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4 (x+7)^2 = 1

4x^2 + 56x + 196 = 1       Simplifying the equatation

4x2 + 56x + 195 = 0        Subtracting 1

(2x + 13) (2x + 15) = 0    Factorizing the left side

2x + 13 = 0   and   2x + 15 = 0

x = -13/2   or   x = -15/2

Thanks

the set of possible values of the independent variable or variables of a function

26) 

Cross multiply:

2.4/4.547=v/1.4

2.4*1.4=v*4.547

Now switch sides:

v*4.547=2.4*1.4

Divide 4.547 by both sides. 

4.547v/4.547=3.36/4.547 (4.547v/4.547 Will get crossed out) 

Now, just normally divide 3.36/4.547. 

Answer: 0.7389.....

Since I have demonstrated to you the best practices to find the solution for #26, I'm certain you can do the rest! 

Okay Sorry.

If you have already asked this question then you should include a link to the original question and ask people to answer it on the original. Otherwise you may get two answers and this annoys answerers. 

How many ways are there for 8 people to sit around a circular table if none of Alice, Bob, and Eve (three of the 8 people) want to sit next to each other? Two seatings are considered the same if one is a rotation of the other.

Anyway, I'd just seat the 5 first.  Sit one anywhere and then there are 4! = 24 ways to seat the others.

Now we have 5 between spots where we can sit the other 3 people.  So that woud be 5P3 = 60 ways

So that is  24*60 = 1440 ways I think. 

Bump, so that someone can answer this

Just cross multiply in each case and then solve for the unknown variable!.

Solution 1: We choose any seat for Pierre, and then seat everyone else relative to Pierre. There are 2 choices for Thomas; to the right or left of Pierre. Then, there are 4 possible seats for Rosa that aren't adjacent to Pierre or Thomas. The five remaining people can be arranged in any of 5! ways, so there are a total of 2 x 4 x 5! = [960] valid ways to arrange the people around the table.

Solution 2: The total number of ways in which Pierre and Thomas sit together is 6! times 2 = 1440. The number of ways in which Pierre and Thomas sit together and Rosa sits next to one of them is 5! times 2 times 2 = 480. So the answer is the difference 1440 - 480 = [960].

∑[ 2*0.25^x, x, 0, 15] =2 2/3 =~3

GP      37, ...   925

925/37=25

So the common ratio must be a factor of the form    25 to the power of some number

The obvious ones to try are    \(\pm25\;\;or\;\; \pm5\)

-185/37 = -5    could be that one

-4625/37 = -125 = (-5)^3  or that one

-925/37 = -25  = (-5)^2   or that one, no that cannot work, just by inspection.

481/37 = 13    not that one

37,    37*-5,    37*-5*-5,.....

37,    -185,         925,     -4625,  

so there are two answers and both have the common ratio of  -5

∑[-4.4 + 6.6n], n=1 to 5 - The last one of your 4 choices. So the sequence for 5 terms will be:

2.2, 8.8, 15.4, 22, 28.6.......etc.

20)

? /  6   =  [6 - 4] / 4

? / 6  =  2/4

?/ 6  =  1/2

?  = 3

The side length  = 3 + 6  = 9

21)

10 / 4   =  [2x + 5 ] / 6

5/2  = [ 2x + 5 ] / 6       cross-multiply

30  = 2 [ 2x + 5 ]

30  = 4x + 10   subtract 10 from both sides

20  =  4x     divide both sides by 4

5  =  x

22)

[8 + 2x ] / 4   =  15 / 3

[8 + 2x] / 4  = 5

8 + 2x   =  4*5

8 + 2x  = 20

2x  = 12

x  = 6

11) The common ratio should be - 5. So, you would have the sequence of:

37, - 185, 925, - 4,625........etc.

12)

N=(L - F) / D + 1, where N=Number of terms, L=Last term, F=First term, D = Common difference

N=(65 - (-5)) / 5 +1

N = 15 - Number of terms

Sum = (F + L) / 2 x N 

Sum = (-5 + 65) / 2 x 15 

Sum = (60) / 2 x 15

Sum = 450

16).....I think this is correct...

16/20  = ? / 45

4/ 5   =  ? /45       cross-multiply

45*4  = 5*?

180 = 5*?    divide by 5

36  =  ?

17)  

?/10  = 20/25

?/10 =  4/5      cross-multiply

5?  =  4 * 10

5? = 40     divide both sides by 5

?  =  8 

18)

?/4  =  6/3

?/4  = 2      multiply both sides by 2

?  = 8

19)

12/9  = ? / (33-9)

4/3  = ? / 24     cross-multiply

24*4  = 3* ?     

96  = 3 * ?      divide both sides by 3

32  = ? 

thank ya again

awesome job

You're very good at math Cphill

Good job again Cphill

2 ( 2.5x + 4)   =( 7x - 2 )    simplify

5x + 8  =  7x - 2       add/subtract  2, 5x  to/from both sides

10  = 2x       divide both sides by 2

5  = x 

So  AC   =  7(5) - 2   =  35  - 2   =  33°

Cphill good job

I'm happy I got a good grade

Thx electric pavlov

13...Correct  !!!

14.   

(x  + 2 ) / 15  =  8 /10      

(x + 2) / 15  =  4/5    cross-multiply

5(x + 2)  = 15 * 4

5x + 10  =  60

5x  =  50

x  =  10

15.  This one is a little tougher  !!

9 /15   = [2x - 6] / 20       simplify 

3/5  =  2[x - 3] / 20

3/5 = [x - 3]  / 10     cross-multiply

30  = 5[ x - 3]

6  = x - 3

9  = x 

Good job