geno3141

The tax is 8.5% of $89.95   --->   0.085 x $89.95  =  $7.65  (rounded)

Add the tax to the original cost to get the total cost.

2√(3x + 7) - 2  =  x + 3

Add 2 to both sides:

2√(3x + 7)  =  x + 5

Divide both sides by 2:

√(3x + 7)  =  (x + 5)/2

Square both sides:

3x + 7  =  (x² + 10x + 25)/4

Multiply both sides by 4:

12x + 28  =  x² + 10x + 25 

Subtract 12x + 28 from both sides:

0  =  x² - 2x - 3

Factor:

0  =  (x - 3)(x + 1)

Solve:

x = 3     or     x = -1 

3x + 4  =  2/3

Subtract 4 from both sides:

3x  =  -10/3

Divide both sides by 3:

x  =  -10/9.

You can find the length of the other wall by using the Pythagorean Theorem:  a² + b²  =  c².

--->   (17)² + b²  =  (18.79)²

--->   289 + b²  =  353.0641

--->   b²  =  353.0641 - 289  = 64.0641

--->   b  =  √64.0641  =  8 (approx)

Is the room a square?

IF you have an exponent to an exponent, multiply the exponents together:  

A^3^2  =  A^6          (B^10)^2  =  B^20         √D^10  =  (D^1/2)^10  =  D^5

A^6 / 5 x B^20  =  (A⁶B²⁰)/5 + C²⁰/D⁵

Pie is a dessert.

Pi is the name of the mathematical fraction created when the circumference of any circle is divided by its diameter. Because its an irrational number, you can't write all the digits -- it never ends and it never repeats.

Significant digits do not depend upon the location of the decimal point; the significant digits are 1535.

When you are rounding to 3 significant digits, look at the fourth digit (in this case, the last 5). If this digit is 5 or more, round up the third digit; if this digit is smaller than 5, leave the third digit alone. In both cases, drop the fourth digit, and any that are after it.

So, round 0.01535 to 0.0154.

Since an equilateral triangle has three equal sides, divide the perimeter by 3 to get the length of each side:

(15x + 21) ÷ 3  =  15x/3 + 21/3  =  5x + 7.

If the problem is:  3^{x + 1}  =  6^{4 - x}

--->   ln( 3^{x + 1} )  =  ln( 6^{4 - x} )

--->   (x + 1)ln(3)  =  (4 - x)ln(6)

--->   x·ln(3) + ln(3)  =  4·ln(6) - x·ln(6)

--->    x·ln(3) + x·ln(6)  =  4·ln(6) - ln(3)

--->   x[ ln(3) + ln(6) ]  =  4·ln(6) - ln(3)

--->  x  =  [ 4·ln(6) - ln(3) ] / [ ln(3) + ln(6) ]

Since there are 13 diamonds and 52 cards, the probability that the first card is a diamond is 13/52.

Now, there are only 51 cards remaining and 13 of these cards are spades, so the probability that the second card is a spade is 13/51.

Combining these, the probability that the first card is a diamond AND the second card is a spade is:

     13/52 x 12/51.

Multiply these together to get the final probability.