🧮 algebra

1. **State the problem:** Determine if the variables $x$ and $y$ in each graph are proportional, and if so, find the constant of proportionality. 2. **Recall the definition of prop

1. **Énoncé du problème :** Additionner les fractions $$\frac{7}{x^2 - 10x + 16} + \frac{2x}{x^2 - 13x + 40}$$.

1. **State the problem:** We need to find the sum of $-\frac{5}{3}$ and $-\frac{3}{7}$. 2. **Formula and rules:** To add fractions, we need a common denominator. The sum of two fra

1. The problem asks which relationship represents a function with a lesser rate of change than the graphed function. 2. The graphed function passes through points approximately $(-

1. **State the problem:** Donna earns 50 for each hour she works. We need to find the amount earned for 4, 8, and 10 hours. 2. **Formula:** The amount earned $A$ is given by the fo

1. Stating the problem: Simplify the expression $-\frac{1}{10} + \frac{5}{8}$.\n\n2. To add or subtract fractions, they must have a common denominator. The denominators here are 10

1. Énonçons le problème : Trouver le polynôme $A(x)$ tel que pour toute valeur de $x$ où les fractions sont définies, on ait $$\frac{A(x)}{3x} \times \frac{3x + 3}{x^2 - 2x - 3} =

1. The problem asks which relationship represents a function with the same slope as the function $$y = -\frac{3}{2}x - 4$$. 2. The slope of the given function is $$-\frac{3}{2}$$.

1. **State the problem:** Simplify the product of two rational expressions: $$\frac{k^{12} + 19k^{6} + 88}{5k^{8} + 40k^{2}} \times \frac{k^{4} - 6k^{2}}{2k^{12} + 19k^{6} - 33}$$

1. **Énoncé du problème** : Trouver la fonction réciproque de la fonction affine $g(x) = -2(x - 4)$. 2. **Formule et règles importantes** : Pour trouver la fonction réciproque $g^{

1. **State the problem:** We need to find all values of $x$ such that $f(x) = g(x)$, where $$f(x) = 0.25x^3 - 2x^2 + x + 7.6$$

1. The problem asks us to identify which of the given functions is an exponential function. 2. Recall the definition: An exponential function has the form $$y = a^x$$ where the bas

1. The problem asks to identify which of the given functions is an exponential function. 2. The two functions given are:

1. **State the problem:** We need to find the multiplicity of the zero $x=4$ in the function $h(x) = f(x) \cdot g(x)$, where $$f(x) = 3x^2 (x + 4) (x + 7)^4 (x - 4)^3$$

1. The problem asks to identify which of the given functions is an exponential function. 2. An exponential function has the form $$y = a^x$$ where the base $$a$$ is a positive cons

1. **State the problem:** Solve the inequality $-2(5v - 12) > 6 - v$ and verify the solution $v \leq 2$. 2. **Distribute the $-2$ on the left side:**

1. The problem asks us to identify which of the given functions is an exponential function. 2. Recall that an exponential function has the form $$y = a^x$$ where the base $$a$$ is

1. The problem asks to identify which of the given functions is an exponential function. 2. An exponential function has the form $$y = a^x$$ where the variable $$x$$ is in the expo

1. The problem is to graph the line given by the equation $$y = \frac{2}{3}x + 1$$. 2. This is a linear equation in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope an

1. **State the problem:** Simplify each of the following expressions involving powers of 3: a) $3^4 \cdot 3^3$

1. The problem involves solving for the unknown variable in two equations involving fractions: $$ ? = \frac{30}{100} $$