To find the unique intersection point of two linear equations, one can solve the system of equations by substitution or elimination.
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substitution
Substitution is a common algebraic method for solving systems of equations by replacing one variable with an equivalent expression from another equation.
Question 2
If a price increases from $80 to $100, the percent increase is 25%.
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percent
Percent increase is calculated as the change divided by the original amount, multiplied by 100.
Question 3
The solutions to a quadratic equation are also known as its roots or zeros.
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roots
The roots of a quadratic equation are the values of the variable that make the equation true, often corresponding to the x-intercepts of its graph.
Question 4
For a right triangle with legs of lengths 3 and 4, the hypotenuse must have a length of 5.
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hypotenuse
In a right triangle, the hypotenuse is the longest side, opposite the right angle, and its length can be found using the Pythagorean theorem.
Question 5
In the equation y = 3x + 2, the number 3 represents the slope of the line.
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slope
The slope of a linear function indicates the rate of change of y with respect to x.
Question 6
The arithmetic mean of a dataset is calculated by summing all values and dividing by the number of values.
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mean
The mean is a measure of central tendency representing the average of a set of numbers.
Question 7
The equation of a circle with center (h, k) and radius r is (x-h)^2 + (y-k)^2 = r^2.
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radius
The radius of a circle is the distance from its center to any point on its circumference.
Question 8
When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.
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reversed
Reversing the inequality sign ensures the truth of the inequality is maintained after multiplication or division by a negative value.
Question 9
A ratio compares two quantities by division, often expressed as a:b or a/b.
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ratio
A ratio expresses the relationship between two numbers, indicating how many times one number contains the other.
Question 10
An exponential function describes growth or decay where the rate of change is proportional to the current amount.
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exponential
Exponential functions are characterized by a constant base raised to a variable exponent, modeling rapid increase or decrease.
Question 11
If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.
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proportional
Similar triangles maintain the same shape, meaning their side lengths are scaled by a constant factor.
Question 12
The absolute value of a number represents its distance from zero on the number line, always resulting in a non-negative value.
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absolute
Absolute value measures magnitude without regard to direction.
Question 13
The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.
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probability
Probability quantifies the likelihood of an event happening, expressed as a fraction or decimal between 0 and 1.
Question 14
To add or subtract rational expressions, they must first have a common denominator.
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denominator
Just like with numerical fractions, rational expressions require a common denominator before their numerators can be combined.
Question 15
When two parallel lines are intersected by a transversal, alternate interior angles are congruent.
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congruent
Congruent angles have the same measure.
Question 16
The y-intercept of a line is the point where the line crosses the y-axis, meaning the x-coordinate is zero.
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y-intercept
The y-intercept is a key feature of a linear graph, indicating the value of y when x is zero.
Question 17
A line of best fit on a scatterplot helps to show the general trend in the data and can be used for prediction.
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trend
The line of best fit visually represents the correlation and direction of the relationship between two variables in a scatterplot.
Question 18
The domain of a function is the set of all possible input values for which the function is defined.
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domain
The domain specifies the valid x-values that can be used in a function without resulting in undefined operations.
Question 19
In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
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tangent
Tangent is one of the primary trigonometric ratios, commonly remembered as SOH CAH TOA (TOA: Tangent = Opposite/Adjacent).