To find out if a triangle is a right triangle, you can use the Pythagorean theorem(which can only be used for right triangles):
a² + b² = c² (c is the hypotenuse or the longest side) And you can plug in the side lengths into this equation. If they are the same number on both sides, it is a right triangle, if they are different numbers it is not a right triangle.
6.) a² + b² = c²
(4√3)² + (11)² = (13)²
(16(3)) + 121 = 169
48 + 121 = 169
169 = 169 It IS a right triangle
7.) a² + b² = c²
(5)² + (2√14)² = (9)²
25 + (4(14)) = 81
25 + 56 = 81
81 = 81 It IS a right triangle
8.) a² + b² = c²
(6)² + (√49)² = (√82)²
36 + 49 = 82
85 = 82 It is NOT a right triangle
9.) a² + b² = c²
(13)² + (2√39)² = (16)²
169 + (4(39)) = 256
169 + 156 = 256
325 = 256 It is NOT a right triangle
Any with an odd number of minus signs.
Perhaps the 1st and 4th, if I read it right.
Problem One
Find AM
AM = 71.5 - 22 = 49.5
Step Two
State the Givens.
AM = 49.5
MN = 71.5
MB = x
MP = 97.5
Step Three
Set up the Proportion
AM : NM :: x : PM
49.5 : 71.5 :: x : 97.5
Substitute and solve
49.5 / 71.5 = x / 97.5 Cross Multiply
49.5 * 97.5 = 71.5 * x Combine the numbers on the left.
4860.375 = 71.5 * x Divide by 71.5
4860.375 / 71.5 = x
x = 67.98
Problem Two
Remark
This is just a straight application of the Pythagorean Theorem
a^2 + b^2 = c^2
a = 10
b = 24
c = ??
10^2 + 24^2 = c^2
100 + 576 = c^2
676 = c^2
sqrt(c^2) = sqrt(676)
c = 26 <<<< answer
Answer:
400 mL
Step-by-step explanation:
0.50x + 0.20(600-x) = 0.40*600
50x + 20*600 - 20x = 40*600
30x = 20*600
x = 20*20
x = 400 mL
