Numbers and Algebra - Patterns and Algebra - Quiz 6

Line QR is graphed on the xy-plane. Which of the following data tables corresponds to the graph?

-1, -1 0,1 1,3 2,5

Evaluate the expression: 5(4 - 1)2 - (4 + 3)2

-4 This question is about order of operations. First, solve what is inside the parenthesis: 5(3)2 - (7)2. Next, solve the exponents: 5(9) - 49. Then, multiply: 45 - 49. Finally, subtract: -4

Values of the linear function f are listed in the table. What is the value of f(85)? x f(x) 30 5 45 8 60 11 85

16 To find the pattern in the data, find the change in f(x) and divide by the change in x. Change in f(x): 8-5 = 3 Change in x: 45-30 = 15 so the final ratio is 3/15 which equals ⅕. This means that for every 1 unit increase in f(x), there is a 5 unit increase in x. From 60 to 85 there is a 25 unit increase in x. 25 ÷ 5 = 5. 11 + 5 = 16.

How many terms are in the expression 3x² + 6x +3?

3 A term is either a single number, a variable, or numbers and variables multiplied together. The equation 3x² + 6x +3 has three terms: 3x², 6x, and 3.

The state sales tax is 7.5%. Which number could also represent 7.5%?

3/40 There is always the option of arriving at the answer by eliminating incorrect answer choices, but it is always a good idea to double-check the final choice. In the case of this question, 3/40 = 3 ÷ 40 = 0.075 = 75/1000 = 7.5/100 = 7.5%.

Which equation below models xª•xᵇ = xª⁺ᵇ?

5³ • 5⁴ = 5⁷ xª is a multiplication problem where "x" identifies the factor to be multiplied "a" times. These are some rules to follow when you are modeling an algebraic expression: 1) choose numbers other than 0 or 1 to replace the variables; 2) choose a different number for each variable; 3) replace the variables with the sample numbers you have chosen; and 4) evaluate to see if the relationship/equation is true. So, for this problem, the following sample numbers have been chosen: x = 5; a = 3; b = 4. Now, let's see if 5³ • 5⁴ = 5⁷. 5³ = 5 • 5 • 5 and 5⁴ = 5 • 5 • 5 • 5. So, 5³ • 5⁴ = (5 • 5 • 5) • (5 • 5 • 5 • 5) = 5 • 5 • 5 • 5 • 5 • 5 • 5 = 5⁷. This tells us that 5³ • 5⁴ = 5⁷ is a good model of the equation.

Students in Mr. Walton's class were independently trying to solve the problem below. The graph above shows the amount of money in dollars, y, that Bobby has saved after x weeks. If he continues saving money at the same rate, how much money will Bobby have saved after 12 weeks? Gabriel is a student in Mr. Walton's class. He is struggling to get started on the question, and raises his hand to get some help. Gabriel says he knows he needs to figure out the value of y when x = 12 weeks, but is stuck because the graph is cut off after x=6. Which of the following is not a possible responses to help Gabriel know how to start the problem?

Create a proportion using an ordered pair from the graph and solve for $y in 12 weeks. For example, \frac{1 week}{\$2}=\frac{12 weeks}{\$y}$21week​=$y12weeks​. Using a proportion to solve for a missing value will work only if the relationship is proportional. You can tell if a relationship is proportional if the graph is a straight line that goes through the origin. This relationship is not proportional because it does not go through the origin, and therefore setting up and solving a proportion will not give the correct value of y when x = 12.

Which of the following comparisons between equations and inequalities is NOT true?

Equations are solved using inverse operations while inequalities cannot be solved with inverse operations. This is false; both equations and inequalities can be solved using inverse operations to isolate the variable.

Sally walks into class and tells her teacher that a local candy store had a "buy one candy bar, get one candy bar free" promotion this weekend. The teacher asks Sally how many candy bars she purchased, but she can only remember how many candy bars she received. The teacher asks the class to create an equation that would help Sally find out how many candy bars a person would receive (r) if for any candy bar they purchased (p), they received one candy bar for free. One student says the equation would be 2p + 1 = r. Which of the following activities would best help Sally recognize the error in her answer?

create a function table This is the correct answer because it will clearly show the relationship between different pairs and allow the students to see the pattern of the equation. For example, we know that if you purchase 1 candy bar (p = 1), you get 1 free, so you receive 2 candy bars (r = 2). If these values are not shown in the function table, then it would be easy for the student to see that the equation is incorrect.

What equation describes the linear relationship shown in the table? x 2 6 9 12 y 7 19 28 37

y = 3x + 1 The table above is correctly represented by the equation y = 3x + 1 because each (x, y) pair presented in the table makes the equation true. 7=3 \left( 2 \right) +1; 19=3 \left( 6 \right) +1;28=3 \left( 9 \right) +1;37=3 \left( 12 \right) +17=3(2)+1;19=3(6)+1;28=3(9)+1;37=3(12)+1.