# Recent questions in Algebra

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

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

Exponential growth and decay

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

Exponential models

Sequences

### 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.

Linear equations and graphs

### 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

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

Equations and inequalities

### 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 asked 2021-07-04 ### 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 asked 2021-07-04 ### Solve the equation and inequalities. $$\displaystyle{\left|{3}+{x}\right|}-{9}\leq{21}$$ Algebra foundations ANSWERED asked 2021-07-04 ###$30,000 is invested for 3 months at an annual simple interest rate of 3%. How much interest will be earned?

Exponential growth and decay

### Without graphing, determine whether the function $$y = 0.3(1.25)x$$ represents exponential growth or decay. State how you made the determination.

Exponential growth and decay

### Determine whether the function $$\displaystyle{y}={156}{\left({0.825}\right)}^{{t}}$$ represents exponential growth, exponential decay, or neither. Explain

Exponential growth and decay

Functions

### If f$$(x) = x + 4$$ and $$\displaystyle{g{{\left({x}\right)}}}={4}{x}²$$, find $$(f + g)(x)\ and\ (f + g)(2).$$

Rational functions

### Given the domain of the rational functions. Write your answers in set notation and interval notation.

Rational functions

### For the following exercises, find the domain of the rational functions. $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}-{1}}}{{{x}+{2}}}$$

Exponential models

### Find the mean of the data. 9,12,11,11,10,7,4,8

Exponential models