🧮 algebra

1. The problem is to understand how to perform algebraic long division, which is a method to divide one polynomial by another. 2. The formula used is similar to numerical long divi

1. **Problem:** Calculate the value of the expression $2\cdot 2^{2026} + 3\cdot 2^{2027}$ and identify which option (a-f) it equals. 2. **Formula and rules:** Use properties of exp

1. **State the problem:** Determine which statement is true among the following comparisons involving exponents: $$\frac{3^{-15}}{3^{7}} \quad \text{and} \quad (3^{-8}) \cdot (3^{-

1. **State the problem:** Solve the quadratic equation $$16x^2 - 81 = 0$$. 2. **Formula and rules:** This is a difference of squares problem, which can be factored using the identi

1. **State the problem:** Find the solution set of the inequality $x - 9 < -15$ where $x$ is an integer. 2. **Write the inequality:**

1. **State the problem:** Find the least common multiple (LCM) of 72 and 120. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using their greatest common

1. **State the problem:** Solve the inequality $$-4(3x + 2) < -3x + 2$$. 2. **Apply the distributive property:** Multiply $$-4$$ by each term inside the parentheses.

1. **State the problem:** Find the points of intersection of the curves given by the equations: $$y = x^2 - 3x + x$$

1. **State the problem:** We need to find the decay constant $k$ for plutonium-240 given its half-life $t_{1/2} = 6300$ years. 2. **Recall the formula for radioactive decay:**

1. **Énoncé du problème :** Développer l'expression $$A = (x + 1)(x + 2)(x + 3)(x + 4)(x^2 - 2x + 1 - (x - 1)^2)$$.

1. **Problem:** Vilken av kurvorna är grafen till $f(x) = (x - 2)^2 + 5$? 2. **Formel och regler:** Funktionen är en andragradsfunktion i vertexform $f(x) = a(x - h)^2 + k$, där $(

1. **State the problem:** Simplify the expression $(x+1)^{30}$. 2. **Formula used:** The expression is a binomial raised to a power. The binomial theorem states:

1. **Problem a:** Gegeben sind zwei Summen, die jeweils 100 ergeben.

1. **Problemstellung:** Gegeben ist das Gleichungssystem: $$x \cdot y = 12$$

1. The problem is to solve for $x$ given the $y$ values: 0.303, 0.228, 0.1995, 0.269, 0.188, 0.1905, 0.1895, 0.18. 2. To solve for $x$, we need a function or equation relating $y$

1. **State the problem:** We need to solve the quadratic equation $$y = -7 \times 10^{-6} x^2 + 0.0028 x + 0.0899$$ for $x$ given different values of $y$: 0.1, 0.0855, 0.0845, 0.08

1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{4} = 5.$$ 2. The formula used here is to solve for $x$ by isolating it on one side of the equation. We do t

1. **Énoncé du problème :** Calculer le déterminant des vecteurs $\vec{u}$ et $\vec{v}$ dans les deux cas suivants et déterminer s'ils sont colinéaires.

1. **Problem:** Explain the 4 quadrants and how they relate to positive and negative values. 2. **Formula / rule:** A point $\left(x,y\right)$ on the coordinate plane is classified

1. **Problem:** Explain the 4 quadrants of the coordinate plane for **positive** and **negative** values. 2. **Formula/rule:** In the coordinate plane, a point is written as $ (x,y

1. Let’s name the pictures. 🍎 = apple