Okay so to represent juice we are going to use X, and to represent water we are going to use Y.
We also know that the first two starting equations are:
6x + y = 135
4x + 2y = 110
We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:
y = -6x +135
Now you can take that equation and plug into either one of the starting two equations. I chose the second equation. We just substitute what y equals in for y in the equation, so we have:
4x + 2(135 - 6x) = 110
Now solve
4x + 270 -12x = 110
-8x + 270 = 110
Subtract 270 from both sides
-8x = -160
Now divide by -8 on both sides
x = 20
We can now confirm that juice costs $20
Now lets plug that into the equation where we solved for y, to get the actual value of y.
y = 135 - 6(20)
y = 135 - 120
y = 15
The price of water costs $15
From this we can conclude that the cost of juice is $20 and the price of water is $15
Problem 1, part (a)
<h3>Answer: False</h3>
For instance, 200 feet in real life can be reduced to scale down to say 2 inches on paper. So we have a reduction going on, and not an enlargement.
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Problem 1, part (b)
<h3>Answer: true</h3>
This is because a scale drawing involves similar polygons. This is true whenever any dilation is applied.
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Problem 2
I'm not sure how your teacher wanted you to answer this question. S/he didn't give you any numbers for the side lengths of the polygon. The angle measures are missing as well.
This is exponential decay which can be expressed as:
y=ab^t, y=final value, a=initial value, b=rate, t=time
In this case a=25000, r=(100-20)/100=0.8 so
y=25000(0.8^t), so in 4.5 years...
y=25000(0.8^4.5)
y≈$9158.93 (to nearest cent)
Answer:1/4 hour remaining
Step-by-step explanation:
Presenter 1 - 1/3 hour
Presenter 2 - 1/6 hour
Presenter 3 - 1/4 hour
Convert to least common denominator of 12
4/12 + 2/12 + 3/12 = 9/12
12/12 - 9/12 = 3/12
Reduce 3/12 to get 1/4 hour remaining
