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We can use Vieta's Formulas. Because 2x^2 + 7x + 11 = 0, we have \(a=2, b=7, c=11.\)

The sum of the roots is \(-\frac{b}{a}=-\frac{7}{2}\) and the product of the roots is \(\frac{c}{a}=\frac{11}{2}\).

Let's rewrite the expression:

\(ab + (a+b) = \frac{11}{2} - \frac{7}{2} = \boxed{2}.\)

The foci of an ellipse are at \((\pm c, 0)\) if the equation of the ellipse is \(\frac{x^2}{49} + \frac{y^2}{b^2} = 1\).

That means that c = 5 and \(b=\sqrt{49-25}=2\sqrt{6}.\)

The length of the semi-major axis is \(2b = 4\sqrt{6}\)

They mean ax²+bx+c (quadratic formula). Hope this helps so now the question can be answerd :)

\(3+\sqrt{x}+6=-12\)

\(\sqrt{x} = -21\)

No real number has a negative square root, so the solutions to this equation are extraneous.

1. f(x-3) is the graph of f(x) but shifted right 3 units. The vertex of the original parabola shifted right 3 units is (4, -2).

Factor the expression: \(\frac{y+6}{(y-1)(y-4)}\)

The asymptotes are at y = 1 and y = 4, so the sum is 5.

Rearrange the equatinos:

-11x + y = 14            . (1)

-ax - y = 4               . (2)

Multiply equation (2) by -1:

-11x + y = 14

ax + y = 4

Therefore, a = -11.

The top triangle is a 45-45-90 triangle, so x = 14sqrt(2).

The bottom triangle is a 30-60-90 triangle. The hypotenuse is 28, so y = 14 and z = 14sqrt(3).

A  graph  might  help  to  see  what  we  have

Rearrange  the  equation of the  circle  as

x^2  - 6x + y^2  +  8y   =  0      complete the square on x  and  y

x^2  - 6x  +  9   + y^2  + 8y  + 16    =  9 + 16       

(x - 3)^2  +  ( y + 4)^2   =  25

This is  a  circle  with  a  center  of  ( 3, -4)    and a  radius   of  5

We  cab write  the equation of the given line as    3x + 4y   -  25   =   0

Using  the  formula  for the  distance  between a point (  the center of the circle )  and the given line we have  that

l 3(3)  + 4(-4)  - 25  l    / sqrt   ( 3^2 + (4)^2)   =     

l -32  l  / sqrt (25)  =

32   / 5

Since  rhe  radius of the  circle  is  5.......then  the  distance  between  the  circle and  the  line  =

32/5  -  5   =

32/5  - 25/5   =

7 / 5    =    

1.4  units

tan(x) = -35/12

sin(x) = -12/37

cos(x) = 35/37

From there, use the half-angle formulas to derive sin(x/2), cos(x/2), and tan(x/2).

Let C be a point on line BT. We can extend SO to draw angle SOT. So, we have

Because \(\angle RTB = RB - SC = 3x - x = 2x = 29\)

Now, we know that arc RS = 180 - 4x = 180 - 58 = 122 degrees.

The denominator is (x)(x-1)(x-2). There are three factors, so there are three asymptotes: x = 0, x = 1, and x = 2.

The sum of the numbers is 0 + 1 + 2 = 3.

tan  K  = opp  / adj      =  24 / 45   =   8 /  15

Call the first  three terms   10  , 10 + d , 10 +  2d

So.....

10   +  (10  + d)  +  (10 + 2d)   = 39     simplify

30  +  3d   =  39

3d  =  39 -  30

3d    = 9

d   = 3

Call   the  last  4  terms      n , n + 3, n + 6 , n + 9

So

n  +  (n + 3) + ( n + 6)  + ( n + 9)  =  178

4n +  18    =  178

4n   =  178  -  18

4n   = 160

n =  40

The first term is  10     and  the last  term  =   40  + 9 =  49 =    10  + 3 (14  - 1)

There  are   14  terms

Their sum    =  [  first term  +  last term ]  *  number  of terms    /  2  =    [ 10  + 49] * 14/2   =  413

The  average  =     413 /  14    =    29.5

I'm really sorry that I got it wrong. Could you tell me the answer so I can see where I made a mistake?

Edit: It seems like you mistyped the problem according to this:

https://web2.0calc.com/questions/help_12091

The solution would have been:

\(x(\sqrt{2}+1)+y(\sqrt{2}+1)=\frac{1}{2}(\sqrt{2}+1)\\ x+y=\frac{1}{2}\)

Since the sum of the circumference of the circle is 2 times the radius times pi, just multiply 2pi to get the final answer:

\(\frac{1}{2} \cdot 2 \cdot \pi = \boxed{\pi}\)

We can write f(n) = ax^3 + bx^2 + cx + d. We can write a system of equations:

d = 1

a + b + c + d = 2

8a + 4b + 2c + d = 4

27a + 9b + 3c + d = 8

(a, b, c, d) = (1/6, 0, 5/6, 1)

So, \(f(4) = \frac{1}{6}(4)^3 + \frac{5}{6}(4) + 1 = \boxed{15}\)

Cross multiply and simplify:\(\frac{3+x}{5+x} = \frac{1-x}{2+x}\)

\((3+x)(2+x) = (1-x)(5+x)\)

\(x^2 + 5x + 6 = -x^2 - 4x + 5\)

So, \(x = -\frac{9}{4} \pm \frac{\sqrt{73}}{4}\)

Sorry, but that answer is wrong.

z^2  -  12z  +  7   =   0

We  have  the form   ax^2   + bx  +  c    =   0

The  sum  of  the  z  values  that solve this equation   =     -b / a   =    -(-12)  /  1   =    12

Average   =   Total points   /  Total students    =

 [ 20(80)  + 8(90)   + 2(94)  ]  /  30        =    83.6

As   shown below.....

20  +  20  + 8  +  12  =   60   participate in track

Thank you for your efforts and response, but the answer is wrong

We can factor accordingly: \(25^x - 9^y = (5^x + 3^y)(5^x-3^y)\)

Therefore, \(18 = (5^x+3^y)(3)\)

and the answer is 6.

We have two cases.

Case 1: x <= 3

8x + 3 = 0

x = -3/8

x is less than or equal to 3, so this solution is valid.

Case 2: x > 4

16 - 2x = 0

x = 8

x is greater than 4, so this solution is valid.

Add the solutions to get 61/8.

Good work , CTP....I forgot to calculate the MAXIMUM   ....but you didn't !    ~ EP