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1. Zoe and Claire both get on. At the other side, drop Zoe off.

2. Claire returns to the other side and gets out of the boat. Then Kristin goes to the other side.

3. Kristin gets off and Zoe gets back on to go to the other side. Zoe picks up Claire, and all three friends make it to the other side.

\(\frac{x^2 + 8x+16}{x+3} \cdot \frac{x^2-9}{2x+8} = \frac{(x+4)^2}{x+3} \cdot \frac{(x+3)(x-3)}{2(x+4)}= \frac{(x+4)(x-3)}{2} = \frac{x^2+x-12}{2}\)

\(\frac{170}{130} \cdot 100\)

(price of original divided by sale price multiplied by 100 to convert to percent)

The first term of the sequence, a, is 10. The common difference, d, is -5. We can use the formula for an arithmetic sequence.

a + (n-1)d

10 + (n-1)(-5) = -5n+15.

The quilt is a giant square with 5 smaller squares on each side with side length 30. The perimeter is \(4(5(30)) = \boxed{600} \quad \text{cm}.\)

\(x^2 - 6x = (x-3)^2 -9\)

First, we need to find the slope of the equation, which is \(\frac{6-4}{0+7} =\frac{2}{7}\).

We know the coordinates of one point and the slope, so we can write the equation in point-slope form:

\(y-y_0 = m(x-x_0)\)

\(y - 6 = \frac{2}{7}(x)\)

\(5h>3(3h+4)\)

\(5h > 9h+12\)

\(-4h > 12\)

\(\boxed{h < -3}\)

Simply plug in the coordinates of the point into both equations to see if it works.

6 = (-5) = -11

6 - (-5) = 11

As you can see, the ordered pair satisfies neither of the equations. So, it is not a solution to the system.

sorry, but the answer was 1620

We are essentially finding the solutions to \(\frac{x-2}{3x+4} = \frac{x+5}{x}\).

Cross multiply: \((x-2)(x) =(3x+4)(x+5)\)

\(x^2-2x =3x^2 + 19x + 20\)

\(0 = 2x^2 + 21x + 20\)

Using the quadratic formula, we see that the solutions are at \(-\frac{17}{4} \pm \frac{\sqrt{129}}{4}.\)

It is only raining in Seattle if all three friends are truthful. This happens with probability \((\frac{2}{3})^3 =\boxed{\frac{8}{27}}\)

Here's my attempt.  I assume that the closest will be when AB is stretched taut:

If EF is a midsegment of a trapezoid ABCD then angle BAD is NOT 35º.

Find a cubic polynomial with integer coefficients that has \( \sqrt[3]{2}+\sqrt[3]{4}\) as a root.

Why are you having a problem with this.  Have you tried to answer it?

The last digit is 5.  So where do you put 5_

The other clues are easy too. 

You can do this yourself!   

Thank you very much for solving it!

Could you help me with b)? 

When the first digit is 1, there are only 3 choices for the 2nd digit: 0, 2, 4
When the 2nd digit is 0, there are 10 choices for the 3rd digit and only 8 choices for the 4th digit:2, 3, 4, 5, 6, 7, 8, 9. So: 10 x 8 ==80

When the 2nd digit is 2, there are 10 choices for the 3rd digit and only 6 choices for the 4th digit: 4, 5, 6, 7, 8, 9. So:10 x 6 ==60

When the 2nd digit is 4, there are 10 choices for the 3rd digit and only 2 choices for the 4th digit: 8 and 9. So: 10 x 2 ==20

Therefore beginning with 1 as the 1st digit from the left, we have a total of: 80 + 60 + 20 =160 such integers.

This pattern is repeated for every 1st digit from 1 to 9. Therefore, there are a total of: 9 x 160 =1,440 such 4-digit integers.

Note: I wrote a short computer code in C++ and confirms the above total of 1440 integers. If needed, it can be printed.

That is really cool Textot.

Thanks very much for showing me.   

Here's    (a)

-2x^2   + 8x   =   3x  +  2          rearrange  as

2x^2  - 5x  + 2  =  0

(2x  - 1)  ( x - 2)    = 0

Two  break-even  pts

2x   - 1  =   0                                                 x  -  2 =  0

2x =   1                                                          x =  2  ( thousand) = 2000 items

x = 1/2 (thousand)  = 500 items

a)   at  t  =  0.....the initial  concentration  is  0   →    (10)( 0) /  ( 25  + 0)  =  0 / 25   =  0

b)  as  t increases.......so  does  the salt concentration

c)   

10t / ( 25 + t)  = 3.75

10t   =  3.75  (25 + t)

10t  = 93.75  + 3.75 t

10t - 3.75 t  =  93.75

6.25 t  =  93.75

t  =  93.75  /  6.25    =   15  minutes

a  +  b  =   4

(a + b)^2 =   16

a^2  +  2ab  + b^2  =  16

a^2  + b^2  =   16 - 2ab

a^3  + b^3  =  ( a + b)  ( a^2   - ab  +  b^2)  = 

44  =  ( 4) ( 16 - 2ab - ab)

44/4  =  16  -  3ab

11  =  16 -  3ab

3ab  =  16 - 11

3ab  = 5

ab  =  5/3  

In  the  form   ax^2  + bx +  c

a =  3

c = 5

The sum  of the roots  =   4  =   -b/a

So

4  = -b/ 3

12 = -b

-12  = b

The  quadratic   is    3x^2 - 12x  +  5

The largest integer, n, is when n =233. 

Since  80 = 2^4 * 5  and  942! === 2^935 * 3^467 * 5^233 * 7^155 ........etc.

Therefore: 942! mod 80^233 ==0.

I don't have a solution but I think its

5sqrt(2)??
I kinda guessed on some parts.

This problem  looks  interesting, but  I  have  no clue  as to the  solution......anyone  out there in TV Land   know  an approach  ????