geno3141

( 1.2 x 10⁴ ) / ( 6 x 10^-2 )

Dividing into the two types of numbers:

( 1.2 / 6 ) x ( 10⁴ / 10^-2 )

( 0.2 ) x 10⁶      (when you divide numbers with the same base, subtract the exponents                                    4 - -2  =  6

( 2 x 10^-1 ) x 10⁶

2 x 10⁵             (when you multiply numbers with the same base, add the exponents                                        -1 + 6  =  5

[ a² / 3 · b³ ] x [ a² · b^1/2 ] / [ a^3/2 · 2b^1/4 ]

When multiplying similiar terms, add the exponent; when dividing similar terms, subtract the exponents.

For the a's:  a² x a² / a^3/2  =  a^{[ 2 + 2 - 3/2 ]}  =  a^5/2

For the b's:  b^1/2 / b³ / b^1/4   =  b^{[ 1/2 - 3 - 1/4 ]}  =  b^-11/4  =  1/b^11/4

Multiplying the numbers;  3 x 2  =  6 (in the denominator)

Answer:  a^5/2 / [ 6 · b^11/4 ]

When graphed in the usual x-y plane:  tan θ  =  y/x.

tan θ  =  y/x   and   tan θ  =  9/5 (if you assume that the angle is in the first quadrant).

The Pythagorean Theorem applies with  x² + y²  =  r²     --->   5² + 9²  =  r²

--->   25 + 81  =  r²     --->   106  =  r²

:  r  =  √106.

sec θ  =  1/ cos θ     and     cos θ  =  x/r     --->    cos θ  =  5/√106    

                                                              --->   sec θ  = √106/5.

However, the angle could be in the third quadrant which makes  y = -9  and  x = -5.

r is still √106, but  cos θ = -5/√106  and sec θ  = - √106/5.

This was corrected after notes from Melody and Alan -- thank you.

6 x (3 + 20)  =  6 x 23  =  138

Shimmy is correct, but you can rewrite the equation "in terms of x", by solving for x:

c  =  90x + 35

Subtract  35  from both sides:

c - 35  =  90x

Divide both sides by 90:

(c - 35)/90  =  x         or:  x  =  (c - 35)/90

There are 52 weeks in a year, so divide $57,300 by 52 to get the answer.

Draw a line segment from the end of the 14 base that is connected to the 17 side perpendicular to the 24 base. This meets the 24 base 10 units from the 17 side.

A right triangle is formed, the hypotenuse is 17, one base is 10, and the other base (the height of the trapezoid is unknown, call it 'x'.

Since it's a right triangle, use the Pythagorean Theorem: x² + 10²  =  17².

--->   x² + 100  =  289     --->   x²  =  189     --->   x  =  √189     --->   x  ≈  13.75

Each number term has degree 0 (zero).

Any term which has one or more variable has a degree equal to the number of variables; so, 3x has degree 1 (because there is one variable, the 'x').

Any expression with more than one term has a final degree equal to the degree of its highest degree term, so the expression 3x + 12 has degree 1.

There is a total of 35 cards, 26 + 10.

The probability that the first card contains a numeral is 10/36.

If the first card is a numeral, the probability that the second card also contains a numeral is 9/35. 9 numerals remain, 35 cards remain.

The probability that both are numerals is (10/36) x (9/35) = 1/14.