Answer:
C. ⅐
Step-by-step explanation:
Recall: the slope of a line that is perpendicular to another is the negative reciprocal of the slope of the other line that it is perpendicular to.
Thus:
Slope of red line = -7
The green line that is perpendicular to the red line will have a slope that is the negative reciprocal of -7.
Negative reciprocal of -7 = ⅐
The slope of the green line is therefore ⅐
Here is your answer and an explanation
Answer: y = -2/3x
Explanation:
This can be determined by calculating the gradient of the straight line, using:
m=ΔyΔx
=−6−34−(−2)
=−96
=−32
Then we use the slope-point form of the straight line:
y−y1=m(x−x1)
to give:
y−3=−32(x−(−2))
∴y−3=−32(x+2)
∴y−3=−32x−3
∴y=−32x
Da answer is cCbecause it is
Answer:
255 m
Step-by-step explanation:
From the given question, the surface of the water body is the reference point. And this point is assumed to be 0, so that any distance above it is positive, and any distance below is negative. This is synonymous to the number line system.
Thus,
For the aircraft, its height = +200 m
For the submarine, its depth = -55 m
So that the difference between the submarine and aircraft can be determined as;
200 - (-55)
= 200 + 55
= 255 m
The distance between the submarine and aircraft is 255 m.
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
---------------------
The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
