equation 6(x + 2) = -2(x + 10) and find the answer of -4, we follow these steps:

1. Start by distributing 6 to both terms inside the parentheses:
6x + 12 = -2(x + 10).

2. Distribute -2 to both terms inside the parentheses:
6x + 12 = -2x - 20.

3. Combine like terms on both sides:
6x + 2x = -20 - 12,
8x = -32.

4. Divide both sides by 8 to isolate x:
x = -32 / 8,
x = -4.

Therefore, the solution to the equation 6(x + 2) = -2(x + 10) is x = -4.

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