🧮 algebra

1. **State the problem:** Calculate the product $9^7 \times 9^8$. 2. **Formula used:** When multiplying powers with the same base, use the rule:

1. **State the problem:** Solve the equation $$\ln\left(\frac{e^3}{\sqrt{x+0}}\right) \cdot x = \ln\left(\frac{e^3}{\sqrt{n+1}}\right)$$ for $x$.

1. **State the problem:** We need to find the dimensions of a rectangular container with volume 50 ft³. The container has dimensions: length = $4x + 10$ ft, width = $x$ ft, and hei

1. **State the problem:** Solve the equation $16-2t=5t+9$. 2. **Use the goal of isolating $t$:** Put all $t$ terms on one side and constants on the other.

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **State the problem:** We are given two linear equations: $$2x + 3y = 7$$

1. **Problem:** Bestimmen Sie die Nullstellen der Gleichungen a) bis i) im Kopf. 2. **Formel:** Nullstellen einer Funktion sind die Werte von $x$, für die $f(x) = 0$ gilt.

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

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.