Algebra 2 Unit 2

You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?

$162.50

Which ordered pair is the solution to the given system of equations? x - 3y = 9 x - 2y = 5

(-3,-4)

Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.

(-5/7,3)

A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish.The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?

(0, 0), (0, 53), (71.76, 0), (28, 46); t = 28 and s = 46

What is the vertex of the graph of y = |x| - 6?

(0,-6)

The sum of two numbers is 36. Twice the first number minus the second is 6. Find the numbers.

(14, 22)

State the solution of the system of equations graphed below.

(3,-1)

Use the substitution method to solve m - n = 7 and 3m + 2n = 6.

(4,-3)

The value of y varies directly with x. What is k the constant of variation for this function, and what is y for the given value of x? y=-.5 x=6 find y when x=-3

k=-1/2, 1/4

Which line, having the given slope and passing through the given point, represents a direct variation?

m= 2/3 ; (9, 6)

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

no solution

A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?

0

The length of an object's shadow varies directly with its height. A boy who is 4 feet 6 inches tall casts a shadow that is 6 feet 3 inches long. What is the height of a tree that casts a shadow that is 25 feet long?

18ft

Which system of inequalities has this graph?

2x-3y≤12 x≥0 y≤0

The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?

48

Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?

Brenda ran 9 miles; Anne ran 6 miles

A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?

Bus: d1 = 45t + 90; Car: d2 = 60t

In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?

C. 100/250=v/150

A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.

False

A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.

False

The graph of an absolute value function will always be an upward-pointing V shape.

False

Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?

From the origin, move forward 7 units, left 6 units, and down 5 units.

Which is the graph of 0.4x + 0.1y≥ 1?

Graph B

An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?

Graph C

The freezing temperature of water is 32°F and 0°C. The boiling point of water is 212°F and 100°C. Which equation and graph represents the linear relationship between these two temperature scales?

Graph C. 55s+77p≥385

Which is the graph of y = |-x- 4|?

Graph D

Classify the system. x-y=-3 -3x+2y=3

Independent

If you use the elimination method to solve the system of equations, 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method? Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations. Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.

Method II

A dependent system of equations will have infinitely many answers.

True

An equation using three variables is graphed in coordinate space.

True

The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.

True

This is the graph of y < |x - 3|.

True

Two parallel lines form an inconsistent system of equations that has no solution.

True

Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.

True

Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).

True

When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.

True

An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?

x+y≤200 60≤x≤80 120≤y≤150 p:1.25x+2.25y

A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them.

x+y≥100 40x+35y≥4400 x≥0 y≥0

Graph the system of inequalities. x≤4 y≤-5

x≤4 SOLID LINE y≤-5 SOLID LINE Bottom left side of crossing lines is shaded

What is an inequality for this graph?

y - 3x ≥ -5

The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?

y = 1.25x + 1; y = 21

The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?

y = 4x + 10

The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?

y = x + 6

What is the equation of y = |x| translated 1 unit up and 6 units to the left?

y = |x + 6| + 1

What is the equation of the graph of y = |x| shifted 3 units up?

y = |x| + 3

This graph represents a translation of the graph of y = |x|. What is the equation of this graph?

y= |x-2|

One equation of a system of equations is 5x + 2y = 10. What is the second equation such that the system is independent?

y=5/2x+5

Identify the graph that shows the solution to the system of inequalities. y≤6 y>|5-x|

y≤6 SOLID LINE y>|5-x| DOTTED LINE (0,0) DOES NOT WORK