Find the perimeter of the triangle whose vertices are the following specified points in the plane. (4,−−10,−4) and (3,−7)

  √205 +√178 +1 ≈ 28.6595

Step-by-step explanation:

The distance formula tells you the distance between points (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)^2 +(y2-y1)^2)

Taken pairwise, the distances between the given points are ...

  d1 = √((-10-4)^2 +(-4-(-7))^2) = √(196+9) = √205

  d2 = √((3-(-10))^2 +(-7-(-4))^2) = √(169+9) = √178

  d3 = √((4-3)^2 +(-7-(-7))^2) = √1 = 1

Then the sum of the distances gives the perimeter:

  P = d1 +d2 +d3 = √205 +√178 +1 ≈ 28.6595

_____

In the attached figure, the distance "a" is the sum of the two long sides of the triangle.

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1