🧮 algebra

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: $$ ? = \frac{30}{100} $$

1. **State the problem:** We need to find the cost of 5 tulips and 6 roses given two purchases: 7 tulips and 9 roses cost 25.90, and 4 tulips and 8 roses cost 19.80. 2. **Define va

1. **Problem statement:** Find the sum of the first 40 terms of an arithmetic series given that the sum of the first 12 terms is 186 and the 20th term is 83.

1. **State the problem:** Solve the equation $3x - 4 = 5x + 2$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the inequality $$3m + 5 > 2(m - 7)$$. 2. **Apply the distributive property:** Expand the right side:

1. The problem asks for the average rate of change in bounce height as the drop height changes from 20 inches to 60 inches. 2. The average rate of change formula is:

1. **State the problem:** We need to find the value of $f(-2)$ for the function $y = f(x)$, which is a parabola with vertex at $(-5, -9)$ and passes through $(-2, -4)$. 2. **Recall