Step-by-step explanation:
First you need to make a line perpendicular to y=2/3x+5. To do that you have to know that, if we use y=ax+b, a1*a2=-1. That is if a1 and a2 are perpendicular. So we get 2/3*a2=-1. -1/ 2/3=a2. a2=-1.5. We get y=-1.5x+b. Fill in (4,0) on y=-1.5x+b abd we get 0=-1.5(4)+b. b=6
The area is 36 units squared.
You have three ways you can solve this question.
Method 1:
Split the rhombus into two equal triangles.
You will get triangle ACD and triangle ACB.
Count the base length and height length of each triangle using the diagram.
You will get base = 6 units and height = 6 units. Plug this into the area of a triangle and then multiply it by 2.
A = bh/2 * 2
A = 6(6) / 2 * 2
A = 36 / 2 * 2
A = 18 * 2
A = 36
Method 2:
Calculate the length of DP.
The length of line segment DP is √28.8
Calculate the length of DC.
The length of line segment DC is 3√5
Put into equation A = bh.
A = bh
A = 3√5(√28.8)
A = 36
Method 3:
Calculate the length of each diagonal and put into formula A = 1/2(d1 * d2)
Diagonal DB = 12 units
Diagonal AC = 6 units
A = 1/2(d1 * d2)
A = 1/2(12 * 6)
A = 1/2(72)
A = 36
I love procrastinating my history essay for this :D
Solving <span>8x-5y=10 for y helps us to identify the y-intercept:
-5y = -8x + 10. Dividing both sides by -5, we get (8/5)x -2. Therefore, y = (8/5)x - 2; the y-intercept is (0,-2).
The equation </span><span>-6x-7y=-6 can be solved for its slope in the same manner.
7y = -6x + 6; then y = (-6/7)x + 6/7. Its slope is -7/6. A line perpendicular to this line has slope equal to the negative reciprocal of -7/6, which is 6/7.
So, using the slope-intercept form, y = mx + b becomes y = (6/7)x -2.</span>
Answer:
Option D = 16π/3 ft
Step-by-step explanation:
Arc length formula is written Mathematically as:
Arc length = 2πr × θ /360
r = 4 ft
θ = Central angle in degrees = 240°
2 × π × 4 × 240/360
8π × 240/360
8π × 20/30
16π/3 ft
So, the arc length is 16π/3 ft