Points (1, 7) and (-3, 2)
Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)
The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4
Slope = 5/4
Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5
By condition of perpendicularity
For points (1, 7) and (-3, 2),
Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)
Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)
= (-1, 9/2)
Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)
Equation y - y₁ = m (x - x₁)
y - 9/2 = (-4/5) (x - -1)
y - 9/2 = (-4/5)(x + 1)
5(y - 9/2) = -4(x + 1)
5y - 45/2 = -4x - 4
5y = -4x - 4 + 45/2
5y + 4x = 45/2 - 4
5y + 4x = 22 1/2 - 4 = 18 1/2
5y + 4x = 37/2
10y + 8x = 37
The equation of the line to perpendicular bisector is 10y + 8x = 37
Answer:
1/4
Step-by-step explanation:
Answer: The correct answer is option A: 6
Step-by-step explanation: We shall start by splitting the word problem into bits to ease our calculations.
We start with “the quotient of a and 6...” and that can be expressed as
a/6 where a equals 186, this becomes
186/6 and this equals 31.
Note that quotient means the result derived from dividing two numbers/values.
Next, “The difference of ... and b squared”
The missing part of this statement has been calculated as 31, so this can now be written as “The difference of 31 and b squared” where b equals 5 and b squared now equals 25. Hence what we have is the difference of 31 and 25
That is, 31 - 25 and that equals 6.
Therefore, the expression can now be written out as;
(a/6) - b^2
When a equals 186 and b equals 5, the answer is 6
Answer:
Step-by-step explanation:
Given that t represents a number which is unknown to us, the difference of the number and 9 can be expressed algebraically as:
.
The difference of t and 9 = .
Answer:
The intersection point of the two curves is 
.
Step-by-step explanation:
From statement we get the following equations:
Supply curve
(1)
Demand curve
(2)
Where:
- Quantity, measured in thousands of metric tons.
- Price, measured in US dollars per metric tons.
If we add both equations, then we find that quantity is:
Then, we finally find the price by substituting on (2):
The intersection point of the two curves is .
