Answer:
∠APB = 106°
Step-by-step explanation:
Method 1: Focus on Triangle APB
Every angle of equilateral triangle ABC is 60°
∠BAP = 60°
∠ABP = 60° - 46° = 14°
Total degrees in one triangle is 180°
∠APB = 180° - 60° - 14° = 106°
Method 2: Exterior Angle Theorm
∠APB = ∠PBC + ∠PCB
∠APB = 46° + 60°
∠APB = 106°
Answer:
D
-3 * (-4) matches, as well as the powers (I guess you wanted to communicate that these are powers, but it would also be correct if these where factors)
There's only one system of equations here.
Let's eliminate x first,
x - y + z = -1
x = -1 + y - z
Substituting into x + y + 3z = -3 gives
(-1 + y - z) + y + 3z = -3
2y + 2z = -2
y + z = -1
Substituting for x into 2x-y+2z = 0 gives
2(-1 + y - z) - y + 2z = 0
-2 + 2y - 2z - y + 2z = 0
y = 2
Got lucky on that one.
z = -1 - y = -1 - 2 = -3
x = -1 + y - z = -1 + 2 - -3 = 4
Answer: x=4, y=2, z= -3
Check:
x-y+z = 4 - 2 + -3 = -1, good
x+y+3x = 4+2+3(-3) = -3, good
2x-y+2x = 2(4)-2+2(-3) = 0, good
Answer:
Area = 16
Step-by-step explanation:
The plan is to find the area of the large triangle (blue and white together) and subtract the white triangle's area.
Area of blue + white.
h = 8
b = 5 + 4
b = 9
Area = 1/2 * 8 * 9
Area = 1/2 * 72
Area = 36
===============
Area of white.
h = 8
b = 5
Area = 1/2 * 8 * 5
Area = 20
==============
Area of the shaded region (blue) = Area of both triangles - Area of the white
Shaded = 36 - 20
Shaded = 16
Answer:
x=88
Step-by-step explanation: x-44
add on both sides = to 88
