Wanda is trying to locate the fermat point p of triangle abc, where a is at the origin, b is at (8,-1), and c is at (5,4) (the fermat point is the point such that the sum of its distances from the vertices of a triangle is minimized). she guesses that the point is at p = (4,2), and computes the sum of the distances from p to the vertices of $\triangle abc$. if she obtains m + n\sqrt{5},
where m and n are integers, what is m + n?

9514 1404 393

  8

Step-by-step explanation:

The distance formula is used to find the distances to each of the points:

  d = √((x2-x1)² +(y2-y1)²)

  d = √((4-0)² +(2-0)²) +√((4-8)² +(2-(-1))²) +√((4-5)² +(2-4)²)

  d = √20 +√25 +√5 = 2√5 +5 +√5

  d = 5 +3√5

Comparing to the form ...

  d = m +n√5

we see that m=5, n=3. The the sum m+n = 5+3 = 8.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )