🧮 algebra

1. **State the problem:** We are given the quadratic function $$c(x) = -x^2 + 11x - 24$$ and three statements about it: - #1: The x-intercepts are (3,0) and (7,0).

1. **State the problem:** Rewrite the fractions $\frac{2}{7}$ and $\frac{9}{11}$ with a common denominator. 2. **Find the least common denominator (LCD):** The denominators are 7 a

1. **State the problem:** Add the fractions $\frac{4}{7}$ and $\frac{1}{5}$. 2. **Formula:** To add fractions, use the formula $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$.

1. **State the problem:** Subtract the fractions $\frac{3}{8}$ and $\frac{1}{5}$. 2. **Formula:** To subtract fractions, use the formula $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}

1. The problem asks us to find equivalent fractions for $\frac{1}{4}$ and $\frac{1}{9}$ using the least common denominator. 2. To find equivalent fractions with the same denominato

1. The problem asks us to write equivalent fractions for $\frac{1}{10}$ and $\frac{1}{2}$ using the least common denominator (LCD). 2. To find the LCD, we find the least common mul

1. **Problem:** Berechnen Sie den Wert von $-\frac{1}{2} \times \frac{3}{7}$. 2. **Formel:** Multiplikation von Brüchen:

1. **Problem statement:** We need to solve the problem where the variable $r$ is changed from 0.65 to 0.065. The original problem context is not fully given, but we will assume it

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. Here, factorization is simpler.

1. Das Problem lautet: Löse die Polynomgleichung. 2. Um eine Polynomgleichung zu lösen, sucht man die Werte von $x$, für die das Polynom den Wert 0 annimmt, also $P(x) = 0$.

1. **State the problem:** We need to find the equation of any line passing through the point $(-4,2)$. Then, find the equations of two lines through $(-4,2)$ whose perpendicular di

1. **Problem Statement:** Sketch the graph of the function $y = (x + 1)(x + 3)$. 2. **Formula and Important Rules:** The function is a quadratic in factored form. To sketch it, fin

1. **State the problem:** Simplify the expression $$\frac{50x}{930,965 - 20x - 350,877}$$. 2. **Rewrite the denominator:** Combine the constants in the denominator:

1. The problem is to find the equation of a line passing through a given point on the Cartesian coordinate system. 2. Since no specific point or slope is given, we need at least on

1. **State the problem:** Given the table of points $(2,7)$, $(0,3)$, $(-2,-1)$, and $(-4,-5)$, determine which of the given linear equations matches the data. 2. **Recall the form

1. **Stating the problem:** We are given the system of equations:

1. **State the problem:** We have a line $l$ with equation $2x - 3y = 12$.

1. **Problem statement:** Sketch the graph of the quadratic function $$y = - (x-1)(x+6)$$. 2. **Formula and rules:** This is a quadratic function in factored form. The x-intercepts

1. Problem: Simplify the expression $$\frac{2x^{4/3} \cdot x^{2/3}}{x^2}$$. 2. Formula and rules: When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a

1. Problemet är att lösa ekvationen $$x^{\frac{1}{3}} = 2$$. 2. Formeln för att lösa en ekvation med en rot är att upphöja båda sidor till den inversa potensen: $$\left(x^{\frac{1}

1. **State the problem:** Simplify or factor the quadratic expression $y^2 + 8y + 16$. 2. **Recall the formula:** A quadratic expression $ay^2 + by + c$ can be factored if it can b