🧮 algebra

1. The problem is to graph the equation $$2x - 4y = 12$$. 2. First, rewrite the equation in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-interce

1. The problem is to simplify the expression $\sqrt{49}$.\n\n2. Recall that the square root of a number $x$ is a value that, when multiplied by itself, gives $x$.\n\n3. Since $49 =

1. **State the problem:** Analyze the polynomial function $$y = -2x^3 + 5x^2 + 4x - 12$$ for its degree, intercepts, end behavior, and transformations. 2. **Degree:** The degree of

1. **State the problem:** Solve the equation $-5 + x + 16 = -3$ for $x$. 2. **Combine like terms on the left side:**

1. The problem is to use synthetic division to find the root of a polynomial. 2. Synthetic division is a shortcut method for dividing a polynomial by a binomial of the form $x - c$

1. **State the problem:** Solve the equation $5 - 4x + 3 = -30$ for $x$. 2. **Combine like terms on the left side:**

1. **State the problem:** Find the roots of the cubic polynomial $$-5x^3 + 3x^2 - 4x + 18 = 0$$. 2. **Recall the formula and rules:** Roots of a polynomial are values of $x$ that m

1. **State the problem:** Analyze the polynomial function $$f(x) = -5x^3 + 3x^2 - 4x + 18$$ for its degree, intercepts, end behavior, and transformations. 2. **Degree:** The degree

1. Das Problem lautet: Finde die Achsenschnittpunkte der Funktion $y=4-x^2$. 2. Achsenschnittpunkte sind die Punkte, an denen die Funktion die x-Achse oder y-Achse schneidet.

1. The problem is to compare the function $y = -4x - 98$ to the parent function $y = x$. 2. The parent function $y = x$ is a linear function with slope 1 and y-intercept 0.

1. The parent function for comparison is typically the simplest form of the function type, for example, the parent function of a quadratic is $y=x^2$. 2. To compare, identify the t

1. **Problem statement:** Fred is 4 years older than Barney. Five years ago, the sum of their ages was 48. Find their current ages. 2. **Define variables:** Let $B$ be Barney's cur

1. We are asked to simplify the fraction $\frac{17}{34}$. 2. The formula for simplifying fractions is to divide numerator and denominator by their greatest common divisor (GCD).

1. **State the problem:** A father is 4 times as old as his son. In 20 years, the father will be twice as old as his son. We need to find their present ages. 2. **Define variables:

1. **State the problem:** Analyze the function $$y = -5^3 + 3^2 - 4x + 18$$ for its degree, intercepts, end behavior, and transformations. 2. **Simplify the expression:** Calculate

1. **State the problem:** Simplify the expression $$4(fg + 3g) + 5g$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses:

1. **State the problem:** Factor the polynomial $$9x^3 - 54x^2 - x + 6$$ completely. 2. **Group terms:** Group the polynomial into two parts to factor by grouping:

1. **Problem Statement:** Given that $f(0) = -7$, determine which statement correctly describes the graph of $y = f(-x)$ in the $xy$-plane. 2. **Understanding the problem:** The fu

1. **State the problem:** We need to find the length of a rectangular tank given its volume, width, and height. 2. **Formula:** The volume $V$ of a rectangular tank is given by:

1. **State the problem:** We need to find the equation of a parabola with x-intercepts at $x = -3$ and $x = 5$, and a minimum value (vertex) at $y = -4$. 2. **Recall the form of a

1. **Problem statement:** A parabola intersects the x-axis at $x=3$ and $x=9$. We need to find the $x$-coordinate of the parabola's vertex. 2. **Formula and concept:** The parabola