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To determine if something is a function, remember: 'A function cannot have the same input paired with more than one output.' This means each input corresponds to only one output.
In the equation y = 80x + 2, 'x' is the independent variable (time in hours), and 'y' is the dependent variable (Carli's speed in miles per hour). The correct interpretation shows how speed changes with time.
To find the median, arrange your data in numerical order and identify the middle value. If there's an even number of data points, calculate the average of the two middle numbers.
Derivatives in calculus measure how a function changes as its input changes. They provide the slope of the tangent line at any point on a graph, indicating the instantaneous rate of change, such as velocity in motion.
The domain of a function refers to all possible values of the independent variable. For the function f(t) = 8(2)^t, if t represents days since an event, the domain is 0 ≤ t ≤ 5 for 5 days.
To find points on a graph, start with the y-intercept and then choose another point where the line intersects the grid. This will help you understand the relationship between x and y values.
To convert square yards to square miles, remember that 1 square mile equals 3,097,600 square yards. This comes from multiplying 1 mile (1,760 yards) by itself.
To find a missing number in an arithmetic sequence, determine the common difference by subtracting consecutive terms. Use this difference to calculate the missing term based on its position in the sequence.
To find the nth term of an arithmetic sequence, identify the first term and the common difference. Use the formula: an = a1 + (n - 1)d.
To solve a geometric sequence, identify the first term and the common ratio. Use the formula a_n = a_1 * r^(n-1) to find any term in the sequence.
Exponential depreciation occurs when an asset loses value at a consistent percentage each year. For example, if a bakery's equipment originally worth $80,000 depreciates at 6% annually, it retains 94% of its value each year, leading to the correct formula: $a_n = 80,000(0.94)^{n-1}$.
Fractions represent parts of a whole, consisting of a numerator (top number) and a denominator (bottom number). For example, in the fraction 1/4, 1 is the part you have, and 4 is the total number of equal parts in the whole.
To find the y-intercept of a function, substitute 0 for x in the equation and solve for y. The resulting value of y is the y-intercept, where the graph crosses the y-axis.
To find the maximum height of a quadratic function like -x² + 14x - 40, use the vertex formula x = -b/2a. Substituting values gives a maximum height of 9 feet.
To calculate 2000 x 45, you can break it down into simpler parts. First, multiply 2 by 45 to get 90, then add the three zeros from 1000, resulting in 90,000.
Not all decimals that go on forever are irrational. Repeating decimals, like 2.333... or 4.686868..., are rational since they can be expressed as fractions, while non-repeating decimals, like π, are irrational.
To solve the equation x² - x = 144, first rearrange it to x² - x - 144 = 0. Then, you can use factoring or the quadratic formula to find the values of x.
To analyze the path of a rocket modeled by a quadratic function, first find the vertex to determine the maximum height, and then find the x-intercepts to see when the rocket is on the ground.
To determine the rule for generating terms in a number sequence, identify the common difference between consecutive terms. For example, in the sequence 23, 19.5, 16, 12.5, the common difference is -3.5, meaning you subtract 3.5 from each term to find the next.
$30 is approximately 22.2% of 135. To find this, divide 30 by 135 and convert the result to a percentage.
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