Systems of Equations
Solve:
x+y=5
x-y=7
x=6
y=-1
PV = nRT for T
PV/nR
Write an equation for a line that passes through (6,5) and (7,1).
y=-4x+29
A flight costs $15,000 to operate, regardless of the number of passengers. Each ticket costs $212. Express the profit P as a linear function of the number of passengers on the flight. How many passengers are needed to make a profit?
15,000 = 212p
At least 71 passengers.
a) What is the constant of variation?
b) What are the units of variation constant?
a) What is 2205
b) What is Dollars
Solve:
3x-4y=7
y=4x-5
x=1
y=-1
A=P(1+rt) for r
A/(tP)-1 = r
Write an equation of a line that passes through (-1,-8) and is parallel to y=5x-2.
In other words, an equation has a slope of 5 and it passes through the point (-1,-8). What's the equation?
y=5x-3
Clint is buying large bottles of lemonade and small bottles of soda for a party. Each bottle of lemonade costs $6 and each bottle of soda costs $2. He wants to spend exactly $40 on drinks. Write an equation to represent the situation.
6L+2S = 40
The slope of lines that are perpendicular to each other are
What is opposite recirprocal
Solve:
20n+50m=15
70m+30n=22
m=
1/10
n=
1/2
F = (mv2)/R for R
(mv2)/F = R
Write an equation of a line that passes through (12,20) and is perpendicular to y= -4x-3.
In other words, an equation passes through the point (12,20) and has a slope of 1/4 . What's the equation?
y=1/4 x+17
You are considering hiring a plumber to do some work for the new house you are building. The plumber charges $75 per hour plus a base fee of $299. If C represents the total cost to hire the plumber, and H represents the number of hours of time, what is the relationship between C and H?
C = 75H+299
The slope of lines that are parallel are
What is equal to each other
At a restaurant, the price for an adult seafood platter is $19, and the price for a child seafood platter is $8. One day a total of 32 seafood platters were served, and the restaurant made a total of $487 from seafood platter sales. How many adult platters and child platters were sold?
Adult = 21
Child = 11
1/R = 1/R1 + 1/R2 for R
The Answer is on the Board.
Write an equation of a line that is perpendicular to the equation 2x-3y=24, but passes through the point (1,1).
In other words, an equation has a slope of 3/2 and passes through the point (1,1).
y=3/2x-1/2
\text{Solve: }5y+7+3y=5(2y+1)-8
y=5
The value of a car V that is a-years old is given by the following equation
V=20000-2500a
a) What's the domain?
b) What's the range?
a) What is [0,8] years
b) What is [0, 20,000] dollars
Last month a fitness club sold 55 new memberships. The Gold memberships sold for $10.50 each and the Platinum memberships sold for $15.50 each. If the total sales for new memberships was $682.50 last month, how many of each type of membership were sold?
Gold = 34
Platinum = 21
v=-g t+v_0 \text{ for t}
Answer on the Board.
An equation has a slope of zero and runs through the point (3,4). What's the equation?
y=4
Solve:
2(8x-28)+4=-4(-11x-9)-4
x=-3
Let g(t) give the market value (in $1,000s) of a house t years after 2000. Say what the following statements tells you about the house.
1) g(7)-g(2) = 12
2) (g(15)-g(9))/(15-9)=-3
a) What is the change in home value in 2002 to 2007
b) What is the average rate of change of the home value between 2009 and 2015
Solve:
3p+4q=-1
2p-3q=22
What is p=5 and q=-4
Solve for v
KE = 1/2mv^2
What is (Answer on the board)
Let f(x)=2x^2-7x+9 .
Evaluate f(-3) and f(a+4)
What is 48 and
2a^2+9a+13
On a day in September, the temperature, T, in degrees is T = 1.2h+50 where h is the number of hours since noon.
What is the slope and interpret the meaning.
The slope is 1.2. The temperature increases at a rate of 1.2 degrees per hour after 12pm.
Let f(t) be the number of students who get a Ph.D Statistics in year t, where t is measured in years since 1990. Consider f(15) = 20.
1) What are the units for 20?
2) What are the units for 15?
3) Interpret f(15) = 20
1) What is number of students
2) What is years
3) In 2005, there are 15 students who get a Ph.D in Statistics.
The bill for two lattes and three cappuccinos was $10.95, while the bill for one cappuccino and two lattes was $6.65. Write a system of equations to model this and determine how much each latte and cappuccino was.
Each Cappuccino is $2.15 and Each Lattee is $2.25. The system of equations that models this would be:
2L+3C=10.95
2L+1C =6.65
Solve the following formula for m_2
F=(Gm_1m_2)/(r^2)
m_2=(Fr^2)/(Gm_1)
The population P of s certain town, t-years after it was founded in 1970 is given by P(t)=8000+600t
a) What is the population in 1970?
b) What was the population this year?
c) What is the practical interpretation of the rate of change?
a) What is 8000
b) What is 39,800
c) The town is growing at a rate of 600 people per year.
What is the dependent and independent variable?
The value V in dollars of an antique is a function of the time, t, in years after 2000 and is given by
V(t)=3200(1.08)^t
Dependent: Value
Independent: Time
On a late spring day, the temperature, T, in degrees Fahrenheit, is T=60+15h where h is the number of hours since 9:00am.
a) What's the initial value?
b) What's the rate of change?
b) What is 15 degrees per hour