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1.   Since  y  =  f(x)  ,  f(x)  is positive at every point that has a positive  y  value.

f(x) is positive when  x  is in the intervals  [-8, -6)  and  (-2, 4) .

2.   f(x)  =  x⁵ + 2x

To find out if this function is even or odd, we need to find  f(-x) .

f(-x)   =   (-x)⁵ + 2(-x)

f(-x)   =   - x⁵  -  2x

f(-x)   =   (-1)(x⁵ + 2x)

f(-x)   =   (-1)( f(x) )

Since  f(-x)  =  -f(x) ,  f(x) is an odd function.

can you help for 10?

Anyone for number 10?

Here's the graph of 8

It's the cube root function shifted 5 units to the right and 1 unit down 

https://www.desmos.com/calculator/8neckfvbrw

Can you help with number 8

9.

P(x)   =   55000√[ x - 1945 ]

In which year was the population of the city  220,000 ? That is, what is  x  when  P(x) = 220,000 ?

220,000   =   55000√[ x - 1945 ]

                                                      Divide both sides of the equation by  55000

4   =   √[ x - 1945 ]

                                 Square both sides of the equation.

16   =   x - 1945

                                 Add  1945  to both sides.

1961   =   x

Check:    P(1961)   =   55000√[ 1961 - 1945 ]   =   55000√[ 16 ]   =   55000(4)   =   220,000

First, add 5 to both sides. then square both sides, and then expand, and solve. The answer should be $-2$

Very nice, RainbowPanda  !!!

11.

The input value is put into one function and evaluated. Then, this result is put into a second function  and the result of this is the output. 

12. To give a simplistic answer, if the prime factors and variables under the radicand have individual powers on them that are less than the index of the root, it is fully simplified.

That is correct, CPhill!

Avg rate of change  =

[ f(14 )  - f(8) ]  /  [ 14 - 8 ]   =  

[ ( √ [14 - 4] )  - (√ [8 - 4])  ] / 6  =

[ √10 - √4 ]  /  6  = 

0.19 

Yeah questions I need help with answer CPhill

If we have a regular polygon, we can just add the areas of the individual triangles to find the total area....actually....we only need the area of one of these triangles....all the rest will have the same area

Here's the way lynx got the second answer

√2 - √6

______        multiply top/bottom by the conjugate of the denominator ⇒ √2 - √6

√2  + √6

√2 -√6     √2 - √6                 2 - 2√12 + 6          8  - 2*2√3

______    _____      =        ___________   =  __________    =

√2 + √6    √2 - √6                   2  -   6                     -4

8/-4   +     -4√3  / - 4

-2 +  √3

This is the question.

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triangles 

no problem legend cphill

Thanks lynx and RainbowPanda  !!

For the second, we can never have a real  number answer for a negative under a square root....  (Note....this is not true for a cube root )

question 4:

=-2+√3

A. 0.06 and -0.06 is the answer

No prob....

question 1:

=0.06 and -0.06

We know that the skid marks (d)= 150 feet.

S= speed in miles per hour (what we have to figure out)

0.75*150=112.5 (left side is now figured out)

Now we have to figure out s^2/30.25

Let's multiply both sides by 30.25

s^2*30.25/30.25=112.5*30.25

s^2=3402.125

Square root of 3402.125=58.3277378

Rounded: 58

So our answer is about 58 miles per hour.