Answer:
y=-4x-6
Step-by-step explanation:
y=mx+b, where m is the slope and b is the y-intercept
Slope is given as -4, so:
y=-4x+b
To find b, sub in the point we were given (-2,2):
2=-4(-2)+b
2=8+b
b=2-8=-6
So we have: y=-4x-6
I'm not 100% positive but I believe it would be the 14th person. 10+4=14. That's just my guess.
Answer:
35 ways
Step-by-step explanation:
Alex has 9 friends and wants to invite 5 friends. Since Alex requires two of his friends who are twins to come together to his birthday party, since the two of them form a group, the number of ways we can select the two of them to form a group of two is ²C₂ = 1 way.
Since we have removed two out of the nine friends, we are left with 7 friends. Also, two friends are already selected, so we are left with space for 3 friends. So, the number of ways we can select a group of 3 friends out of 7 is ⁷C₃ = 7 × 6 × 5/3! = 35 ways.
So, the total number ways we can select 5 friend out of 9 to party come to the birthday include two friends is ²C₂ × ⁷C₃ = 1 × 35 = 35 ways
Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.
Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.
The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.
The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes
42.528 minutes for the temperature of the coffee to reach 180 °F.
The area of a square is A=s^2
We already have the area, so we solve for the side length:
169=s^2
13=s
The perimeter of a square is P=4s
We plug in 13 for s:
P=4(13)
P=52
So the perimeter of the square is 52 m^2
Hope this helped!