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16+16*3/4+16*3/4+16*9/16+16*9/16+16*27/64

=64.75 meters

Because both the leading coefficients of f(x) and g(x) are 1, the x^6 term would cancel out, giving a maximum degree of 5.

f(x)  = 2x^5 - x^4  + x^2 - 3

g(x)  =   degree  ???

f(x) + g(x) =   degree 3

The only way  that this is possible  is if   g(x)  = -2x^5 + x^4  + ax^3 +...........

So  g(x)   must be of degree 5

Thanks, heureka......I really liked this problem and your solution  !!!!!

I think that only works for where n=1, but it says it must work for all odd integers, sorry D:, also I think 60+71*k doesnt equal 131k

Also, yes, calculators are allowed.

The degree of \(f(x)+g(x)\) is 3, and the only way that \(g(x)\) can cancel the term of \(2x^5\) in f(x) is if \(g(x)\) contains the term \(-2x^5.\) Therefore, the degree of \(g(x)\) is \(\boxed{5}.\)

Sorry, I am not experienced in this topic, my answer may be wrong.

In order for f(x) with a degree of 5 to decrease to a degree of 3, g(x) must have a degree of 5 in order to eliminate the degrees of 5 and 4 in f(x).

Sorry, I am not very experienced in this topic, my answer may be wrong.

Let's pretend that f(x) is  x⁸. Since f(x) has a degree of 8.

Let's also pretend that h(x) is 3x⁸ + 4 * g(x). Where it has a degree of 9.

Now, it should be obvious with the deduction that g(x) must also have a degree of 9 to make the h(x) have a degree of 9.

So the minimum possible degree of g(x) should be 9 ??????????

It is 3x⁸ because in the problem it states: 3 * f(x)

Does this problem let usage of a calculator? Because I used a calculator to discover that the factors of 1441 are 131 and 11.

Are you looking for the values of x and also A through K? There are so many solutions. Perhaps infinite.

B)

There are 6 possibilities for the first person, 6 for the second, 6 for the third, and 6 for the fourth.

6^4 = 1296 total die roll possibilities.

Out of these 1296,

there are 6 possibilities for the first person but only 5 for the second. Again 5 for the third, and 4 for the fourth.

6*5*5*4 = 600

600/1296 = 75/162

You are very welcome!

:P

https://web2.0calc.com/questions/help-me-please_48077

When it falls the first time, it goes 16 meters.

When it goes up the first time, it goes up 16*3/4 = 12 meters.

When it falls the second time, it goes 12 meters.

When if goes up the second time, it goes up 12*3/4 meters = 9 meters.

When it falls the third time, it goes 9 meters.

When it goes up the third time, it goes 9*3/4 = 27/4 meters.

16+12+12+9+9+27/4 = 16+24+18+27/4 = (64+96+72+27)/4 = (160+99)/4 = 259/4.

You are very welcome!

:P

Solution: 

When two (2) distinct lines intersect, four (4) vertical angles are formed.

For five lines:

The first line forms 4 angles with each of the four other lines.  4(4) = 16

The second line forms 4 angles with each of the three other lines.  3(4) = 12

The third line forms 4 angles with each of the two other lines.  2(4) = 8

The fourth line forms 4 angles with the remaining line.  1(4)  = 4

There are 16 + 12 + 8 + 4 = 40 vertical angles.

GA

3a + b + c  =  -3    (1)

a  + 3b + c  = 9       (2)

a + b +  3c  =  19     (3)

Multiply (1) through by -3   and we get   -9a - 3b - 3c  = 9

Add this to  (2)   and we get that  -8a - 2c  = 18    (4)

Multiply  (3)  through by -3  and we get that -3a - 3b -9c  = -57

Add this to (2)  and we get that  -2a - 8c  = -48   (5)

Add (4)  and (5)  and we get that

-10a - 10c   = -30      divide through by -10

a + c  = 3 

Sub this into (2)  to find b

3b + 3  = 9

3b = 6

b = 2

And since  a + c  = 3      then c = 3 - a

Sub this into (3) to find a

a + 2 + 3(3 - a)  = 19

a + 2 + 9 - 3a  = 19

-2a + 11  = 19

-2a   = 8

a  = - 4

And using (1)

3(-4) + 2 + c = -3

-10 + c  = -3

c = 7

So  {a, b, c}  =  { -4, 2, 7 }

So   abc   =  (-4)(2)(7)  =  -56

Nope, it's incorrect. I have one more try, though.

p (q(x))  =  √ [ - ( 8x^2 + 10x - 3) ]

For the domain to be defined, - (8x^2 + 10x - 3 )  must be ≥ 0

So

-(8x^2 + 10x - 3)  ≥ 0

-8x^2 - 10x + 3 ≥ 0        

To solve this, set this = 0    and solve for x

-8x^2 - 10x + 3  = 0          multiply through by -1

8x^2 + 10x - 3  = 0           factor

(4x - 1) ( 2x + 3)   = 0

Set each factor to  0  and solve for x

4x - 1  = 0           and        2x + 3  = 0

4x  = 1                               2x   = - 3

x = 1/4                                 x  = - 3/2

The solution will either come from  x  = (-inf, -3/2] U [1/4, infinity)  or   x  = [-3/2, 1/4]

Testing a point in the second interval  [ I'll pick x = 0 ].....we can see that

√ [ - ( 8(0)^2 + 10(0) - 3) ]   =   √ [ - ( -3) ]  =  √ 3     gives us a real number

So....the interval that solves this is   [ -3/2, 1/4 ]

So  b  - a  =    1/4  - (-3/2)  =  (1/4) - (-6/4)  =  7/4

Here's a graph to  show that the solution interval is correct : 

https://www.desmos.com/calculator/6jhmgavfr0

this is my geuss

a=-1

b=3

c=19/3

Travisio

If  f(x)  is defined on  [ -8, 4].....this implies that  the function is defined for f(-8) to f(4) inclusive

So

g(x)  = f(-2x) = f(-8)   implies that   -2x = - 8  ⇒  x  = 4

And

g(x)  =  f(-2x)  = f(4)  implies that  -2x  = 4  ⇒  x = -2

So....the domain for g  is  [ -2, 4 ]

x^2 - 6x + c < 0

Set this  = 0

If this has real solutions, then the discriminant  is  ≥ 0

So

6^2 - 4c ≥ 0

36 - 4c ≥ 0

36 ≥ 4c

c ≤ 9

When c  = 9...the parabola will have its vertex at (3,0)......so....since it turns upward, this is the low point on the graph....so...it is not less than 0  at any point

So.....this implies  that  the inequality will be < 0 [ i.e., have real solutions for x ]   when c  = (0, 9)

Here's a graph to show this : https://www.desmos.com/calculator/frqkypfzn8

If the number doubles every two years, then we have five doublings  from 1990 to 2000....so we have

1,000,000 (2)^5  =  

32,000,000  in year 2000

OOPS!!!....thx, guest!!!....correction made

LOL!!!!!

The x coordinate of the vertex  can be found as   -b / (2a)  =  2   ⇒  -b = 4a  ⇒  b  = -4a

So.....we have the following quadratic

y = ax^2 - 4ax + c

And since  (2,1)   and (-4, -3)  are on the graph, we have that

a(2)^2 - 4a(2) + c  =  1  ⇒   4a - 8a + c  = 1  ⇒    -4a + c  =  1   ⇒   -32a + 8c  = 8    (1) 

a(-4)^2  - 4a(-4) + c  = -3  ⇒   16a + 16a + c  = -3  ⇒  32a + c  = -3      (2)

Add (1)  and (2)   and we have that

9c = 5

c = 5/9

And

-4a + 5/9  =  1

-4a =  4/9

a  = -1//9

And b  = -4(-1/9)  = 4/9

So....the quadratic  is

y  = (-1/9)x^2 + (4/9)x + 5/9

Setting this to 0  and we have that

(-1/9)x^2  + (4/9)x + (5/9)  =  0         multiply through by  -9

x^2 - 4x - 5  = 0       factor

(x - 5) ( x + 1)  = 0      set each factor to 0 and solve for x and we have that

x - 5  = 0                x + 1  = 0

x  = 5  = m             x  = -1 = n

So....m - n  =   5 -(-1)   =   6