🧮 algebra

1. **Problem:** Simplify $x^{12} \times x^3$. 2. **Rule:** When multiplying powers with the same base, add the exponents: $a^m \times a^n = a^{m+n}$.

1. **State the problem:** We are given a downward-opening parabola with vertex near $(0,20)$ and x-intercepts near $-5$ and $5$. We want to find the equation of this parabola. 2. *

1. **State the problem:** Find the sum of the polynomials \( (2x^2 + 5) + (-x^2 + 4) \). 2. **Write the polynomials:**

1. **Problem:** Simplify $x^{12} \cdot x^3$. 2. **Formula:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$

1. The problem is to find 5.6% of 12. 2. The formula to find a percentage of a number is:

1. Énonçons le problème : isoler $x$ dans l'inéquation $-13x + 2 < \frac{x}{2} + 3$. 2. Soustrayons $\frac{x}{2}$ des deux côtés pour regrouper les termes en $x$ à gauche :

1. **State the problem:** We need to find the mass of fuel required for the model rocket to reach a height of 20 meters. 2. **Analyze the graph:** The graph shows a linear relation

1. **State the problem:** Solve the equation $$-5 = -6 + \frac{n}{14}$$ for $n$. 2. **Isolate the term with $n$:** Add 6 to both sides to move the constant term on the right to the

1. **State the problem:** Solve the inequality $$3 \leq 2 + \frac{a}{16}$$ for $a$. 2. **Isolate the variable term:** Subtract 2 from both sides:

1. The problem asks to find the x values, which typically means solving for x in an equation or finding the x-intercepts of a function. 2. To find x values where a function equals

1. **State the problem:** We are given a function with values at specific points and asked to find on which interval the average rate of change is greatest. 2. **Recall the formula

1. **State the problem:** Solve the equation $$4(t - 15) + 3 = 19$$ for $$t$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses.

1. The problem is to analyze the function $y = f(x)$ over the domain $-5 \leq x \leq -2$ based on the given graph points and features. 2. The graph shows points at $x = -8, -6, -4,

1. **State the problem:** Solve for $j$ in the equation $$-12j - 6j - (-13) = -5$$. 2. **Rewrite the equation:** Note that subtracting a negative is the same as adding a positive,

1. **State the problem:** We need to find the average rate of change of the function over the interval $3 \leq x \leq 7$. 2. **Recall the formula for average rate of change:**

1. **State the problem:** We need to determine the domain on which the given quadratic function is increasing. 2. **Identify the function type:** The graph is a downward-opening pa

1. **State the problem:** We are given the function $f(x) = -x^3 + \frac{2}{3}$ and asked to find $f(x) + 2$ expressed as a polynomial in standard form. 2. **Recall the formula:**

1. **State the problem:** We need to find the equation of the straight line in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 2. **Identify points on the

1. El problema es resolver un sistema de ecuaciones por el método de sustitución. 2. El método de sustitución consiste en despejar una variable en una de las ecuaciones y luego sus

1. **State the problem:** We need to find the slope $m$ and the y-intercept $c$ of the line $Q$ given by the equation $y = mx + c$. 2. **Identify points on the line:** From the des

1. The problem asks which of the given relations is a function. 2. A relation is a function if every input $x$ has exactly one output $y$.