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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.
To solve the equation 2x - 5 = 3(4x + 5), first apply the distributive property, then move x terms to one side, and solve for x. The solution is x = -2.
To calculate the cost of carpet for an area of 148.71 ft², you'll need to determine the number of cases required and compare prices per square foot and square yard. Buying by square foot is cheaper in this example, costing $159.12 versus $164.39 for cases.
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. To solve it, you can use substitution or the quadratic formula, ensuring to simplify the equation first.
To determine if a value is a solution to the quadratic equation x² + 3x + 2 = 0, substitute the value into the equation. If the result equals zero, the value is a solution; if not, it isn't.
To solve the equation $5x^2 + 75x = 0$, factor out $x$ to get $x(5x + 75) = 0$. This gives solutions $x = 0$ and $x = -15$.
To factor the quadratic equation $x^2 + 4x - 32 = 0$, find two numbers that multiply to -32 and add to 4. The numbers -4 and 8 work, leading to the factored form $(x - 4)(x + 8) = 0$.
To maintain a 90% average with a current grade of 98%, you need to score at least 60.6 on the midterm. However, since grades can't exceed 100%, achieving this average is impossible without adjusting your expectations.
To complete the square for the equation x² + 6x = 2, take half of the coefficient of x, square it, and add to both sides. This transforms the equation into a perfect square trinomial, simplifying the solution process.
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