Answer:
y=-4x-24
Step-by-step explanation:
The equation of a line is always in the form y=mx+c. By subbing in the values given by the two points, we get:
0=-6m+c
-24=c
∴0=-6m-24
6m=-24
m=-4
∴the equation is: y=-4x-24
Okay, so a general rule for finding perpendicular lines in the form of y = mx + b is y = (-1/m) + b.
First, let's ignore b (-7) because we're going to find that later.
A perpendicular line to y = 4x + b is y = -1/4x + b.
Alright, so now let's plug in the values. They are in the form of (x,y), so let's plug them in accordingly.
3 = -1/4(4) + b
3 = -1 + b
b = 4
y = -1/4x + 4
So a line perpendicular to y = 4x - 7 is y = -1/4x + 4.
Let's call one number x and one number y.
x/2=y
x+y=57
We can set these equations equal to each other to solve for the numbers by subtracting x from both sides of the second equation. Now the equations are:
y=-x+57 and x/2=y
Since both equations equal y, they are also equal to each other:
-x+57=x/2
First, multiply both sides by 2:
-2x+114=x
Add 2x to both sides.
114=3x
Divide both sides by 3.
38=x
One of the numbers is 38. Now, we can plug 38 in for x in either of the equations to solve for y:
(38)+y=57
Subtract 38 from both sides:
y=19
The two numbers are 38 and 19.
I hope this helps :)
The height starts at 40.5 ft. Over 7.5 years, it grows to be 57.
40.5 + 7.5g = 57 where g = annual growth rate
7.5g = 16.5
g = 2.2 ft/yr
Given:
Sample size, n = 40
Sample mean, xb = $6.88
Population std. deviation, σ = $1.92 (known)
Confidence interval = 90%
Assume normal distribution for the population.
The confidence interval is
(xb + 1.645*(σ/√n), xb - 1.645*(σ/√n)
= (6.88 + (1.645*1.92)/√40, 6.88 - (1.645*1.92)/√40)
= (7.38, 6.38)
Answer: The 90% confidence interval is (7.38, 6.38)
