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g.  The functions will return the same value when  x ≥ 0

      When  x  < 0,  the graph of g(x) will be the graph of  f(x)  reflected across the x axis

h  No such value exists.......when x ≤ 0,   the first function will produce a positive value  and the second function will produce the negative of this value....thus......their sum wil  = 0

i   Note that  when  x = 5 ..... f(x)  =  (5)^2 =  25   and  g (x)  = 5 l 5 l  = 25

So  f(5)  + g(5)  = 25  + 25   = 50

We need to  solve this :

Beginning amount  +  amountt filled per second  = 1000

243.2  + 4.4 t   = 1000      subtract 243.2 from both sides

4.4 t   =  756.8   divide both sides by 4.4

t  = 756.8 / 4.4  =   172

It took 172 seconds to fill the drive

a       f (1/3)  = (1/3)^2   = 1/9

b       g (4)  = 4  l 4 l   =  4 * 4  = 16

c       g ( -√3)  = (-√3) l -√3 l  =  ( -√3 ) √3  =  - √9   =  -3

d   The domain is all real  numbers

e  The range is all real numbers

f    f(-67)  + g(-67)   =   

 (-67)^2  +  -67 l -67 l    =

67^2  - 67 (67)  =

67^2  - 67^2   =

0

tan (pi - x)

And

tan x  = (2/5)

So

tan (pi - x) =  tan (pi) - tan x                   0  - (2/5)                -(2/5)

                     ______________ =       ___________  =       ____   =     -2/5

                     1 + tan (pi)*tan x              1 + 0 * (2/5)               1

r = 4, as each term divided by the previous term is 4.

f(-3) = -2(-3) + 5

f(-3) = 6 + 5

f(-3) = 11

f(0) = -2(0) + 5

f(0) = 0 + 5

f(0) = 5

f(¼) = -2(¼) + 5

f(¼) = -0.5 + 5

f(¼) = 4.5

real:   -11

Now, do you think you can deduce the imaginary part?

f(x) = -2x +5

f(-3) = -2(-3) + 5

       =   6 + 5

f(-3) = 11                          See how it is done?   Now...you try the other two!   G'Luck!

Sequence three has a common difference of 4, as it is an arithmetic sequence and 4 is the constant amount of change between the numbers in the sequence.

Domain:

{-3, 0, 2, 9, 23}

Range:

{14, 7, 0, -18, -99}

The first set of ordered pairs is not a function. In a function, an input cannot have more than one output. However, one of the inputs in the first set, 3, is paired with two outputs, 1 and 2.

The numbers are ordered from least to greatest in this order:

-0.123, -0.0123, 0.112233, 0.1223, 0.123, 1/8 (or 0.125), and 0.13.

The sum of the second and sixth numbers, -0.0123 and 1/8, is 0.1127. So, 0.1127 is the answer.

−10cos(2π/3*x)+10

Solve for b:

2 log(a - 2 b) = log(a) + log(b)

Subtract log(a) + log(b) from both sides:

-log(a) + 2 log(a - 2 b) - log(b) = 0

-log(a) + 2 log(a - 2 b) - log(b) = log(1/a) + log((a - 2 b)^2) + log(1/b) = log((a - 2 b)^2/(a b)):

log((a - 2 b)^2/(a b)) = 0

Cancel logarithms by taking exp of both sides:

(a - 2 b)^2/(a b) = 1

Multiply both sides by a b:

(a - 2 b)^2 = a b

Subtract a b from both sides:

(a - 2 b)^2 - a b = 0

Expand out terms of the left hand side:

a^2 - 5 a b + 4 b^2 = 0

The left hand side factors into a product with two terms:

(a - 4 b) (a - b) = 0

Split into two equations:

a - 4 b = 0 or a - b = 0

Subtract a from both sides:

-4 b = -a or a - b = 0

Divide both sides by -4:

b = a/4 or a - b = 0

Subtract a from both sides:

b = a/4 or -b = -a

Multiply both sides by -1:

b = a/4    So, a / b = 4

Area of a circle = pi r^2

for the semicircle portion the area will be  1/2 pi r^2 = 1/2 pi (4^2)

For the triangle portion, area = 1/2 b h      b = 8  h = 4      1/2 (8)(4)

Add the reds together for the total area.....

5.3 years

If this represents their debt when it equals zero, they are out of debt:

0 = -4x^2 +10x +60     solve for 'x' using the quadratic formula    a=-4 b=10 c=60

x = 5.3 yrs

First one:

sin = opposite/ hypotenuse

so  sin c  =  h/a         or    a sin c = h

commutative property (they can be multiplied in any order)

Reflecting it over the x axis :  Multiply by -1

-cos(x)

Shifting it DOWN 2 units :   Subtract 2

-cos(x)  -  2

-10 cos ( 2 pi x / 3) + 10      I believe it is your second choice, though there is a typo.

10!= 1*2*3*4*5*6*7*8*9*10

= 2*3*2*2*5*2*3*7*2*2*2*9*2*5

= 2*2*2*2*2*2*2*2*3*5*3*7*9*5

=   4 *  4  *  4  *  4  *3*5*3*7*9*5

=        4^4              *3*5*3*7*9*5

So the highest value of x is 4

To reflect a function over the x-axis, we put a negative sign in front of it.

\(-cos(x)\)

To shift it 2 units down, we subtract 2.

\(-cos(x)-2\)

Four people put their hats on the table as they arrive.
When they leave, each person picks up one hat.
It happens so no-one has picked up his own hat.
In how many ways can this have happened?

This have happened in 9 ways.

Formula: