geno3141

_nP_r  =  n! / (n - r)!     --->     ₈P₁  =  8! / (8 - 1)!  =  8! / 7!  =  8

_nC_r  =  n! / [ (n - r)! · r! ]    --->     ₅C₃  =  5! / [ (5 - 3)! · 3! ]  =  5! / [ 2! · 3! ]  =  10

So the answer is  8 x 10  =  80

Let's take a particular example; let's say that f(x)  =  7x + 29.

y  =  f(x) + 3  =  (7x + 29) + 3  =  7x + 32

y  =  f(x + 3)  =  7(x + 3) + 29  =  7x + 21 + 29  =  7x + 50

This shows that, for this case, the two lines are parallel because they have the same slope but different y-intercepts.

This says that the answer is (A).

f(x) + 3  takes the original function, f(x), and moves it up 3 spaces but leaves the slope alone.

f(x + 3)  makes the y-value of f(x) the y-value of f(x + 3); it moves it 3 spaces down the line but leaves the slope alone. 

My suggestion to doing problems like this:  take a particular example but don't use values for m and b that are special numbers, such as 0, 1 or -1. Then, analyze what happens to the particular beginning example.

Let W = number of wristbands.

Let B = number of belts.

Number equation:  W + B  =  30

Value equation:  5.50W + 8.75B  =  204.00

Multiply the top equation by 5.50 and subtract it from the bottom equation:

     5.50W + 8.75B  =  204.00              <---  5.50(W + B  =  30)

     5.50W + 5.50B  =  165.00

     ---------------------------------

--->             3.25B  =  39.00                <---  subtract down the columns

--->                    B  =  12                     <---  divide by 3.25

Since W + B  =  30   --->   W + 12  =  30   ---?   W  =  18

There were 12 belts and 18 wristbands.

I'm assuming that you mean degrees, minutes, seconds:

There are 60 minutes in each degree and 60 seconds in each minute (making 3600 seconds in one degree).

sin( 351° 22' 58" )  =  sin( 351 + 22/60 + 58/3600 )  =  sin( 351.3827777...)  =  - 0.14983...

If that's not what you mean ????

Functions will not have real answers if the denominator is zero.

Factoring the denominator:  x² - 8x - 20  =  (x - 10)(x - 2)   ---> therefore the two numbers, 10 and 2, must be excluded.

Also, functions will not have real answers if there is a negative number under the square root sign.

All numbers smaller than 3 will give a square root of a negative number, therefore, they must all be excluded. This is an infinite number of numbers.

The answer, then, is (d) -- you must exclude an infinite number of numbers. 

Wait until you're in calculus  --  then, you'll be able to "just du it!"

1 ton  =  2000 lbs

So, 1/4 ton  =  2000/4  =  500 lbs

and 1 1/4 tons  =  1 + 1/4 tons  =  2000 lbs + 500 lbs  =  2500 lbs

To find cos^-1(-324/-440), use  (2nd) (cos)  or  (acos).

cos^-1(-324/-440)  =  42.58° (approximately)

I'm assuming that you mean:  (2/5)^{x - 2}  =  (8/25)^{2x + 1}

Write  8/125  as  2³ / 5³   =  (2/5)³.

(2/5)^{x - 2}  =  ((2/5)³)^{2x + 1} 

--->    (2/5)^{x - 2}  =  (2/5)^{6x + 3}          (Simplfying by multiplying exponents)

Since the bases are equal, the exponents must be equal:

--->   x - 2  =  6x + 3

--->      -2  =  5x  + 3

--->      -5  =  5x

--->      -1  =  x

To evaluate means to find the value, to solve it, to work it out.

8³  =  8 x 8 x 8  =  512