algebra unit test.

What is the first step in solving and graphing the inequality 2x-6y≥8?

A. Subtract 2x from both sides of the inequality.

Is the equation below written in standard form? If not, select which explanation best applies to why the equation is not written in standard form. -2x+3y=-5

A. the requirement that A≥0 is not satisfied

Which statement best applies to the slope of the line that passes through the blue and red points below? 2003-09-02-00-00_files/i0040000.jpg

A. the slope is negative

If the slope of a straight line is 0 and the y-intercept is -2, what is the equation of the line?

A. y = -2

The graph of an equation is shown below. Which of the following points is a solution to the equation? 2003-09-01-00-00_files/i0180000.jpg

A. (0,1)

In 2005, a Nevada silver mine exported 200 tons of silver. In 2008, as the silver supply became exhausted, it only exported 25 tons of silver. What is the rate of change of the mine's silver output?

A. -175/3

Rewrite the equation below in standard form. 2/3x=-5/2y+2

A. 4x+15y=12

A very old vending machine accepts only nickels (n) and dimes (d). Candy costs up to $0.50, but sometimes the machine will dispense candy without any coins being inserted into the machine. Which inequality shows all of the ways to obtain a candy bar from the machine?

A. d≤-1/2n+5

2003-09-03-00-00_files/i0050000.jpg What is the equation of line k?

A. y=-1/2x+1

A line passes through the point (0,-3/2) and has a slope of 1/2. What is the equation of the line?

A. y=1/2x-3/2

2003-09-04-00-00_files/i0120000.jpg What inequality is graphed above?

A. y>3/4x+3

Which graph shows the inequality y < -2x + 3?

B.

Which graph shows the inequality y≤-3x-1?

B.

Which of the following graphs represents the line that passes through (-2, -3) and has a slope of 2/3?

B.

You have two summer jobs. At the Burger Palace you earn $8 per hour. At the community center you teach soccer clinics for $10 per hour. You want to earn at least $200 a week. If x is the number of hours you work at Burger Palace and y is the number of hours you work at the community center, which graph shows all the ways you can earn at least $200 a week?

B.

A student must find the slope of a line that passes through the points (2, 2) and (-1, 3). Which of the statements below best applies to the sample mathematical work? Given the points above, I plug these values into the formula 2003-09-02-00-00_files/i0260000.jpg, which yields the expression 2003-09-02-00-00_files/i0260001.jpg, which gives a slope of -3.

B. the student failed to plug in the proper values into the slope formula

Calculate the slope of the line passing through the two colored points below. 2003-09-02-00-00_files/i0070000.jpg

B. -2/3

A college student is looking at her monthly checking account records. On September 1, 2008, her checking account held a balance of $1,050. At the end of March 2009, her checking account held a balance of $800. What is the monthly rate of change for the student's checking account over the period September 1, 2008 through March 31, 2009?

B. -250/7

Which of the following equations is written in standard form?

B. 3x+5y=-15

Which of the following is not a requirement of a standard form equation Ax+By=C?

B. B≥0

At a candy store a bag holds up to 1 pound of candy. Each jawbreaker (x) weighs 0.25 pounds and each gumball (y) weighs 0.1 pounds. Which inequality shows the solution for all combinations of the two candies that will fit in the 1-pound bag?

B. Y≤-5/2x+10

What is the equation of line l? 2003-09-03-00-00_files/i0020000.jpg

B. y=3x-3

Which inequality is shown above?

B. y≤2x-3

Is the equation below written in standard form? If not, select which explanation best applies to why the equation is not written in standard form. 12=2x+4y

C. A, B, and C do not have a greatest common factor of 1

Which statement best applies to the slope of the line that passes through the blue and red points below? 2003-09-02-00-00_files/i0050000.jpg

C. the slope is positive

Which of the following is a solution to the inequality y > 3x - 4?

C. (1,1)

The graph below illustrates 2 intersecting lines. If a new line is drawn so that it passes through the red line at x = -1 and the blue line at y = 2, what is the slope of the new line? Please select the best answer from the choices provided

C. 2/3

2003-09-04-00-00_files/i0080000.jpg What inequality is shown above?

C. y≥-1/4x+2

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature (4072-03-01-01-00_files/i0270000.jpg) 30 35 36 36 34 30 28 Determine the average rate of change (including units and sign) of temperature with respect to time over the entire twelve-hour period given in the table.

a. The average rate of change of temperature with respect to time over the entire 12-hour period is approximately -0.167 degrees per hour.

The table gives the outside temperature in degrees Fahrenheit on a winter day in Death Valley, California. Time (A.M.) 7:00 8:00 9:00 10:00 11:00 Temp. (°F) 75 79 82 88 92 Calculate the average rate of change in temperature between 8:00 am and 11:00 am. Round your answer to two decimal places.

a. 4.33°

Which of the following equations is written in standard form?

3x +6y=13

In 1987 a recording artist sold 14,000 albums. In 1998 that same artist sold 4,683 albums. Find the rate of change in record sales from 1987 to 1998.

B. -847 albums per year

Calculate the slope of the line passing through the two colored points below. 2003-09-02-00-00_files/i0080000.jpg

B. 0

Match a standard form equation with the graph below. 2003-09-01-00-00_files/i0200000.jpg

B. 3x + 4y = -2

Which statement best applies to the slope of the line below? 2003-09-02-00-00_files/i0020000.jpg

B. the slope is zero

Calculate the slope of the line below. 2003-09-02-00-00_files/i0100000.jpg

B. -1/3

What is the y-intercept for the graph of 3x - 5y = 6?

B. -6/5

Abby wants to buy some fruit. She has $10.00 to spend. Apples (x) cost $0.50 a pound and bananas (y) cost $1.50 a pound. Which graph shows all of the ways she can spend up to $10.00 on apples and bananas?

C.

Which of the following graphs represents the line that passes through (-2, 1) and has a slope of -2?

C.

Which of the following graphs represents the line that passes through (3/2, -1/2) and has a slope of 1?

D.

Find the slope of the straight line that passes through (-2, -4) and (3, -5).

m=-1/5

The graph of the equation Y=-2x+5 will intersect the y-axis when y equals what value? y =

5

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature (4072-03-01-01-00_files/i0280000.jpg) 30 35 36 36 34 30 28 Over which period(s) of time is the average rate of change zero? What, if anything, can you conclude about the actual temperature fluctuation within this period?

b. The average rate of change of temperature is 0 from 2 PM to 4 PM and also from 10 AM to 8 PM; Nothing can be concluded about the actual temperature fluctuation.

Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 Gallons Consumed Per Passenger Car 668 760 576 520 530 538 544 552 Determine the average rate of change, in gallons of gas per year, from 1960 to 1990.

b. ∆g/∆t=-4.93 gal/year

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Median Age 25.1 24.6 24.3 24.3 22.8 22.8 23.2 24.7 26.1 26.8 Determine the average rate of change in median age per year from 1930 to 1960.

c. -0.05 years of age per year

Which of the following graphs represents the line that passes through (3/2, 2/3) and has an undefined slope?

A.

What is the y-intercept of the equation 3y + 2x = 12?

A. (0,4)

A high school basketball team has a budget specifically for towels and extra basketballs. A towel costs $6 and a basketball costs $30. Assume the budget is $300 and that 25 towels are needed for the team for the entire season. Use a standard form equation to determine how many basketballs may be purchased by the team.

A. 5

When comparing the graphs of y = x and y > x, what is a difference in the graphs?

A. An ordered pair solution that lies on y = x, is not a solution for y > x.

The inequality 10x + 20y > 500 models all of the combinations of scores of 10 and 20 points that will give a total greater than 500 points in a game. What is not true about the values for x and y?

D. They will each be greater than 5.

What does the graph of -3-5y≥20 look like?

D. solid boundary line, shaded below the line

Calculate the slope of the line below. 2003-09-02-00-00_files/i0110000.jpg

D. the line does not have a slope

Which of the following is a solution to the inequality y < -2x + 3?

D. (0,0)

Use the graph to determine which of the following points is a solution to the equation. 2003-09-01-00-00_files/i0170000.jpg

D. (3,0)

A line passes through the points whose coordinates are (c, 3c) and (2c, 5c). Assuming that c is not 0, find the slope of the line.

D. 2

Rewrite the equation below into standard form. -3/2x=-2/5y-10/3

D. 45x-12y=100

Which equation is equivalent to 3x - 4y = 8?

D. y=3/4x-2

Rewrite the equation below in standard form. -3x+6y=12

D.x-2y=-4

Match a standard form equation with the graph below. 2003-09-01-00-00_files/i0210000.jpg

A, x-y=-1

Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 Gallons Consumed Per Passenger Car 668 760 576 520 530 538 544 552 Determine the average rate of change, in gallons of gas per year, from 1995 to 1997.

C. ∆g/∆t= 4gal/year

Use substitution to determine which of the following points is a solution to the standard form equation below. 5x-2y=10

C.(0,-5)

What is the slope of the line 6x + 8y = 12?

C.-3/4

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Median Age 25.1 24.6 24.3 24.3 22.8 22.8 23.2 24.7 26.1 26.8 Is the average rate of change zero over any ten-year period? If so, when?

C.Yes, both 1930 - 1940 and 1950 - 1960

Which of the following is not the equation of the graphed line? 2003-09-03-00-00_files/i0150000.jpg

C.x-2y=2

In a video game, Bob can score 3 points (x) or 4 points (y) by hitting targets. To win the game he must score at least 20 points. Which graph shows all of the ways Bob can win the game?

D.

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910,1920,1930,1940,1950,1960,1970,1980,1990,2000 Median Age 25.1, 24.6, 24.3, 24.3, 22.8, 22.8, 23.2, 24.7, 26.1, 26.8 Determine the average rate of change in median age per year from 1950 to 1990.

a. 0.0825 years of age per year

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Median Age 25.1 24.6 24.3 24.3 22.8 22.8 23.2 24.7 26.1 26.8 What does a rate of change of zero mean in this situation?

a. The median age of a man at the time of his first marriage is, on the average, constant.

The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City. Time of Day 10 AM 12 Noon 2 PM 4 PM 6 PM 8 PM 10 PM Temperature (4072-03-01-01-00_files/i0290000.jpg) 30 35 36 36 34 30 28 What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.

c. -1.5°ƒ degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129 Write the ratio of the change in weight for the first five weeks to the change in time for the first five weeks. Interpret the meaning of this ratio.

c. -13/5, 13 pounds was lost in 5 weeks

In the formula for average rate of change, what does the triangle in front of the x and y stand for?

c. delta notation-change in y over change in x

What is the slope of the line 4x + 6y = 12?

c. -2/3

Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 Gallons Consumed Per Passenger Car 668 760 576 520 530 538 544 552 Determine the average rate of change, in gallons of gas per year, from 1960 and 1999 and then determine what the result means in this situation.

d. -2.97 gal/year; the average fuel consumption per year of a passenger car in the U.S. decreased by nearly 3 gal/year.

Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Median Age 25.1 24.6 24.3 24.3 22.8 22.8 23.2 24.7 26.1 26.8 What is the average rate of change over the ninety-year period described in the table?

d. 0.019 years of age per year

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129 During which time period is the average rate of change zero?

d. From week 5 to week 6