Algebra Class: Systems of Linear Equations

False (B)

(x, y)

<p>substitution</p> Signup and view all the answers

<p>Graphing = Visually representing equations on a coordinate system Substitution = Replacing a variable with an expression Elimination = Adding or subtracting equations to eliminate variables Standard form = Expressing equations in the form Ax + By = C</p> Signup and view all the answers

<p>Graph the first equation (C)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>opposites</p> Signup and view all the answers

<p>x = 0 (D)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Population Doubling Time Model</p> Signup and view all the answers

<p>median</p> Signup and view all the answers

<p>Mean = Sum of observations divided by number of observations Mode = Value that appears most frequently Median = Middle value of ordered data Relative Frequency = Frequency divided by total number of observations</p> Signup and view all the answers

<p>Has two modes (A)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>(1, 0)</p> Signup and view all the answers

<p>Each input value corresponds to one unique output value. (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>For every element in the codomain, there is at least one corresponding element in the domain.</p> Signup and view all the answers

<p>bijective</p> Signup and view all the answers

<p>Injective = Each element in the codomain has at most one corresponding element in the domain. Surjective = Each element in the codomain is associated with at least one element in the domain. Bijective = Each element in the codomain is associated with one and only one element in the domain. Function = Each input is assigned a unique output.</p> Signup and view all the answers

<p>Whether a relation is a function. (B)</p> Signup and view all the answers

<p>y = 0 (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Identify input values and exclude those that cause the denominator to equal zero.</p> Signup and view all the answers

<p>(0, 1)</p> Signup and view all the answers

<p>increasing</p> Signup and view all the answers

<p>log_b(1) = 0 log_b(b) = 1 log_b(bx) = x b log_b(x) = x</p> Signup and view all the answers

<p>Domain is (0, ∞) (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>b &gt; 0 and b ≠ 1</p> Signup and view all the answers

<p>logarithmic</p> Signup and view all the answers

<p>log_b(1) = 0 log_b(b) = 1 log_b(bx) = x b^log_b(x) = x</p> Signup and view all the answers

<p>$P(E) = \frac{Number of favorable outcomes}{Total number of outcomes}$ (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Highest Value - Lowest Value</p> Signup and view all the answers

<p>$\frac{Range}{Number of Classes}$</p> Signup and view all the answers

<p>Contiguous boxes representing frequency of continuous data. (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>P(A or B) = P(A) + P(B) - P(A and B)</p> Signup and view all the answers

<p>Bar Charts = Used to represent categorical data with separated bars Pie Charts = Circular representation emphasizing relative weightage Histograms = Contiguous boxes showing frequency of continuous data Probability = Likelihood of an event occurring</p> Signup and view all the answers

<p>$A = P + I$ (A), $A = P(1 + rt)$ (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>I = Prt</p> Signup and view all the answers

<p>combinations</p> Signup and view all the answers

<p>$A = Pe^{rt}$ (D)</p> Signup and view all the answers

<p>Simple Interest = $I = Prt$ Total Amount with Simple Interest = $A = P + I$ Compound Interest (Continuous) = $A = Pe^{rt}$ Discount = $D = Mr t$</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Interest</p> Signup and view all the answers

A set of two or more linear equations grouped together.

The values of the variables that make all the equations in a system true.

A solution to a system of two linear equations represented as an ordered pair (x, y).

A method to solve a system of linear equations by plotting the graphs of each equation and identifying the point of intersection.

A method to solve a system of equations by isolating one variable in one equation and substituting it into the other equation.

A method to solve a system of equations by manipulating the equations to eliminate one variable by adding them together.

Writing an equation in the form ax + by = c, where a, b, and c are constants.

A process used in the elimination method where you multiply equations by constants to make the coefficients of one variable opposites.

The set of all possible output values of a function.

A function where every element in the domain maps to exactly one unique element in the codomain. In other words, no two inputs produce the same output.

A function where every element in the codomain has at least one corresponding element in the domain. In simpler terms, all possible outputs are actually achieved by the function.

A function that is both one-to-one and onto. It maps each input to a unique output, and every output is achieved by some input.

A visual test to determine if a graph represents a function. If any vertical line intersects the graph more than once, it's not a function.

A test to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, it's not one-to-one.

The set of all permitted input values for a function.

The process of identifying and excluding values from the domain that could lead to undefined results, such as dividing by zero or taking the square root of a negative number.

A function with the form f(x) = b^x, where b is a positive constant, b ≠ 1, and x can be any real number.

A horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

The set of all possible x-values for a function.

The set of all possible y-values for a function.

The point where a graph crosses the x-axis.

The point where a graph crosses the y-axis.

A function where each x-value corresponds to only one y-value and vice versa.

When the base of an exponential function is greater than 1 (b > 1), the graph increases as x increases.

When the base of an exponential function is between 0 and 1 (0 < b < 1), the graph decreases as x increases.

A function where the base is greater than 0 and not equal to 1, and the input is raised to the power of x.

A vertical line that the graph approaches but never touches. In logarithmic functions, the vertical asymptote is x = 0.

A key point on the graph of a logarithmic function, used for sketching. It's always (b, 1), where 'b' is the base.

A model that describes population growth where the population doubles at a constant rate. It's represented by the formula: P = P0 * 2^(t/d), where 'P' is the population at time 't', 'P0' is the initial population and 'd' is the doubling time.

A model that describes exponential decay where the amount of a substance decreases at a constant rate. It's represented by the formula: A = A0 * e^(-kt), where 'A' is the amount at time 't', 'A0' is the initial amount, 'k' is a positive constant and 't' is time.

A type of chart used to represent categorical data using bars that are separate.

A type of chart that represents categorical data using sectors in a circle, where the size of each sector is proportional to the frequency of the category it represents.

A chart that uses contiguous boxes to represent data, with the horizontal axis representing the data categories and the vertical axis representing frequency.

The measure of how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of an event not happening is equal to 1 minus the probability of that event happening.

A rule that helps calculate the probability of two events happening together by adding their individual probabilities and subtracting the probability of both events happening simultaneously.

Events that cannot occur at the same time. The probability of both events happening together is zero.

The number of ways to arrange 'n' objects where some are identical, with 'r1' identical, 'r2' identical, etc., is calculated by dividing the factorial of 'n' (n!) by the product of factorials of the repetition counts (r1! * r2! * ... * rk!).

The number of ways to choose 'r' objects from a set of 'n' distinct objects. It's calculated by dividing the factorial of 'n' (n!) by the product of the factorial of 'r' (r!) and the factorial of the difference between 'n' and 'r' (n-r!)

The product of all positive integers less than or equal to 'n'. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

Interest calculated only on the initial principal amount, regardless of any accumulated interest.

The difference between the original amount borrowed and the actual amount received after deducting the discount.

Interest calculated on both the principal and accumulated interest over time. It leads to exponential growth.

The effective annual interest rate represents the actual rate of return considering the compounding frequency. It's calculated as the difference between (1 + (r/n))^n and 1.

Interest calculated continuously, assuming an infinite number of compounding periods. This results in the highest possible return.