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Expanding both sides of the equation, we get

a^2 + 1 + b^2 + 1 + c^2 + 1 = (a + b + c) + (1/a + 1/b + 1/c)

Simplifying the right side, we get

a^2 + 1 + b^2 + 1 + c^2 + 1 = a + b + c + (1 + 1/a + 1/b + 1/c)

Subtracting 1 from both sides, we get

a^2 + b^2 + c^2 = a + b + c

Multiplying both sides by 3, we get

3a^2 + 3b^2 + 3c^2 = 3a + 3b + 3c

Using the equation abc = 13, we can write

3(a^2 + b^2 + c^2) = 3(a + b + c)/abc = 3(a + b + c)/13

Solving for a + b + c, we get

a + b + c = 3(a^2 + b^2 + c^2) * 13 = 39.

Therefore, the answer is 39.

>>>>> is a 9-10-11 right triangle <<<<<  

I don't know about the rest of the answer, but 9-10-11 is not a right triangle.  

nvm...i found the answer...it's 88

that wasn't correct...

Let M be the number of dollars in the original pile. Then, Jeri's left pocket will have 50+32​(M−50) dollars, and her right pocket will have M−50−32​(M−50)=31​M dollars.

If Jeri keeps the right pocket money, she will have 31​M dollars. If she gives away 200 dollars from the original pile, she will have M−200 dollars left.

We are told that Jeri will have more money in her right pocket if she keeps it than if she gives away 200 dollars. So, we have the inequality 31​M>M−200. Solving for M, we get M>600.

Since the original pile must have at least 200 dollars, the possible values of M are 200

here's a hint!

try using the 30-60-90 triangle rule!

could you draw a diagram?

that might be helpful

sorry, but none of these are correct...

thanks for trying though....


I still need help

thank you you too! :))

N==Noah,  W==William

[N - 50] / [W + 50] ==1/5

[N - 60] / [W + 60] ==1 / 11, solve for N, W

N==70 stickers - what Noah had at the start

W ==50 stickers - what William had at the start.

Let CH ==y
Let AH ==x
Let CB ==z

x^2 + y^2=18^2...................(1)  
15^2 + y^2==z^2.................(2)   
z^2 + 18^2=(15 + x)^2..   ....(3), solve for x, y, z 

x ==12,  y==6*sqrt(5),  z=9*sqrt(5)

Area of ABC==1/2 * (12+15) * 6*sqrt(5)==181.1215 u^2

Thank you :)

First we  denote the length of PX as 'x'. By applying the Angle Bisector Theorem, we have:

PR / RQ = PX / XQ

22 / 26 = x / (26 - x)

22 * (26 - x) = 26x

572 - 22x = 26x

48x = 572

x ≈ 11.92

Now, let's find the length of XQ:

XQ = QR - PX ≈ 26 - 11.92 ≈ 14.08

Since M is the midpoint of PQ, we can determine the length of PM:

PM = PQ / 2 = 36 / 2 = 18

Since MY is perpendicular to PQ and MY = 8, we can determine the length of PY:

PY = PM - MY = 18 - 8 = 10

Therefore, AY is equal to PY:

AY = PY = 10

Now, we have all the side lengths of triangle AXY. We can calculate its area using Heron's formula:

s = (XY + AY + AX) / 2 = (14.08 + 10 + 11.92) / 2 ≈ 18

Area_AXY = sqrt(s * (s - XY) * (s - AY) * (s - AX))

Area_AXY = sqrt(18 * (18 - 14.08) * (18 - 10) * (18 - 11.92))

Area_AXY ≈ sqrt(18 * 3.92 * 8 * 6.08) ≈ 24.48

Finally, the area of triangle PQR is twice the area of triangle AXY:

Area_PQR = 2 * Area_AXY ≈ 2 * 24.48 ≈ 48.96 square units

R==Common Ratio

R==99 / 400

SUM== 150.50 * [1 - (99/400)^100] / [1 - (99/400)], solve for SUM

SUM==200

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR    

I was trying to draw the figure, and then       

you threw me a curve when you said AX. 

Where did that come from?   

Then I saw that you have the values of all   

three sides.  You don't need anything else. 

Add all three sides, then take half of it.    

Call this "s".       

                                                                               36 + 22 + 26   

                                                                       s  =  ——————  =  42     

                                                                                      2    

Then use the following to get the area.         A  =  sqrt[(s)(s – a)(s – b)(s – c)]   

This is called Heron's Formula.  

                                                                      A  =  sqrt[(42)(42 – 36)(42 – 22)(42 – 26)]   

                                                                      A  =  sqrt(42 • 6 • 20 • 16)    

                                                                      A  =  sqrt(80,640)    

                                                                      A  =  283.97 square units    

That answer looks weird,but it has     

to be right ... it's Heron's Formula. 

_.

sumfor(n, 1, 100, (2 +6*n) /(4^(101 - n)))==It converges to 200

Thank you for your help.

thats what i just said bro

Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?  

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

Note that (0.29 min • 60 sec/min)  =  17 seconds

The time on the clock is                                             2:54:17 pm 

_.

4^n=26 find n     

When I open the calculator on my iPhone   

then turn the phone on its side   

then select 2^nd functions    

one of the buttons is labeled log_y   

What that does, you can choose your own base    

and the phone will provide the log of any number  

I found that log₄(26) is  2.350219859 (rounded)  

check answer    

using the x^y function on my iPhone    

4^2.350219859  =  25.99999999    

Close enough for government work.  

_.

Find the ordered triple (p,q,r) that satisfies the following system:  

p - 2q = 3  

q - 2r = -2 + q  

p + r = 9 + p  

I first answered this problem, jeez, it must have been at least a year ago by now.  

Since then, I've copied and pasted the answer in again a dozen times or more. 

Oh well, once more unto the breach.........  

Let's number those equations, for identification only:  

(1)  p – 2q  =  3  

(2)  q – 2r  =  –2 + q  

(3)  p + r  =  9 + p  

Per equation (2), r = 1  

Per equation (3), r = 9  

You can't have both at the same time.  The system has no solution.  

_.

can anyone please help,...iv'e been stuck on this problem for hours!