Answer:
slope of the line is -0.5
y-intercept is 13
Explanation:
The general formula of the linear equation is:
y = mx + c
where m is the slope and c is the y-intercept
1- getting the slope:
We are given the two points:
(6,10) representing (x1 , y1)
(12,7) representing (x2 , y2)
The slope of the line will be calculated as follows:
m = (y2-y1) / (x2-x1) = (7-10) / (12-6) = -3/6 = -0.5
The equation of the line now becomes:
y = -0.5x + c
2- getting the value of the y-intercept:
To get the value of the y-intercept (c), we will use any of the given points, substitute in the equation of the line and solve for c. I will use the point (6,10) as follows:
y = -0.5x + c
10 = -0.5(6) + c
10 = -3 + c
c = 13
Based on the above, the equation of the line would be:
y = -0.5x + 13
Hope this helps :)
This is the correct graph for that equation!
Answer:
$80
Step-by-step explanation:
You are being asked to find a value for price (x) that makes the quantity (y) in each equation be the same:
y (for manufacturer) = y (for retailer)
25x -600 = -5x +1800 . . . . . substitute the given expressions for y
30x = 2400 . . . . . . . . . . . add 5x+600 to both sides
x = 80 . . . . . . . . . . . . . . . . divide by 30
The equilibrium price is $80.
__
<em>Check</em>
The manufacturer is willing to sell 25(80) -600 = 1400 phones at that price. The retailer is willing to buy -5(80)+1800 = 1400 phones at that price. These quantities are the same, hence $80 is the equilibrium price.
_____
Apparently, you are expected to graph the supply curve and the demand curve. Conveniently, they are straight lines. The point where they intersect is the point where manufacturer and retailer can agree on price and quantity. This is the "equilibrium point."
Answer:
2.45 miles
Step-by-step explanation:
24.5 divided by 10 (or multiplied by 1/10) = 2.45
Answer:
4585.8 feet
Step-by-step explanation:
If we draw the triangle, the opposite side to 3° angle would be "10" less than total height of 250 because Nick is 10 feet above water level, so that side will be:
250 - 10 = 240
The hypotenuse of the triangle is the length of line of sight. We can call this "x".
So, using trigonometric ratio of sine (opposite/hypotenuse), we can write:
![Sin(3)=\frac{240}{x}](https://tex.z-dn.net/?f=Sin%283%29%3D%5Cfrac%7B240%7D%7Bx%7D)
Now, we cross multiply and solve for x, line of sight length:
![Sin(3)=\frac{240}{x}\\x=\frac{240}{Sin(3)}\\x=4585.8](https://tex.z-dn.net/?f=Sin%283%29%3D%5Cfrac%7B240%7D%7Bx%7D%5C%5Cx%3D%5Cfrac%7B240%7D%7BSin%283%29%7D%5C%5Cx%3D4585.8)