Hello,
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
The three consecutive integers are 26, 27, 28
Answer:
-4 is the larger integer
Step-by-step explanation:
n = smaller integer
n + 2 = larger integer
4(n+2) = n-10
4n + 8 = n - 10
3n + 8 = -10
3n = -18
n = -6
n+2 = -4
Answer:
π\6
Step-by-step explanation:
The reference angle is the smallest angle measured from the terminal side of the angle (where the angle ends) to the x axis. The reference angle is an acute angle (i.e less than 90° or π/2)
For O = 11π/6 = 1.833π
1.833π is in the fourth quadrant between 3π/2 radians and 2π radians. Since it is in the fourth quadrant, the reference angle is given as:
reference angle = 2π - 11π/6 = π\6
Given:
Scale of the map 1 1/4cm : 8 yards
Rectangular Park: width : 2 1/2 cm ; length : 6 1/4 cm
Circular Pond: pi = 3.14 ; diameter 1 1/4 cm
Convert mixed factions into fractions.
Scale 1 1/4 = (4*1+1)/4 = 5/4
Width: 2 1/2 = (2*2+1)/2 = 5/2
Length: 6 1/4 = (4*6+1)/4 = 25/4
Diameter: 1 1/4 = (4*1+1)/4 = 5/4
width / scale * 8 yds = width in yards
5/2 ÷ 5/4 = 5/2 * 4/5 = 20/10 = 2 * 8 yds = 16 yds
length / scale * 8 yds = length in yards
25/4 ÷ 5/4 = 25/4 * 4/5 = 100/20 = 5 * 8 yds = 40 yds
Area of a rectangular park = l * w = 40 yds * 16 yds = 640 yds²
diameter / scale * 8 yds = diameter in yards
5/4 ÷ 5/4 = 5/4 * 4/5 = 20/20 = 1 * 8 yds = 8 yds.
radius = d/2 = 8/2 = 4
Area of a circular pond = πr² = 3.14 * 4² = 3.14 * 16yds² = 50.24 yds²
