Alg Keystone Item Sampler Ch 3

An equation involving polynomials is shown below. (ax + 5y) + (x – y) – (3x – by) = 2x + y What are the values of a and b?

• a = 4, b = -3

• a = 4, b = 3

• a = 5, b = -5

• a = 5, b = 5

Which linear equation has the points (1/2, 3/4) and (4, 3) as solutions?

• 9x – 14y = -6

• 9x + 14y = 78

• y – 3 = 14/9 (x – 4)

• y – 4 = 9/14 (x – 3)

The scatter plot below shows nine points from a data set. The equation of the line of best fit for the nine points is determined. Then, three more points are added to the scatter plot, but the equation of the original line of best fit remains unchanged. Which three ordered pairs are most likely the added data points?

• (4, 4), (5, 5), (6, 6)

• (4, 10), (4, 11), (4, 12)

• (8, 9), (8, 10), (8, 11)

• (10, 10), (10, 11), (10, 12)

The scatter plot below shows the relationship between the age of a house and the number of days it takes for the house to be sold after being listed for sale. The equation y = 0.95x + 17.56 describes the line of best fit for the scatter plot. Based on the equation, which value is most likely the number of days it takes for a 60-year-old house to be sold after being listed for sale?

• 45

• 70

• 75

• 83

An equation and some of the steps used to solve the equation are shown below. One step is missing. 2(x – 3) + 10x = 5(3 + x) ? 2x – 5x + 10x = 15 + 6 7x = 21 x = 3 Which set of statements is most likely the missing step and the property that justifies the step?

• 2x – (3 + 10x) = 5(3 + x) This step is justified by the associative property.

• 2(x – 3) = 5(3 + x) – 10x This step is justified by the associative property.

• 2x – 6 + 10x = 15 + 5x This step is justified by the distributive property.

• 2x – 3 + 10x = 15 + x This step is justified by the distributive property.

A teacher buys some pencils. - He buys 2 pencils for each of his students. - He buys 10 additional pencils. - Each pencil costs $0.10. Which equation describes the total amount of money (y), in dollars, that the teacher spends on pencils as a function of the number of students (x) he has?

• y = 1.20x

• y = 2.00x

• y = 0.20x + 1

• y = 0.10x + 12

The scatter plot below shows the relationship between the number of video files (x) stored on a computer and the number of gigabytes (y) of storage space available on the computer. Based on the scatter plot, which equation represents a line of best fit that could be used to predict the number of gigabytes of storage space available on the computer based on the number of video files that could be stored on the computer?

• y = -14x + 250

• y = -9x + 116

• y = -8x + 227

• y = -4x + 189

A scatter plot shows the relationship between the distances (x), in miles, from a local airport to airports in various cities and the time (y), in minutes, a flight between the airports takes. The equation below describes the line of best fit for the scatter plot. y = 0.16x + 58.62 Based on the equation, which value is the most likely distance, in miles, between two airports when a flight between the airports takes 240 minutes?

• 1,134

• 1,441

• 1,866

• 2,251

Kylie and Rhoda are solving the equation 4(x – 8) = 7(x – 4). - Kylie uses a first step that results in 4x – 32 = 7x – 28. - Rhoda uses a first step that results in 4x – 8 = 7x – 4. Which statement about the first steps Kylie and Rhoda use is true?

• Kylie uses the associative property, resulting in a correct first step.

• Kylie uses the distributive property, resulting in a correct first step.

• Rhoda uses the associative property, resulting in a correct first step.

• Rhoda uses the distributive property, resulting in a correct first step.

The scatter plot below shows the cost (y), in dollars, of orange trees based on their ages (x), in years. Based on the scatter plot, which equation represents the line of best fit for the cost of the orange trees?

• y = 11.8x

• y = 11.8x + 29.2

• y = 15.7x

• y = 15.7x + 40.0