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Because:

\(\begin{align} 4-5x(-1)&=9\\ 4+5x&=9\\ 5x&=9-4\\ x&=\frac{5}{5}\\ x&=1 \end{align}\)

You do it like this:

\(\begin{align} \frac{3122}{1}\cdot \frac{3}{100}&=\\ \frac{3122\cdot 3}{100}&=\\ 93.66 \end{align}\)

hehehe

Hello, I think i expressed myself wrong, the square root includes all of them, it includes  8^(1/3) and 9^(3/2) too, can you solve it again with this information, please? Thank you

5*4*3*2*1 = 120

5 x +10 = +50

Probability first card is a heart: p1 = 13/52

Provability that second card is a clover (club): p2 = 13/51

p1 and p2 = (13/52)*(13/51) → 13/204

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Electric field:

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Hello xrabia!

Solve 2^2x-5(2^x)+4=0

2^2x - 5 * 2^x + 4=0         [2^x = u

u² - 5u + 4 = 0

u_1;2 = 2.5 ±√(6.25 - 4)

u_1;2 = 2,5 ± 1.5

u₁ = 4

2^x1 = 4

2^x1 = 2²

x₁ = 2

u₂ = 1

2^x2 = 1

2^x2 = 2⁰

x₂ = 0

Greeting asinus :- )  !

96 + 96 + 969 + 96 + 74 + 58 + 6847 + 4546  + 4 = 12786

You have a double negative and you have confused our guest answwrer.

Yes it is impossible.

It is a specific very large number. It is not infinity.

Sometimes calculators call numbers, that are too big to calculate, infinity. But they aren't really.  :))

108/5.4

\(​ \frac{108}{5.4} = \frac{1080}{54}= \frac{2^{3}\times 3^{3} \times 5 }{2\times 3^{3} }= 2^{2}\times 5 = 20 \)

Once the overall interest is found, then the PV of all the 60 payments can be summed up on any good calculator, such as Wolfram/Alpha: Here is the same value summed up on W/A:

http://www.wolframalpha.com/input/?i=%E2%88%91%5B1+%2F+1.00348276693478333333333333333333%5E(n%2B1)%5D,+n%3D0+to+59

=54.06119752239511449364170823961036475493978759735782576366

To solve this problem, at least 2 common TVM formulae will be used repeatedly:

1 - PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD

This formula will find the PV of $1 per period, or $12 for each year at their respective interest rates.

Then these PV's will be brought forward to the present, discounting them each year at their respective rates using this 2nd and very common TVM formula:

2- PV=FV[1 + R]^-N=PV OF $1 IN THE FUTURE.

Then these PV's for the 5 years will be added together to give us the PV of all 60 payments.

Then we simply divide $1,000,000(I'm taking it as $1,000,000. If it is $10,000,000, then just multiply everything by 10).

Doing it by hand will involve about a dozen calculations. However, my computer is already programmed with all these financial formulae and will arrive at the answer very rapidly. Plugging in all numbers, the computer gives the accumulated PV as=54.0611975224. Now we simply divide $1,000,000 by this number and we get the even monthly payment of:$1,000,000/54.0611975224

=$18,497.56. Sixty payments of this amount will be made to pay off the entire $1,000,000 loan in 5 years.

Total interest paid will be: $18,497.56 x 60 - $1,000,000=$109,853.31.

The overall cost to the Company, or the combined interest rate, will be=4.17932032174%.

Finally, amortization of this loan confirms that all these numbers are accurate.

Is 1000! really = infinity... Is that not mathematically impossible?

No, it is not impossible. It is very large number:

 1,000!=4.02387260077093773543702433923 x 10^2567

Solve for x over the real numbers:
4-5 2^x+2^(2 x) = 0

Simplify and substitute y = 2^x:
 4-5 2^x+2^(2 x) = 4-5×2^x+(2^x)^2 = y^2-5 y+4 = 0:
y^2-5 y+4 = 0

The left hand side factors into a product with two terms:
(y-4) (y-1) = 0

Split into two equations:
y-4 = 0 or y-1 = 0

Add 4 to both sides:
y = 4 or y-1 = 0

Substitute back for y = 2^x:
2^x = 4 or y-1 = 0

4 = 2^2:
2^x = 2^2 or y-1 = 0

Equate exponents of 2 on both sides:
x = 2 or y-1 = 0

Add 1 to both sides:
x = 2 or y = 1

Substitute back for y = 2^x:
x = 2 or 2^x = 1

Express both sides with bases 2:
x = 2 or 2^x = 2^0

Equate exponents of 2 on both sides:
Answer: |x = 2     or     x = 0

Henry is one third as old as Dave the difference of Their Age is 4 years, how old is Henry and Dave?

Let Dave's age =D

Henry's age =D/3

D - D/3 =4

2/3D = 4 multiply both sides by 3/2

D = 4 x 3/2

D=6 - Dave's age

6/3 = 2 - Henry's age.

Average speed=Distance/Time

Time=Distance/Average speed

Time=D/10 going to the Park.

Time=D/8   Returning trip

D/10 + D/8 =1 1/5, solve for D(distance).

D=5 1/3 Km - The distance one way

Time=(5 1/3) / 10 =8/15 of an hour=32 minutes - Time taken to cycle to the park.

Time=(5 1/3) / 8 =2/3 of an hour =40 minutes - Time taken to cycle back home.

The solution depend upon whether you meant (1/4)^x + 2  =  16  or  (1/4)^{x  + 2}  =  16 ...

      (1/4)^x + 2  =  16     

            (1/4)^x  =  14                      Since the unknown is an exponent, find the log of both sides:

   log( (1/4)^x )  =  log(14)               A property of logs allows the exponent to come out as a multiple:

    x · log(1/4)  =  log(14)

                    x  =  log(14) / log(1/4)     --->     x = -1.9036...

(1/4)^{x +  2}  =  16                             Since 1/4  =  4^-1:

 (4^-1)^{x + 2}  =  16                             Since you have an exponent to an exponent, multiply the exponents:

      4^{-x - 2}  =  4²                              Since the bases are equal, the exponents must be equal:

       -x - 2  =  2

            -x  =  4

             x  =  -4

(1/4)^x+2=16 x=? someone please help. i need to know how this is done, step by step.

x≈0.174098.

P.S. There is no direct solution for this type of problems. Instead, the computers use iterations and interpolations to find the value of x.

11885,65 what is 2 percent of this

11,885.65 x 2/100 =237.71

\(\frac{5}{6} = \) 0.8333...¯

10/350 simplified

\(\frac{10}{350} = \frac{2\times 5}{2\times 5^{2}\times 7 } \)   \(= \frac{1}{5\times 7} \)

Thank you,asinus!Nice explanation and graphics representations.