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ss7ja [257]
3 years ago
11

How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

Mathematics
1 answer:
VladimirAG [237]3 years ago
4 0

Answer:

Infinite

Step-by-step explanation:

3(4x + 1) - 2

= 12x + 3 - 2 (Multiply the sum in the bracket by 3)

= 12x + 1 (Simplify)

This means that:

12x + 1 = 3(4x + 1) - 2

is the same as

12x + 1 = 12x + 1

Hence, anything that is used to substitute x is correct.

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Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe
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Answer:

a) 1/2

b) 250

Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for p such that 1000p(1-p) is maximized. Once we have that p, we can easily find the answer to part b.

Finding the value that maximizes 1000p(1-p) is the same as finding the value that maximizes p(1-p), just on a smaller scale. So, we really want to maximize p(1-p). To do this, we will do a trick called completing the square.

p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4.

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of p such that the inner part of the square term is equal to 0.

p-1/2=0\\p=1/2.

So, the answer to part a is \boxed{1/2}.

We can then plug 1/2 into the equation for p to find the answer to part b.

1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250.

So, the answer to part b is \boxed{250}.

And we're done!

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How do you use protractors, its been printed on the paper, this is gonna be a little confusing for me sorry if I give this app a
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Answer:

  see below

Step-by-step explanation:

A protractor is usually a transparent measuring device laid intended to be laid over an angle to be measured. The centerpoint of the protractor's scale is made to coincide with the angle's vertex, and the baseline of the protractor is aligned with one of the angle's rays. The appropriate scale is used to read the angle where the other ray crosses the scale. You usually have to visually determine if the angle is acute or obtuse, so you can choose the correct scale to read.

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If you're drawing an angle, first draw one ray and locate the vertex on it. Then do the steps above as you would for measurement. Make a mark on your paper corresponding to the desired angle measure, and connect the vertex to that mark to create the other ray of the angle.

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If you're working with a printed protractor, you may need to do your work on a piece of translucent paper or transparency material, so you can see the protractor scale through the page you're drawing on.

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<em>Comment on a printed protractor</em>

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