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g^4 + 12g^2 + 9    we can write

(g^2 + 6)^2 - 27

Where c  = 1    and q  = -27

Those questions are from here I think: https://web2.0calc.com/questions/please-help-functions-and-graphing

The constant is a coefficient of x^0. I think you are incorrect. :)

We know that the sum of the coefficients is found by plugging in 1 into the polynomial. We are given f(1) as 32, so the answer is 32.

^{I think that you might need physics for this, as the answers for each is 90 degress and 12 feet. I am possibly incorrect, but this question's wording does not make sense.}

^{– asdf335}

^{To have the shortest possible and maximum angle of elevation, we want the incline to have the maximum ratio, 12:1. So, we know that it is a right triangle with base 1 and height 12. So, our answers are tan^-1(12) and sqrt145. – asdf335}

You do not need physics to solve this; however, you may need a physic (laxative) to purge yourself of the bullshit that’s impeding your access to the trigonometry needed for solving it.

$\text{Ramp angle } = \arctan (\dfrac{1}{12}) \approx  4.8°\\ \text{Ramp length } =  \dfrac{12}{sin (4.76°)} \approx     144.6 ft$

You are hopping this helps, but I’m sure the gimps of world are hoping you do not pursue a career in architecture. 

GA

Yeah, I've seen it happen to me too. One vote might not seem like much, but the troll searches up the person's profile and repeatedly thumbs down each post. Usually I have 0-2 thumbs ups for most of my math responses, but the troll keeps on disliking my posts every hour. I have noticed that the same person can downvote or upvote the same post; he or she just has to wait a couple of hours before the program forgets that the user has already voted. That's what happened when I had around 850 one day, and when I checked later in the evening, I was down to 700. I don't know why this person is doing it, and honestly I think it's a bit dissapointing for the user to find out that they have lost 50 status points in a few minutes. 

(And I think the troll doesn't have anything to do in his/her life, so he/she just feasts on other people's likes)

- PM

We know that odd x odd = odd. Here's a quick proof:

Say the odd number are a = 2x + 1 and b = 2y + 1. Then, we have 

ab = (2x + 1)(2y + 1) = 2y(2x + 1) + 2x + 1 => 2(2xy + y) + 2x + 1 = even + odd = odd.

We know 5^23 = 5 * 5 * 5 * 5 * ..... * 5, with 23 5's. The first two fives pair up into an odd, and so on, so that product is odd. Repeat for 7^17 to get two odd numbers, and we know that odd + odd = even, so the answer is 2.

a)

20 has factors of 1, 2, 4, 5, 10, and 20. So, to make the number as small as possible, we want to use 5 * 2 * 2. We will pair the largest exponents with the smaller primes to get 2^(5-1) * 3 * 5 = 240.

b)

It has 6 perfect square divisors, so we need the smallest number with 6 divisors then square that to get the answer. That is (by counting), 12. So, our answer is 12^2 = 144.

1 & 2)

Notice that angle 2 and the 135 degree angle are on the same line. That means that they are supplementary, or their angle sum is 180 degrees. This implies that angle 2 is 45 degrees.

3)

Because the sum of the angles of a triangle is 180, and we know two of the angles, (90 degrees and 45 degrees), we can use this to find the measure of angle 1 as 180 - 45 - 90 = 45 degrees.

a)

Boris knowledge test z score  = [ 57 -60 ] / 4.3 =  -.69   [ ≈ 24th percentile ] 

Boris aptitude test z score  =  [ 106 -110] / 7.1  = -.56 [ ≈  28th percentile ]

He did better on the aptitude test

b)

Callie knowledge test z score  =  [ 63 - 60] / 4.3 = .69    [ ≈ 75th percentile ]

Callie aptitude test z score  =  [ 114 - 110 ] / 7.1 =  .56  [ ≈  71st percentile]

She did better on the knowledge test

c) -0.93  =  [≈ 17th percentile ]

He still did the best on the aptitude test

a)  multiplying g   by  a constant other than -1/2  will  not change the degree of  f(x) + a* g(x)

Its degree will still  be 4

b)  multiplying g by -1/2   will result  in     -x^4 + 3x^2 - x  + 1/2

When added to   f(x)   we get    -x +   5/2    ⇒    degree 1

Here :   https://web2.0calc.com/questions/help-due-today#r1

LCM 20

1, 2 , 3, 2^2, 5, 6, 7, 2^3, 3^2, 10, 11, 12, 13, 14, 15, 2^4, 17, 18, 19 , 20  =

5 * 7 * 3^2 * 11 * 13 * 2^4 * 17 * 19   

It will have

2 * 2 * 3 * 2 * 2 * 5 * 2 * 2  = 

960 positive divisors

$36$.

$6\sqrt2^2$

Square root of $2$ squared$=2$

$6^2=36$

$36\cdot2$$=72$

So $6\sqrt2^2=72$

Area of triangle$=(l1\cdot{l2})\div2=a$

We already calculated the parentheses so now we divide by $2$

$72\div2=36$

Area of$\triangle{PQR}=36$

π

I figured it out :D

yes that works

6sqrt 2 ^2 / 2 = 36, by 45-45-90 triangles

Its a bit basic

LOL!!!!....don't worry about it, Guest....we all make mistakes on here!!!

[ I doubt that anyone will press charges against you   .....  ]

I'm the Guest who posted the first answer.  I see how I made a mistake.  40⁸ is 65,536 x 10⁸. 

The 6 at the end of 65,536 times the 5 at the end of 75¹⁸ will produce at least one additional terminal zero.

I need go no further than that to realize the approach to my answer was simplistic, and, worse, it was wrong. 

I'm mortified to make such an elementary arithmetic oversight, and I apologize if my blunder led anyone astray.

edited to add:  Thank you, CPhill, for posting the correct answer. 

. 

The function will have a horizontal asymptote at y  =  (5x^2 / x^2)   =   5

The graph  here  shows  that  the  global minimum occurs at   (-2,3)  :

https://www.desmos.com/calculator/kztvawwhml

So.....the range is  [ 3, 5 )

If we  join  W and Y......then triangle WXY  will  be a 45-45-90   right triangle  with WY as the hypotenuse  =

4 sqrt (2)   =  sqrt (32)

And angle WYZ  =  135 - 45  =  90.....so.....triangle WYZ will also be a right triangle.....with WY as one leg and WZ as the hypotenuse

So...ZY   =   sqrt  ( WZ^2  - WY^2)  =   sqrt (  9^2  -  (sqrt(32))^2 )  =  sqrt ( 81 - 32)  =  sqrt (49)  = 7  =  a

Note that we can write  40^8 * 75^18  as

( 4 * 10)^8  * ( 3 * 5^2)^18  =

( 2^3 * 5)^8 *  ( 3 * 5^2)^18  =

(2 ^3)^8 * (5)^8  * 5^36 * 3 ^18 =

2^24 * 5^44 * 3^18  =

2^24 * 5^24  * 5^20 * 3^18

(2 * 5)^24  *  5^20 * 3^18  =

5^20 * 3^18  *  ( 2 * 5) ^24

[5^20 * 3^18  ]  * (10)^24       which   has  24  terminal zeroes

How many terminal zeroes does 40^8 * 75^18 have?

Well, 40 to the 8th will have 8 terminal zeros.  However many terminal zeros in the base, there will be that many times the exponent in the answer.      examples:  10²=100  10³=1,000  10⁴=10,000  100²=10,000  1,000²=1,000,000 

As regards the second factor, any number ending with 5 no matter to what exponent you raise it, the answer will always end with a 5.     examples: 5²=25  15²=225  25²=625  105²=11,025  etc.  So the second factor adds no terminal zeros to the product. 

Multiplying the two factors together, there are 8 terminal zeros in the product. 

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