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pantera1 [17]
3 years ago
8

Mike and alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice. How many bottles did alive recyc

le
Mathematics
2 answers:
meriva3 years ago
8 0

total=147

a:m

1:6 =7

147÷7=21

21×1=21

alice recycled 21 bottles

Hitman42 [59]3 years ago
6 0

Answer:

21

Step-by-step explanation:

We have an equation in the first sentence we are given.  Mike and Alice together recycled 147 bottles, so in equation form that looks like this:

M + A = 147.

That alone doesn't do us much good because we have 2 unknowns.  The next sentence gives us Mike's number of bottles based on Alice's.  If the number Mike recycles is 6 times as many as Alice, replace the word "is" with an "=" and "6 times as many as Alice" with 6A to get:

M = 6A

Now we can go back to the first equation and replace M with 6A:

6A + A = 147

Now we only have A's.  That's a good thing.  Solve for A:

7A = 147

A = 21

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Answer:  Choice B

\left\{ \ 3, 5, \sqrt{34} \ \right\}

=========================================================

Explanation:

We'll be using the converse of the pythagorean theorem.

If we had a triangle with sides a,b,c and a^2+b^2 = c^2 was true, then we have a right triangle. Note: c is always the longest side

For the first answer choice we have: a = 5, b = 8, c = 12

Then,

a^2+b^2 = c^2\\\\5^2+8^2 = 12^2\\\\25+64 = 144\\\\89 = 144\\\\

which is false. This shows that we do not have a right triangle with sides 5,8,12. This rules out choice A. Choice C is a similar story.

Choice B on the other hand works because

a^2+b^2 = c^2\\\\3^2+5^2 = (\sqrt{34})^2\\\\9+25 = 34\\\\34 = 34\\\\

We have a true statement at the end, which confirms <u>choice B</u> is a right triangle.

7 0
1 year ago
B В<br> (6,8)<br> F<br> IC<br> E<br> (-10,-4)<br> D
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is there a question ?

Step-by-step explanation:

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3 years ago
A parabola is represented by the equation y2 = 5x. which equation represents the directrix?
ivann1987 [24]

The value of the directrix is -5/4.

According to the statement

we have given that the equation of parabola is y2 = 5x. And we have to find that the which equation represents the directrix.

We know that the general equation of parabola is

(y - k)2 = 4a(x - h)  -(1)

and given parabola equation is

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After comparing the both equations we get k=0 and h=0

And the formula to find the directrix is

x = h - a

Substitute the values of h and a in it then

x = 0-5/4

x = -5/4.

Here the directrix is -5/4.

So, The value of the directrix is -5/4.

Learn more about the Parabola here brainly.com/question/4061870

#SPJ4

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