# High school math questions and answers # Recent questions in Secondary

Complex numbers

### An $$8\times8$$ chessboard has a square cell (or box, like square a1) which measures $$\beta$$ inches on one side. Express the two possible moves of your knight in vector form with units in inches. What are the distances of each possible move from your original position in inches? What are their angles from the horizontal (x-axis)?

Equations and inequalities
ANSWERED ### Solve the equation and inequalities. $$\displaystyle{5}{n}^{{2}}-{11}{n}+{2}={0}$$

Differential equations
ANSWERED ### Transform the second-order differential equation $$\displaystyle{\frac{{{d}^{{{2}}}{x}}}{{{d}{t}^{{{2}}}}}}={3}{x}$$ into a system of first-order differential equations.

Differential equations
ANSWERED ### True or False? Justify your answer with a proof or a counterexample. You can determine the behavior of all first-order differential equations using directional fields or Euler's method.

Exponential growth and decay
ANSWERED ### Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $$f(t)=6(0.84)^t$$

Exponential models
ANSWERED ### Sociologists have found that information spreads among a population at an exponential rate. Suppose that the function $$y=525(1−e^{−0.038t})$$ models the number of people in a town of 525 people who have heard news within t hours of its distribution. How many people will have heard about the opening of a new grocery store within 24 hours of the announcement?

Sequences
ANSWERED ### The equations y=-x+4 and y=12x−8y= 21x−8 form a system of linear equations. The table below shows the y-value for each equation at six different values of x. xy=−x+4y=12x−804−822−740−66−2−58−4−410−6−3 What can you conclude from the table? A. The system has one solution, when x=0. B. The system has one solution, when x=4. C. The system has one solution, when x=8. D. The system has no solution.

Scatterplots
ANSWERED ### HOW can you use technology to describe associations in scatter plots?

Linear equations and graphs
ANSWERED ### Regarding linear equations with one independent variable, answer the following questions: a. What is the general form of such an equation? b. In your expression in part (a), which letters represent constants and which represent variables? c. In your expression in part (a), which letter represents the independent variable and which represents the dependent variable?

Linear equations and graphs
ANSWERED ### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{x}}{{3}}=\frac{{x}}{{2}}-{2}$$

Scatterplots
ANSWERED ### When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each. a. Which pair of conditions produces the least squares line with the steepest estimated slope? b. Which pair of conditions produces the least squares line with the largest SSE? c. Which pair of conditions produces the least squares line with the smallest estimate of $$\sigma$$?

Other
ANSWERED ### The sales journal and accounts receivable ledger forms for Johnston Supplies are given in the Working Papers. Work this problem independently. Start a new page for an accounts receivable ledger account for Kelly Di ll er. The account number is 110, and the balance on June 1 of the current year is $185.00 Equations and inequalities ANSWERED asked 2021-07-04 ### Vince worked 18 hours last week. Part of the time he worked in a fast-food restaurant and part of the time he worked tutoring a high school student in mathematics. He was paid$7.25 per hour working in the restaurant and $15 per hour tutoring. If he earned$161.50, how many hours did he work at each job?

Algebra foundations
ANSWERED ### The cost in dollars to produce x youth baseball caps is $$\displaystyle{C}{\left({x}\right)}={4.3}{x}+{75}$$. The revenue in dollars from sales of x caps is $$\displaystyle{R}{\left({x}\right)}={25}{x}$$. (a) Write and simplify a function P that gives profit in terms of x. (b) Find the profit if 50 caps are produced and sold.

Equations and inequalities
ANSWERED ### Solve the equation and inequalities. $$\displaystyle{\left|{3}+{x}\right|}-{9}\leq{21}$$

Algebra foundations
ANSWERED ### \$30,000 is invested for 3 months at an annual simple interest rate of 3%. How much interest will be earned?

Exponential models
ANSWERED ### Transform the given differential equation or system into an equivalent system of first-order differential equations. $$\displaystyle{x}{''}+{2}{x}'+{26}{x}={82}{\cos{{4}}}{t}$$

Other
ANSWERED ### When attempting jump shots, Myles makes 3 and misses 2 . If he makes 36 jump shots during one practice, hov many jump shots did he miss?

Transformations of functions
ANSWERED ### g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. $$\displaystyle{g{{\left({x}\right)}}}=\sqrt{\frac{1}{4}}{x}$$
ANSWERED 