Semester Exam 2024 Flashcard 2

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

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How do you represent the total number of coins in a bag containing quarters and dimes?

Back

You can represent it with the equation: q + d = total number of coins, where q is the number of quarters and d is the number of dimes.

Front

What is the value equation for quarters and dimes?

Back

The value equation can be represented as: 0.25q + 0.10d = total value in dollars.

Front

What does the zero of a function represent?

Back

The zero of a function is the value of x for which the function f(x) = 0. It represents the x-intercepts of the graph.

Front

What is the first step to solve the equation Ax + B = y for y?

Back

The first step is to subtract B from each side of the equation.

Front

How do you transform a function by a scalar multiplication?

Back

To transform a function f(x) into g(x) = kf(x), you multiply the output of f(x) by a constant k, which stretches or compresses the graph vertically.

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you simplify the expression 2(4x - 7)?

Back

Using the distributive property, 2(4x - 7) simplifies to 8x - 14.

Front

What is the purpose of solving a system of equations?

Back

The purpose is to find the values of the variables that satisfy all equations in the system.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.