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To calculate the average rate of change of a function over an interval, use the formula: (f(b) - f(a)) / (b - a). For the interval [2, 4], the average rate of change is -6.
To find the intersection points of two functions, look for x-values where their outputs are equal. In the given example, there are 3 intersection points at x = -1, 0, and 1.
A solution set is the collection of all values that satisfy a given mathematical condition, such as an equation or inequality. In the case of $2x > -8$ and $-5x + 7 = 12$, the solution set is $ ext{-1}$, as it satisfies both conditions.
To identify the vertex form of a quadratic function, look for the format y = a(x - h)² + k, where (h, k) is the vertex. Among given options, only the one in this form directly reveals the vertex without rewriting.
To find the score needed in the seventh game for an average of 25, use the equation: (total of first six scores + s) / 7 = 25. Solve for 's' to find the required score.
To simplify the square root of an expression like √60x³, factor the number and the variable. For √60x³, the solution is 2x√(15x).
The number one is the first counting number and represents a single unit, like one apple or one toy. It's essential in counting and understanding basic math concepts.
To identify the base of a trapezoidal prism, look for the two parallel and congruent trapezoidal faces. These are the bases, while the other faces are known as lateral faces.
To calculate the area of a rectangle, use the formula A = length × width. In this case, the area function is A(x) = x(x - 4) = x² - 4x, where the width is reduced by 4 feet.
An object can be 3 ft tall and 15 ft deep because these measurements refer to different dimensions. Height describes how tall something is vertically, while depth measures how far it extends from front to back.
To find the y-intercept of an exponential function like y = 0.5(6)^x, plug in x = 0. The y-intercept is the value of y when x is zero, which gives you y = 0.5.
To evaluate the function f(x) = x² + 4x + 8 for f(-1), substitute -1 for x, resulting in f(-1) = 5. Your selected answer of 3 is incorrect.
To solve the compound inequalities $x + 1 \geq 5$ and $2x \geq 4$, we find that $x \geq 4$ and $x \geq 2$. The solution set is $\{x | x \geq 4\}$ since both conditions must be satisfied.
To solve simple equations like `3y = 27`, divide both sides by the coefficient of y. For two-step equations such as `5y + 15 = 65`, first subtract the constant, then divide by the coefficient.
To evaluate the function f(x) = 4x² - 3x + 7 at x = -2, plug in -2 for x. This leads to f(-2) = 4(-2)² - 3(-2) + 7, which simplifies to 35.
The coordinate plane consists of an x-axis (horizontal) and a y-axis (vertical) used to plot points in ordered pairs (x, y). Understanding the order of these pairs is crucial, as (3,7) differs from (7,3) in location.
To solve the inequality -7m ≥ -6m - 6, first collect all terms involving m on one side. This results in m ≤ 6, meaning m can be any value less than or equal to 6.
To multiply expressions with exponents, first multiply the coefficients and then apply the exponent rule by adding the exponents for like bases. For example, $(-5d^4)(5d^2)$ results in $-25d^6$.
To simplify the expression $- ext{sqrt}{5}(-10 - ext{sqrt}{3})$, distribute $- ext{sqrt}{5}$ to both terms. The final answer is $10 ext{sqrt}{5} + ext{sqrt}{15}$.
To solve simple algebra equations like '3y = 27', divide both sides by the coefficient of y. This method will help you isolate the variable and find its value.
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