Linear Equations and Inequalities
What is a solution set to
4c+5<4c+3
No solution
The formula below gives the velocity, v, in meters per second, at which sound travels through air that is at a temperature of T degrees Celsius. Which of the following equations correctly gives the air temperature in terms of the velocity of sound?
v=331.3sqrt(1+T/273.15)
T=273.15(v^2/331.3^2-1)
The area, A(x), of a rectangular enclosure that can be made from a limited amount of fencing is shown below, where x is the length of one of the sides of the enclosure, measured in feet. What is the maximum area that can be enclosed?
A(x)=−1/4(x−25)^2 +625
625ft^2
In the year 2000, the average American consumed 8.3 gallons of whole milk per year. This amount has been decreasing by 0.3 gallons per year. Which inequality can be used to find the number of years, t, since 2000 when whole milk consumption was greater than 6.0 gallons per person per year?
8.3-0.3t>6.0
What are the solutions to the equation
2x^2-11/2x-3/2=0
x=-1/4andx=3
What is the possible range of values for 12x + 3 if
9>=4x+1
12x+3<=27
The root-mean-square speed is the measure of the speed of particles in a gas. Root-mean-square speed, v, can be calculated using the equation shown below, where M is the molar mass of a gas, R is the molar gas constant, and T is the temperature. Which of the following equations correctly expresses the molar mass of a gas in terms of root-mean-square speed, temperature, and the molar gas constant?
v=sqrt((3RT)/M)
M=(3RT)/v^2
The number of yeast cells, P(t), in a culture after t days is modeled by the equation shown below. After how many days will the population double in size?
P(t)=25(2)^(t/1.06)
t=1.06
An amusement center charges a $45 flat fee for any birthday party plus $3.50 for each guest after the first one. Josiah wants to spend no more than $200 for his birthday party. If there are x guests, what inequality best models the situation above?
45+3.50(x-1)<=200
How many distinct real solutions does the equation below have?
(t+15)^2+5=0
None
What is the value of
1+5(77-s), Where: 6 = -2+77
31
In genetics, the Hardy-Weinberg Law states that if 2 different versions, or alleles, of a gene are present in proportions p and q, then how they are expressed in successive generations is governed by the equation below, where the proportions, p and q, are numbers between 0 and 1, inclusive. Which of the following correctly expresses allele p in terms of allele q?
p^2+2pq+q^2=1
p=1-q
The Rule of 72 estimates the time, T(r), in years, needed for an investment to double when the annual interest rate is r%, as shown in the function below. What is the meaning of the number 72 in this context?
T(r)=72/r
72 is the number of years an investment takes to double when the interest rate is 1%
Hamadi is renting a car. The rental charge is $17.50 per day plus $0.16 per mile. Hamadi can spend at most $33 for the cost of the car rental. If Hamadi rents the car for one day, what is an equivalent inequality which describes the number of miles Hamadi can drive the rental car?
x<=96
In the equation below, k is a constant. For what value of k does the equation have exactly one distinct real solution?
2x^2+5x-k=0
k=-25/8
What is the value of
w-1, if 16-7w=w+14-6w
w-1=0
The equation below gives the quantity a in terms of the quantities b and c. Which of the following equations correctly gives b in terms of a and c?
a=(5bc)/20+100
b=(4a-40)/c
The equation below models the height, h, in feet above the water for a cable in a suspension bridge at a horizontal distance, x, in feet from the beginning of the span.
h(x)=0.0002(x-1955)^2+100
x=100
To get to school, Da'Quon walks 0.6 miles from his house to the bus stop. He then takes the bus for 3.9 miles. After he gets off the bus, he can choose one of several walking routes to school. The total number of miles he travels, via walking and bus, does not exceed 5.4. What is the greatest possible number of miles he walks after getting off the bus?
0.9>=x
Let x=w and x=z be the solutions to the equation below. What is the value of w+z?
w+z=3/4
What is the value of s if
1/2+2/5s=s-3/4
s=25/12
Which of the following equations correctly gives c in terms of j and m?
j=m/c*78
c=m/j*78
The Yerkes-Dodson law predicts that the relationship between stress level, s, and performance, P(s), of a difficult task can be modeled by a function of the form shown below, where a and b are constants related to the measures of stress and performance for a particular task. What is the best interpretation of
P(s)=-(s-a)^2+b
a in this context?
a is the level of stress at which performance is maximal
Jennifer wants to spend no more than $300 on school clothes. She spends $75 on a jacket and wants to buy some shirts that are on sale for $10 each. What is the solution set which represents the number, s, of shirts Jennifer can buy?
s<=22
What are the solutions to the equation below?
x^2-13x+30=0
x=10andx=3