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what is the square root of 7894      

per my calculator, it is 88.848 185 124 964 71   

_.

Thank you so much!!!

Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...     

Well, I see  (²/₇)⁰  +  (²/₇)¹  +  (²/₇)²  +  (²/₇)³  +  ^{. . .} 

but I don't know what to do after that.   

AC = 2*sqrt(7)..

If EF is equal to FG, you know that the triangle is an isosceles. If BEF is equal to 130 degrees, EFG is also 130. You know that the whole triangle has 180 degrees, and the big angle is 130. 

180-130=50

50/2=25

so x is equal to 25

NOT MY ANSWER--- credit to mathisopandcool

:))

[F / (1 - R) ]==S

3/2 / [1 - 4/9]

3/2 / 5/9 ==3/2  x  9/5 ==27 / 10 ==2.7 - sum of infinite GS

THANKS! ;D

Adam: $\frac{1}{5}x$

Ben: $\frac{1}{5}x + 18$

Carlos: 54

here's an equation to solve for the total amt of marbles:

$(\frac{1}{5}x) + (\frac{1}{5}x + 18) + (54) = x$

if you need the steps here is a link (just input the equation I gave you above):

https://www.symbolab.com/

here is the answer: $\boxed{x = 120}$

hope this helps a little bit :)

I think I'm too late tho haha

2x+8 is between -2 and 12

2x is between -10 and 4

x is between -5 and 2

2/11   of   1/3   of his money represents 12 donuts

                 2/33 of money = 12 donuts

Spends 1/3   leaving 2/3  of his original money

     he spends 5/6 of this 2/3 on donuts    =  10/18 of his original money

               how many  2/33 ^rd's are there in  10/18 ?

                             10/18 / 2/33   * 12 = 110 additional donuts

                      110 + the original 12 donuts = 122 donuts all together.

S==Smaller,    L== Laeger number

S / L ==2 / 3

[S - 6] / [L  + 7] ==2 / 7, solve for S, L

Use substitution to get:

S==14   and   L ==21

The smaller of 2 numbers==14

x + (-11) = 5    add 11 to both sides of the equation to get:

x = 16

' h ' does not change.

I must not understand the question, because this could go on forever and you couldn't write down all of them if you keep writing until the end of time. 

Hi Ron,

You understand the question correctly. Your answer is correct. 

The formal solution is (q < 0)

It’s relationship to (x) is:  q = -x (x + 3)

...And most importantly, you remembered to "mind your peas and queues" 

GA

--. .-

Hi Hectictar,

It is really good to see you here  :)

The parabolas defined by the equations y = x^2 + 4x + 6 and y = 2x^2 + 7x - 4 intersect at points and (a,b) and (c,d), where c >= a. What is c-a?

\(y = x^2 + 4x + 6 \qquad and \qquad y = 2x^2 + 7x - 4\)

These are both concave up parabolas

Looking of  x values the points of intersection

\(x^2 + 4x + 6= 2x^2 + 7x - 4\)

solve that and you will get the 2 x values.

I will leave you to play with it now.   

\(\phantom{=}\quad\dfrac{x^1\cdot x^2\cdot x^3\cdots x^{10}}{x^2\cdot x^4 \cdot x^6 \cdots x^{20}}\\~\\ {=}\quad\dfrac{x^{1+2+3+\dots+10}}{x^{2+4+6+\dots+20}}\\~\\ {=}\quad\dfrac{x^{55}}{x^{110}}\\~\\ {=}\quad x^{55-110}\\~\\ {=}\quad x^{-55}\\~\\ {=}\quad \dfrac{1}{x^{55}} \)

If  x = 2  we get:

\(\dfrac{1}{2^{55}}\ =\ \dfrac{1}{36028797018963968}\)

Let:

f₁(x)  =  ax + 3

f₂(x)  =  x + 5

f₃(x)  =  2x - b

If the function is continuous, that means  f₁(2)  must equal  f₂(2)  and also that  f₃(-2)  must equal  f₂(-2)

f₁(2)  =  f₂(2)

a(2) + 3  =  2 + 5

2a + 3  =  7

2a  =  4

a  =  2

f₃(-2)  =  f₂(-2)

2(-2) - b  =  -2 + 5

-4 - b  =  3

-b  =  7

b  =  -7

And so

a + b  =  2 + -7  =  -5

The distance between the orthocenters of  AHC and BHC is equal to the distance between the circumcenters of these two triangles. 

The complete question is:

The ratio of the two numbers is 2:3. when 6 is subtracted from the smaller of the two numbers and 7 is added to the larger of the two, the new ratio is 2:7. what was the smaller of the two numbers before 6 was subtracted from it?

Ok cool