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Write  3^{2c + 1}  as  (3^2c) · (3)  or as 3·3^2c

This problem becomes:  3·3^2c  =  28·3^c - 9

which is:                      3·3^2c - 28·3^c + 9  =  0

I'm going to replace  3^c  with  x  and  3^2c  with x²:

--->                            3x² - 28x + 9  =  0

--->     Factor:             (3x - 1)(x - 9)  =  0

Which means:              3x - 1  =  0         or         x - 9  =  0

--->                                   x  =  1/3      or              x  =  9

But   x =  3^c  --->              3^c   = 1/3      or             3^c  = 9

--->                                 3^c   =  3^-1      or             3^c  = 3²

So:                                   c  =  -1        or               c  =  2

0 divided by 2 is 0

first turn 2 into a fraction

1/3 divided by 2/1

now use the recipricle and multiply

1/3 x 1/2

multiply across

1/6

there's your answer!

If you have a unit circle, the value of sine is the y-value, the value of cosine is the x-value, and the value of tangent is y/x.

So, if the point is  x = 3/5  and  y = 4/5, the value of tan θ  =  (4/5) / (3/5)  =  4/3

To get an x³ in the answer:

---   Multiply the +1 from the first factor with the 2x³ of the second factor to get 2x³

---   Multiply the -8x times the -7x² to get 56x³

---   Multiply the -3x² times the 3x to get -9x³

---   Multiply the -3x³ times the 4 to get -12x³

Add these terms together to get the coefficient that you want ...

All we really need to do is to look at the first 12 coins..(the common denominator of 2, 3 and 4)....whatever pattern that exists there just repeats itself 7 times

We will have

Q D N P Q N Q P N D Q P

So we have

4 x 7 = 28 quarters

2 x 7 = 14 dimes

3 x 7 = 21 nickels and 21 pennies

The same as geno found....

I'll let you total the money....!!!!  (in pennies, remember !!!)

Write  4^x as  (2²)^x  =  2^2x

Then  4^x - 2^x = 56  becomes  2^2x - 2^x = 56   which is:   2^2x - 2^x - 56  =  0

Now, factor:  (2^x - 8)(2^x + 7)  =  0

Either:  2^x - 8  =  0     --->   2^x  =  8     --->     x  =  3

Or:       2^x + 7  =  0     --->   2^x  =  -7    (impossible for real numbers)

It has different pronumerals, because it's vector.

vector is not only about how long or how big, it's also about the direction of it.

Here you are.

It is a square - so 

OA=OC

so why have 2 different pronumerals?

Ok thanks!

AP and MQ meet at P

I assume that you mean

AC and MQ meet at P  ??

Is that (5) base??

If the problem is:  5log₅(2v + 4) - 4  =  -9

Add 4 to both sides:     5log₅(2v + 4)  =  -5

Divide both sides by 5:  log₅(2v + 4)  =  -1      

Write into exponential notation:  2v + 4  =  5^-1    --->    2v + 4  =  1/5

Subtract 4 from both sides:        2v  =  -3.8

Divide both sides by 2:                v  =  -1.9 

Just divide both sides by 8  

3/4 or .75

Let's see:  you start with 84 quarters.

Now you change every 2nd quarter with a dime; so you now have 42 quarters (those in odd-numbered locations) and 42 dimes (those in even numbered locations).

When you change every third coin with a nickel, half of them will come from odd-numbered locations and half will come from even-numbered locations. Since 84 divided by 3 is 28, 14 nickels will be in odd-numbered locations and 14 will be in even numbered locations. You now have 28 quarters and 14 nickels in odd-numbered locations and 28 dimes and 14 nickels in even-numbered locations.

Changing every fourth coin with a penny, will place 21 pennies, all in even-numbered locations; 14 in locations that have dimes and 7 in locations that have nickels.

In odd-numbered locations, you have 28 quarters and 14 nickels; in even-numbered locations, you have 14 dimes, 14 pennies, 7 nickels and 7 pennies.

Total:  28 quarters, 14 dimes, 21 nickels, and 21 pennies

I draw diagram, it's quite fiddly, plz understand 

By trig Z rule,

Then angle between those is 180-35-51=94

Now you have 3 angles and one side.

You can use cosine rule or sine rule to get it.

Because sine rule is more simple, I will use sine rule here.

$$\frac{50}{sin94}=\frac{x}{sin35}=\frac{y}{sin51}$$

where x and y being opposite side of each angles.

$$x=\frac{50sin35}{sin94}$$

$$x=28.7 (3 s.f.)$$

Hope it helped! 

Oh why thank you. LOL. 

yeah hopefully...Its not fun with all these old folk. I mean melody its alright to mess with her, but i usually get nagged as a result so that stains the fun a little lol and messing with chris is always fun when i make jokes about how ancient he is, but he hardly ever says anything back when i do, Yep they just dont amount to the pointless arguements and debates i have with rosala....

Rosala has not stopped pinning for you since you were lost in the kingdom.

I'm sure she will come back and visit much more, if you stay around.