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y = 25/2.

x = (-3 + 2*sqrt(5))/4

The solution is -5 <= t <= 1.

Bricklayer Ben placed 180 bricks.

(A,B,C) = (4,-3,7)

The rockets will be 300 miles apart.

Ocre bought a mixtures of pencils. 2/3 of the pencils were green. 1/2 of the remaining pencils were white. There were 5 blue pencils. How many pencils were there altogther?  

Assuming that the information is complete and the green, white, and blue pencils are all there are.  

So you've got the green pencils, and then you have all the remaining pencils, which are white and blue.. 

Half of the remaining pencils are white, the other half are blue.  There are 5 blue pencils. 

Therefore there are 5 white pencils.  Half and half.  So those 10 pencils are the remaining 1/3. 

10 pencils are 1/3 of the pencils, so there are 30 pencils altogether.  

20 green, 5 white, 5 blue.  

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I let      p(x)=ax+b            and      q(x)=tx+r

I did all the substitution and got eall the terms in terms of b

I could then find q(-1) in terms of b  but not as a number on its own.

I do not think that my answer is wrong. 

\(a=\frac{3-b}{2}\\ t=\frac{8}{3-b}\\ r=\frac{34-2b}{b-3}\\ \)

etc

The way I see it is that cutting the resistance in half would double the current. 

You also double the voltage, so the current is doubled again.  So 4 • 100 mA  =  400 mA 

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Think about a ratio between the distance Becky travels to the distance Caitlin travels. 

Now, if Becky is 24, how many miles does Caitlin have left to go?

\(x(x+6) > 16+4x\)

\(x^2 + 6x >16 + 4x\)

\(x^2 + 2x > 16\)

\(x^2 + 2x - 16 > 0 \)

\((x+1)^2 > 17\) (understand why)

Solve for x, should be pretty straightforward.

8!/(4!(8-4)!)

(8 * 7 * 6 * 5)/(4 * 3 * 2) = 70

All the factors cancel, and the amount of current is exactly the same, 100 milliamps.

There are \({5 \choose 1} + {5 \choose 2} = 15\) ways to choose 1 or 2 slices of bread. 

There are \(2^7 - 1 = 127\) ways to choose the ingredients (think of it as a binary number 0000000 to 1111111, where each digit represents an ingredient, 0 means it's not there, and 1 means it's there)

So, there are \(15 \times 127 = \text{___}\) sandwichs. 

The answer is 6600 seconds.

suppose you have one quart of water/juice mix that is 40% juice,

and you add 3 quarts of water. What percent juice is the final mix?  

You start out with 1.0 quart of mix that's 40% juice, so 

you have 0.4 qt of juice and 0.6 qt of water. 

You add 3.0 qts of water and the mix becomes 

0.4 qt of juice and 3.6 qt of water. 

That resultant mix is a total of 4.0 qt of which 0.4 qt is juice. 

The final proportion of juice is 0.4 / 4.0 = 0.1 which stated as a percentage is 10%  

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