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Sav [38]
3 years ago
14

In a necklace, there are 2 white beads for every 7 purple beads. There is a total of 8 white beads. How many purple beads are in

the necklace?
Mathematics
1 answer:
tresset_1 [31]3 years ago
4 0

Answer:

OK! So this is a case of circular permutation. While dealing with this type of problems, we consider the circle to be placed in free space i.e it is symmetric when viewed from and point around it. So to break the symmetry we first fix one of the beads.

Here I am taking a red bead. Now we are left with 4 red and 2 blue beads.

6 beads can be placed in 6! Ways as 1st place will have 6 possibilities, 2nd place will have 5 possibilities and so on which gives

6*5*4*3*2*1 = 6!

But this time we have considered some extra cases as well because the red and blue beads are identical so which red bead has occupied a specific position will not at all matter. So we divide the total by 5! For identical red beads (the fixed red bead will also affect the position of other beads) and 2! For identical blue beads.

Finally we have 6!/(5! *2!) = 720/(120*2) = 3.

So we can have 3 different necklaces.

As the number is small, we can even enlist the possibilities…

B B R R R R R

B R B R R R R

B R R B R R R

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Use the quadratic formula to solve 3x2 + 5x + 2 = 0.D. x = 2, –3
Neporo4naja [7]
Quadratic Formula:


         -b  +/-  √b² - 4ac
x = --------------------------
                 2a


In your equation 3x² + 5x + 2 = 0:

a = 3
b = 5
c = 2

Now, plug in these values into the formula.

         -5 +/- √5² - 4(3)(2)                        -5 +/- √25 - 4(6)
x = --------------------------------  ⇒  x = -----------------------------
                   2(3)                                               6
                                                                 
         -5 +/- √25 -24                    -5 +/- √1                  -5 +/- 1
x = ------------------------  ⇒  x =  ---------------  ⇒  x = --------------
                 6                                     6                            6

               -5 +/- 1
Split x = ------------ into two solutions by solving it.
                    6

        -5 + 1         -4
x = ------------ = ------ 
            6             6
 
       -5 - 1          -6
x = ----------- = ------ = -1
           6             6

The two final solutions are x = -1 and x = -4/6


8 0
3 years ago
Which statement best explains whether the table represents a linear or nonlinear function? Input (x) Output (y) −2 7 −5 4 −8 1 −
blsea [12.9K]

Answer:

The table represents a linear function because the rate of change is constant or all the points lie on a straight line.

Step-by-step explanation:

From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).

The slope of the line is

m= y2-y1/x2-x1 = 10-5/4-2 = 5/2

The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.

From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.

Since the rate of change (slope) is same for all points, therefore the table represents a linear function.

If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a  linear function.

3 0
3 years ago
Read 2 more answers
Help!!!
Allushta [10]
The correct answer is Choice B.

The first step in this problem is to divide both sides by 64.
On the left side, you will have b squared.
On the right side, you will have 1/4.

Now, take the square root of both sides.

The square root of 1/4 is positive or negative 1/2.
8 0
3 years ago
When the wheels of a bicycle rotate 30 times the bicycle moves a distance of 175 feet what is the rate
LuckyWell [14K]

Answer: 5 5/6 feet per rotation

Step-by-step explanation:

d/t=175/30=5 5/6

6 0
3 years ago
You now have entered the math zone
Ostrovityanka [42]

Answer:

12-12, it's a decrease so you subtract.

4 0
3 years ago
Read 2 more answers
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