Numbers and Algebra - Patterns and Algebra - Quiz 7

Simplify the expression: 82 - 100 \div÷ 4 + 6 \times× 12

129 Remember to do both multiplication and division before addition or subtraction. 100 divided by 4 is 25. 6 times 12 is 72. Last, 82-25+72 = 129

Susan is planning for volunteer day at the high school. Every person that signs up gets a free lunch for volunteering. This year, lunch includes 3 slices of pizza and a soda. If x = number of volunteers and one pizza has 8 slices, which equation can help her to determine the correct number of pizzas (n) to order?

3x/8 = n This equation multiplies the number of slices by the number of people. Then, it divides that amount by 8 (number of slices in a pie) to account for the number of pizzas needed.

A school fundraiser is selling candy bars to raise money for a new gymnasium. If Billy sells a total of $650 worth of candy bars for $d per candy bar, which expression could be used to represent how many candy bars Billy sold?

650​ To find out how many candy bars were sold, simply divide the total amount of money by the price per candy bar to find the total number of candy bars sold. This would be 650 / d. Another way to write this is d*N = 650, where x is the price per candy bar and "N" is the number of candy bars sold.

A teacher draws a 10x8 grid on the board without any "X"s in the grid. The teacher then writes "X"s in one and a half rows of the grid. The teacher asks the students to create an equation to represent blocks left on the grid, if the "X"s represent the blocks that have been removed. Which of the following is the best equation in response to the teacher's question?

80 - 15 There are 80 blocks on the grid. If 15 are removed, then the equation 80 - 15 represents this.

Which of the following are equivalent to dividing 144 by 9? Select all answers that apply.

A (16 ÷ 4)2 144 ÷ 9 = 16 and (16 ÷ 4)2 = 42 = 16 C (24 ÷ 12)(64 ÷ 8) 144 ÷ 9 = 16 and (24 ÷ 12)(64 ÷ 8) = (2)(8) = 16 E (121 ÷ 11) + (55 ÷ 11) 144 ÷ 9 = 16 and (121 ÷ 11) + (55 ÷ 11) = 11 + 5 = 16

Which of the tables best corresponds to the graph?

From the given image, the following points can be found on the line: (6, 10), (18, 25), and (30, 40). Of those points, two are in the table for the correct answer. The other two points in that table can be estimated to be on the line using the graph.

Which of the following scatterplots is most likely to have a line of best fit represented by the equation below? y=-4x+3y=−4x+3

Graph D The given equation has a y-intercept of (0, 3) and a slope of -4. If a line with these characteristics were to be graphed on the scatter plot, about half the points from the scatter plot would be above the line, and half below the line, making the given equation a suitable line of best fit.

A teacher prompted her students to write an example of an expression on their papers. One student wrote the following on their paper: 2x+3=52x+3=5 The student raises her hand and wants to know if her answer is correct. Of the following, which is the best teacher response to the student?

It is incorrect; this is an equation because it contains an equal sign. There is an expression on either side of the equal sign, which could be possible correct answers. The student response is incorrect because they wrote an equation, not an expression. Because an equation is a statement that two expressions are equal, either expression on each side of the equal sign could be an example of an expression.

If -¼ is the 11th term in a geometric sequence where r = -½, then what is a₁?

a₁ = -256 a₁ = -256 comes from seeing that the sequence is shown to have n = 11, r = -½, and A(11) = -¼. The question is answered correctly by keeping a variable expression in the place of a₁ and inputting all known values so that the formula A(n) = a₁(r)ⁿ⁻¹ becomes A(11) = -¼ = a₁(-½)¹¹⁻¹. This equation will be simplified as far as possible and then solved for a₁. When the order of operations is followed correctly, exponents will be simplified before any multiplication occurs. The resulting equation becomes -¼ = a₁(-½)¹⁰ and then -¼ = a₁(1/1024) or -¼ = a₁(0.0009765625). The final answer is found by dividing 1/1024 or 0.0009765625 on each side of the equation, or by multiplying by the reciprocal of 1/1024 on each side of the equation (1024) in order to isolate the unknown a₁. The result of that step of division or multiplication by a reciprocal is -256, so a₁ = -256.

After a blizzard, Joe tracks the height of the snow day by day. He gathers the following data: Day Height of Snow (inches) 0 24 1 20 2 16 3 12 Given that the snow melts at a constant rate, which of the following equations can be used to model the height of the snow, h, to the days since the storm, d?

h = 24 - 4d This correctly states the relationship between the height of the snow (h) and days since the storm (d). On the first day, the snow is 24 inches high. Each subsequent day, the snow melts by 4 inches.