Answer:
The product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given the lines
y = 2/3 x -3 --- Line 1
y = -3/2x +2 --- Line 2
<u>The slope of line 1</u>
y = 2/3 x -3 --- Line 1
By comparing with the slope-intercept form of the line equation
The slope of line 1 is: m₁ = 2/3
<u>The slope of line 2</u>
y = -3/2x +2 --- Line 2
By comparing with the slope-intercept y = mx+b form of the line equation
The slope of line 2 is: m₂ = -3/2
We know that when two lines are perpendicular, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = (2/3)(-3/2
)
m₁ × m₂ = -1
Thus, the product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Answer:
−9+16
Step-by-step explanation:
1. 10−3(3−2)
10−9+6
2. Add the numbers
3. Rearrange terms
The formula for finding the volume of a rectangular prism (the cargo area of the truck is the shape of a rectangle in 3D; a rectangular prism) is V = (l)(w)(h); where <em>l</em> = length, <em>w</em> = width, and <em>h</em> = height.
First, substitute the known values into the equation:
l = 8.5
w = 6
h = 10.5
V = (8.5)(6)(10.5)
<em>(Note: .5 = 1/2)</em>
Now, all we need to do is simplify:
V = 535.5 ft³ OR 535 1/2 ft³
<em>(Note: ft</em><em>³</em><em> is the condensed form of cubic feet)</em>
You can pick whichever form your test directs you to use. They are both the same value though.
Hope this helps!
Answer:
The vertex is (-3,-2)
Step-by-step explanation:
We can write the equation for a parabola in the form
y = a(x-h)^2 +k where (h,k) is the vertex
y =-2 (x - 3)^2 - 2
h = -3 and k =-2
The vertex is (-3,-2)
3000 s........h hours
3000/h.........1 hour
3000/60h.......1 minute
3000*m/60h....m minutes
