hectictar

If you want the area of all the unpainted surfaces...

the painted area

=   the surface area of the prism

=   2( (3)(5) + (3)(6) + (5)(6) )  cm²

=   2( 15 + 18 + 30 )  cm²

=   2(  63 )  cm²

=   126  cm²

the number of cubes   =   3 * 5 * 6   =   90

each cube has a surface area of  6  cm²

total surface area of all the cubes   =   90 * 6  cm²   =   540 cm²

the area of the unpainted surfaces

=   total surface area - the painted area

=   540 cm² - 126 cm²

=   414 cm²

If  f(x)  is even, that means  f(-x)  =  f(x)  for all  x  values.

If  f(x)  is odd, that means  f(-x)  =  -f(x)  for all  x  values.

On the first graph, for instance,   f(2)  =  4    and   f(-2)  =  -4  =  -f(2)

We can see that it is like this for all  x  values that we could pick.

So   f(-x)  =  -f(x)  for all  x  values.   This function is odd.

On the second graph, for instance,   f(2)  =  4  , but   f(-2)  doesn't equal positive 4 or negative 4.

So   f(-x)  ≠  f(x)   and   f(-x)  ≠  -f(x)   This function is neither.

On the third graph,   f(2)  =  0   but   f(-2)  =  -8

So   f(-x)  ≠  f(x)   and   f(-x)  ≠  -f(x)   This function is neither.

2.

And     g(x)  =  20(1.5)^x

​g(x)​ has a greater y-intercept than ​f(x)​.

the y-intercept of  g(x)   =   g(0)   =   20(1.5)⁰   =   20

the y-intercept of   f(x)   =   15

20  is greater than  15 , so

True

​f(x)​ and ​g(x)​ are negative when x is less than 0.

False – there are no values that cause  f(x)  or  g(x)  to be negative.

f(x) and ​g(x)​ are both increasing on the interval  (−∞, ∞) .

True

​f(x)​  increases at a faster rate than ​ g(x) ​ does on the interval  (−5, −3) .

This is harder to tell....

rate of increase of f(x) on the interval looks like about  0.1

rate of increase of g(x) on the interval   ≈  1.646

so I think its

False

1.

The price of the stock increased the first 3 years.

True

The price of the stock never fell below its original value.

True

The average price in year 11 was less than the relative maximum price between years 1 and 5.

False

The value of the stock is negative between the 3^rd year and midway between the 8^th and 9^th year.

False

The stock started to increase again between the 8^th and 9^th year.

True

lynx7, you need to put a link to the answer if you get it from someone else.

h² + 2h + 5   =   0

                                    First subtract  5  from both sides of the equation.

h² + 2h   =   0 - 5

Now we want to add a number to both sides that will cause the left side of the equation to be a perfect square trinomial. So add  (2/2)²  , which is  1 ,  to both sides of the equation.

h² + 2h + 1   =   0 - 5 + 1

h² + 2h + 1   =   -4

                                       Now that the left side is a perfect square trinomial, it factors like this...

(h + 1)²   =   -4

                                       And we can add  4  to both sides so the right side  =  0  again.

(h + 1)² + 4   =   0

The question didn't say to solve for  h , it just said convert to vertex form...I think that is it.

x - 3y   =   9

                           Subtract  x  from both sides.

-3y   =   -x + 9

                           Divide both sides by  -3 .

y   =   x/3 - 3       The slope of this line is  1/3 .

y   =   -3x + 3       The slope of this line is  -3 .

Since the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.

Hey! I like that way!