Systems of Equations & Inequalities
Solve the system using elimination. Write your answer as an ordered pair (x,y)
−4x − 2y = −12
4x + 8y = −24
(6,-6)
A circular pool of water is shrinking as it drains. The diagram shows the shrinkage.
A formula for the area, A, of the circular pool is given by the equation A=π(r-3)2
What is a formula for r?
r=√(A/π)+3
Interpret the following equation for an automobile cost, C(t)=28,000(0.73)t, where C(t) represents the cost and t represents the time in years to answer the questions.
The initial cost of the automobile is
$28,000
The graph of the following equation f(x)=ax2+bx+c is
quadratic or a parabola
Identify the intercepts of f(x)=5x-45
(0, -45)
(9,0)
A local salsa company makes two types of salsa, tomato and corn. Each batch of tomato salsa takes 2 hours to prepare and 4 hours to package. Each batch of corn salsa takes 2.5 hours to prepare and 3 hours to package. There are 4 preparation workers and 7 packaging workers in the company. Each of them works 40 hours per week.
Create a system of two inequalities that relates the number of batches of tomato salsa, t, and the number of batches of corn salsa, c, that can be made by the 4 preparation workers and the 7 packaging workers each week. Assume t≥0 and c≥0.
2t+2.5c≤160
4t+3c≤280
The circumference C of a circle with radius r can be calculated using the formula
C=2πr. Write the formula that represents r in terms of C. r=
r=C/2π
Interpret the following equation for an automobile cost, C(t)=28,000(0.73)t, where C(t) represents the cost and t represents the time in years to answer the questions.
0.73 represents...
the decay factor or the automobile depreciates 27% over t years, since 1-0.27=0.73
What is the vertex of the function y=(x-1)2-2?
(1, -2)
Consider the graph of f(x)=x is shifted up 8 units, what would be the equation of the new graph?
f(x)=x+8
A local salsa company makes two types of salsa, tomato and corn. Each batch of tomato salsa takes 2 hours to prepare and 4 hours to package. Each batch of corn salsa takes 2.5 hours to prepare and 3 hours to package. There are 4 preparation workers and 7 packaging workers in the company. Each of them works 40 hours per week.
Which combination of batches of salsa could be made in one week based on the constraints?
Select all that apply.
A.20 tomato and 45 corn
B.30 tomato and 40 corn
C.45 tomato and 30 corn
D.50 tomato and 25 corn
E.60 tomato and 10 corn
A, B, E
The formula A=1/2 s2 expresses the area, A, of an isosceles right triangle in terms of the side length, s, or a leg of the triangle.
Write the equation that expresses the length of a leg of an isosceles right triangle in terms of the area.
s=√2A
A scientist began a study with a sample of 1,500 bacteria. He noticed that the number of bacteria in the sample after t days can be modeled by the equation P=1,500∙5t. In this equation, what does 5t represent?
A.The number of bacteria increases by a factor of 5 each day.
Multiply the polynomials (x+3)(2x-4).
What is the product in the form ax2+bx+c?
a=2
b=2
c=-12
(7x+8)(5x+2)
35x2+54x+16
A local salsa company makes two types of salsa, tomato and corn. Each batch of tomato salsa takes 2 hours to prepare and 4 hours to package. Each batch of corn salsa takes 2.5 hours to prepare and 3 hours to package. There are 4 preparation workers and 7 packaging workers in the company. Each of them works 40 hours per week.
To maximize productivity, how many batches of salsa should be made if the company owner wants 20 batches of corn salsa?
55 batches of tomato salsa and 20 batches of corn salsa
Kelly’s monthly profit for selling candles is represented by the function P(x)=7.5x-200, where x represents the number of candles sold.
What is Kelly's monthly profit if she sells 60 candles?
$250
A T-shirt company bought a new packaging and tracking system for $100,000. The formula V=100,000(1-0.125)y models the value of the system, V, in dollars, after depreciating for y years. In this formula, what is the meaning of the term (1-0.125)?
The value of the system will decrease by 12.5% each year.
What are the zeros of the equation y=x2-x-6
(-2, 0) and (0, 3)
Simplify the polynomial expression (5x-7)(9x2-4x-8)
45x3-83x2-12+56
A local salsa company makes two types of salsa, tomato and corn. Each batch of tomato salsa takes 2 hours to prepare and 4 hours to package. Each batch of corn salsa takes 2.5 hours to prepare and 3 hours to package. There are 4 preparation workers and 7 packaging workers in the company. Each of them works 40 hours per week.
The company owner decides to only make corn salsa one week before a local festival. Given the same constraints, what is the maximum number of batches of corn salsa that can be made in one week?
64 batches of corn salsa
Subtract (4x2-x+6) from (3x2+5x-8).
-x2+6x-14
Use the following equation for an automobile cost, C(t)=28,000(0.73)t, where C(t) represents the cost and t represents the time in years to answer the questions.
What will be the value of the automobile after 3 years? Round to the nearest cent.
$10,892.48
The function h(t)=-16t2+48t+160 can be used to model the height, in feet, of an object t seconds after it is launched from the top of a building that is 160 feet tall.
Two other forms of the function are:
h(t)=-16(t-5)(t+2)
h(t)=-16(t-1.5)2+196
Which value of the function represents the maximum height of the object?
h(1.5)
Currently, there are 153 bald eagles in Forest National Park. Bald eagles are an endangered species, and the population of bald eagles is decreasing by 8% every year.
Write a function that represents the number of bald eagles in Forest National Park in t years?
f(x)=153(0.92)t