Numbers and Algebra - Patterns and Algebra - Quiz 2

The graph is a representation of the following situation: Marty purchased a car for $24,000; this included all interest, tax, and title fees. She made payments of $500 per month for 48 months until the car was paid off. What ordered pair would best represent point A at the top of the graph?

(0,24000) The point A, (0,24000), indicates that at the time "0" - or at the beginning of the loan - the amount owed was $24,000. In this situation, the x-axis (horizontal) represents the time in months and the y-axis (vertical) represents the amount of the loan. In the equation y = 24000 - 500x, the - 500 is the $500 paid (subtracted) each month on the loan. As you look at the graph moving from left to right, the line goes "downhill"; this graph represents a linear decrease. The point represented by B on the x-axis would be the point (48,0). This means that after the 48th month, the amount remaining on the loan was $0.

Isabella is creating a function by making a table of values. So far, her table looks as follows: x y -1 5 4 3 0 -6 ? 7 If inserted into the blank in the table, which value of x would invalidate her function?

-1 There is already an input of -1 in the table, which corresponds to the output of 5. Inserting another input of -1 that corresponds to 7 means that her function would violate the vertical line test.

Simplify the expression: 30 - 2 × 50 + 7030−2×50+70

0 To simplify the equation, follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (PEMDAS) and work left to right. The steps to simplify the expression would be: = 30 - 2 × 50 + 70 = 30 - 100 + 70 = -70 + 70 = 0

At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes?

165 The ratio 60/240 = ¼ so ¾ of students are not athletes. Since this can be applied to the sophomores, ¾ × 220 = 165 sophomores.

The ratio of Antone's height to arm span is the same as the ratio of his brother's height to arm span. About how tall is Antone?

39 inches The answer is found by solving the proportion: Antone's Brother's Arm Span/Antone's Brother's Height = Antone's Arm Span/Antone's Height, or (56/60) = (36/x). In this proportion, x is Antone's height. In the first ratio, 56 is Antone's brother's arm span and 60 is his height. In the second ratio, 36 is Antone's arm span, and x, his height. Proportions are solved by cross multiplying. When cross multiplication is performed on this proportion, we get: 56 ∙ x = 60 ∙ 36. When simplified, we get: 56x = 2160; then you divide each side by 56 resulting in x = 2160/56 = 38.57, but because the question says "about", you would use 38.57 ≈ 39".

A runner is running a 10k race. The runner completes 30% of the race in 20 minutes. If the runner continues at the same pace, what will her final time be?

67 minutes To find the answer to this question, set up a ratio; remember that 30% = .3 and 100% = 1. Therefore, (20 / .3) = (x / 1) When you cross multiply to solve for x, you get the equation .3x = 20. Divide each side by .3 to isolate x and the answer is 66.66666. The best answer choice is 67 minutes.

What is the 8th term of the geometric sequence -3, 6, -12, 24, -48,...?

A(8) = 384 A(8) = 384 comes from seeing that the sequence is shown to have a₁ = -3, r = 6 ÷ -3 = -2, and n = 8. The question is answered correctly by keeping an appropriate variable expression in the place of A(n) and inputting all known values so that the formula A(n) = a₁(r)ⁿ⁻¹ becomes A(8) = -3(-2)⁸⁻¹. When the order of operations is followed correctly, exponents will be simplified before any multiplication occurs. The resulting equation becomes A(8) = -3(-2)⁷ and then A(8) = -3(-128). The final answer is the product of -3 and -128, and so A(8) = 384.

x 1 4 7 10 13 y 9 3 -3 -9 -15 The table above shows x and y values that have a linear relationship to each other. Which of the graphs below could illustrate the relationship between these variables?

Graph C The table shows x-coordinates that increase by 3 units at a time and y-coordinates that decrease by 6 units each. The progression from one point to the next includes moving down 6 units and 3 units to the right. This constant change as the values in the table go from one ordered pair to another is the slope of the line. Any pair of points can be selected from the table to perform the calculation and the (reduced) result will be the same. Here, the points (1, 9) and (4, 3) are being used: (y2 - y1)/( x2 - x1) = (3 - 9)/(4 -1) = -6/+3 = -2/1. If this slope is applied to fill in a value from the table to the left of the first point given, (1, 9), the y-intercept (value of y when x = 0) can be determined to be 11 (because the x-coordinate is reduced by 1, the y-coordinate must be increased by 2 units). With a y-intercept of 11 and a slope of -2, the equation for this line is y = -2x + 11, and so the graph must have a point on the y-axis at (0, 11) and a slope of down two units for every movement to the right one unit. Alternatively, the graphs can be inspected to determine which contains at least two points from the table. The point (1, 9) appears in several different graphs, but only one graph also contains the point (4, 3).

Veronica noticed that the more time she spent practicing her piano recital piece, the more of the music she had memorized. Which of the following graphs could represent the relationship Veronica noticed between her time spent practicing and her knowledge of her recital music?

Graph D Since time is the dependent factor, it will be on the x-axis. This graph that shows the Portion of Recital Music Memorized rise as Time Spent Practicing for Piano Recital increases, reflecting the situation that Veronica observed.

Students in Mr. Jaffrey's class were discussing in pairs if the following mapping diagram represents a function: As Mr. Jaffrey was circulating, he overheard Reena tell her partner that the relation is not a function because every input gives the same output. Of the following, which is the best response for Mr. Jaffrey to give Reena?

Reena, you are incorrect. Even though each input gives the same output, there is only one output for every input, so the relation still represents a function. The only thing that determines if a relation is a function is if each input gives only 1 output. This is true for this relation, so it is a function.