Answer:
a) the angle ABC is approximately 106 degrees b) 24
Step-by-step explanation:
1) Using the law of cos
AC*AC= AB*AB+BC*BC-2*AB*BC*cosB
8*8= 5*5+5*5-2*5*5*cosB
64= 50- 50c0sB
cosB= 14/(-50)= -7/25.
B= arccosB= arccos(-7/25)= 106degrees.
2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625
sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)
3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)
A mother decided to record the height of her daughter hair she notices that her kid hair grew about 15 inches every year. however, she would cut off 3 inches because it was damaged. to figure out how much hair her daughter had over the years she used the equation y=15x-3
First let us find the slope between the two points.
Slope = Change in y / Change in x.
(3, 6) and (8, 4) compares to (x₁, y₁) and (x₂, y₂)
Slope = (y₂ - y₁) / (x₂ - x₁) = (4 - 6) / (8 - 3) = -2/5
Slope m = -2/5= -0.4
Using y = mx + c, using point (3, 6)
y = -0.4x + c
6 = -0.4*3 + c
6 = -1.2 + c
6 + 1.2 = c
7.2 = c
c = 7.2
Equation = : y = -0.4x +c
y = -0.4x + 7.2
y = -4/10 + 72/10
10y = -4x + 72
5y = -2x + 36
Equation =: 5y = -2x + 36
Hope this explains it.