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Acute isosceles triangle.

Sides: a = 6   b = 6   c = 5

Area: T = 13.636

Perimeter: p = 17

Semiperimeter: s = 8.5

Angle ∠ A =  65.376° = 65°22'32″ = 1.141 rad

Angle ∠ B =  65.376° = 65°22'32″ = 1.141 rad

Angle ∠ C =  49.249° = 49°14'55″ = 0.86 rad

     The triangle's area using Heron's formula.

Heron's formula gives the area of a triangle when the length of all three sides are known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

T = sqrt{ s(s-a)(s-b)(s-c) },  

T =sqrt{ 8.5(8.5-6)(8.5-6)(8.5-5) }

T =sqrt{ 185.94 } = 13.64 units^2

​

Favorite food for 10 weeks!

I will assume that the 26 letters can be repeated:

26^3 =17,576 possible number of 3-letter words

24^3 =13,824 - all 3-letter words that have no "A's" or "B's" in them

17,576 - 13,824 =3,752 - Three-letter "words" that have at least one "A" or one "B" in them.

V (cone)   = ( pi ^ radius^2 * height )  / 3

104.67  = (3.14) * (radius)^2 *  4 / 3

Multiply both sides by 3  and divide both sides by 3.14

104.67 * 3  / 3.14   =  radius^2

The left side  evautes  to  ≈  100

Taking the square root of both sides  gives that

10  =  radius

Double this value to  find the  diameter....

Glad to help  !!!

Do you see why this answer is  correct   ???.....that's the important thing.....

-39  =  6  - 5x      subtract 6 from both sides

-45  =  -5x         divide both sides by  -5

9  =  x

thx your a life saver 

-3.5

Wall space  if no windows  and  no doors (1)  =  9 (10 + 10 + 12 + 12) =  9 ( 44)  = 396 ft^2

Subtract   windows and doors square footage =   2  (3*6  + 3.5 * 6.5)  =  2 ( 18 + 22.75)  = 2 ( 40.75)  = 

81.5 f^2

So

396  - 81.5    =   

314.5 ft^2  =  sq ft to be painted

−33/5=𝑥

Here are my answers (with diagrams) to a  similar problem....see if they might help.....I think only the angle sizes are different.....

https://web2.0calc.com/questions/circle-gamma-is-the-incircle-of-triangle-abc-and

https://web2.0calc.com/questions/circle-gamma-is-the-incircle-of-triangle-abc-and

Yep......

sqrt (81 - x^2)  + sqrt (-(x - 10))   we can write

sqrt (81 - x^2) + sqrt  ( 10 - x)

As long as the  values for x under each radical don't produce a negative value for the expression in the radical, they will be in the  domain

Considering the  first radical    x  can take on  the vaues  [ -9, 9]

Considering the second radical, x can take on   the values  (-inf, 10 ]

We need to take this  most restrictive interval.....this is the  first  =  [ -9, 9]

[the interval width  = 18 ]

The graph here confirms this   :  https://www.desmos.com/calculator/nvq8fnqsun

So all the possible values of $n$ are $-76,-4,4,76?$

Note  that

I think that answer was for 7x^2  + nx  +11    which  isn't the same as   what you asked    =   7x^2 + nx  -11

In your question, n  has the values   -76, -4, 4 , 76  

You'd have to ask the site owner, Andre Massow  (not trying to discourage you, MS, but I doubt that he needs more mods right now ....)

7x^2  + nx - 11

Note  that  we have   

(7x  - 11)  (x + 1)      =    7x^2 - 11x + 7x  - 11   =   7x^2 - 4x - 11

(7x - 1)   (x + 11)     =     7x^2 -1x + 77x - 11    =    7x^2 + 76x - 11

(7x + 11) (x - 1)       =     7x^2  + 11x - 7x  - 11  =   7x^2 + 4x  -11

(7x + 1) (x - 11)   =         7x^2 - 77x  +1x - 11   =    7x^2  - 76x  - 11

Thx, guest....a faster way

5  integers  in  each  of the hundreds, tens and ones place are odd.....

So  5 * 5 * 5   =   125

If ACB  = 90°, then A,B  are  endpoints of the diameter

Then ACB  is an inscribed angle and its intercepted arc  =  2*90   =180°

So....the  arc length that it intercepts  is just a semi-circle  with a radius  of 18/2  =9

The arc length  =    9pi

i would rather eat my favorite foods for 10 weeks

(111, 113, 115, 117, 119, 131, 133, 135, 137, 139, 151, 153, 155, 157, 159, 171, 173, 175, 177, 179, 191, 193, 195, 197, 199, 311, 313, 315, 317, 319, 331, 333, 335, 337, 339, 351, 353, 355, 357, 359, 371, 373, 375, 377, 379, 391, 393, 395, 397, 399, 511, 513, 515, 517, 519, 531, 533, 535, 537, 539, 551, 553, 555, 557, 559, 571, 573, 575, 577, 579, 591, 593, 595, 597, 599, 711, 713, 715, 717, 719, 731, 733, 735, 737, 739, 751, 753, 755, 757, 759, 771, 773, 775, 777, 779, 791, 793, 795, 797, 799, 911, 913, 915, 917, 919, 931, 933, 935, 937, 939, 951, 953, 955, 957, 959, 971, 973, 975, 977, 979, 991, 993, 995, 997, 999) = 125 such numbers.

Thanks Alan,

I never would have thought of that  g(1)  and   g(-1) method     

G/(x + 5) + H/(x^2 - 4x) = (3x^2 - 13x - 5)/(x^3 + x^2 - 20x)

\(\frac{G}{(x + 5) }+ \frac{H}{(x^2 - 4x)} = \frac{(3x^2 - 13x - 5)}{(x^3 + x^2 - 20x)}\\ \frac{G}{(x + 5) }+ \frac{H}{x(x - 4)} = \frac{(3x^2 - 13x - 5)}{x(x+5)(x-4)}\\ \frac{G*x(x - 4)+H(x+5)}{{x(x+5)(x-4)} }= \frac{(3x^2 - 13x - 5)}{x(x+5)(x-4)}\\ G*x(x - 4)+H(x+5)=3x^2 - 13x - 5\)

Expand then simplify the LHS

Then equate coefficients

$1.8446744$e$+19$