🧮 algebra

1. **Problem:** Heidi and Micah have 51 dimes and nickels. The total value is 4.10. Find how many more dimes than nickels there are. 2. **Define variables:** Let $d$ = number of di

1. **State the problem:** We need to find the value of the function $f(x) = 3x^2 - 5$ at $x = -2$. 2. **Recall the formula:** The function is given by

1. **State the problem:** Find the equation of the line passing through the points $\left(-\frac{3}{2}, 4\right)$ and $\left(\frac{5}{2}, -2\right)$.\n\n2. **Formula used:** The sl

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x + 2y = -9 \\ x - 2y = -3 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{1}{e^3}$$ and write it in the form $$a^p$$. 2. **Recall the rule for negative exponents:** For any nonzero number $$a$$ an

1. **State the problem:** Determine whether the function $t(x) = 4x^6 + 13$ is even, odd, or neither. 2. **Recall definitions:**

1. The problem asks us to determine if the function $p(x)$ is even, odd, or neither based on its graph. 2. Recall the definitions:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations. Important rules: addition a

1. **State the problem:** Simplify the expression $$5 \times \frac{4 \times 10^2}{4 \times 10^1}$$. 2. **Write the formula and rules:** When dividing terms with the same base, subt

1. **State the problem:** Find the equation of the line which contains the point $C$ and is perpendicular to the line $2x - 3y + 6 = 0$. 2. **Find point $C$:** From question 10(i),

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by th

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator. Multiply both sides of the equati

1. The problem asks for the expression that represents "the sum of 6 and the quotient of 9 and n". 2. "Sum" means addition, and "quotient" means division.

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$ nach $x$ auf. 2. Die verwendete Formel ist die lineare Gleichung $ax + b = c$, wobei $a$, $b$ und $c$ Konstanten sind.

1. **State the problem:** We need to find the value of the function $f(x) = 3x^3 + 2x^2 + 1$ at $x=5$. 2. **Formula used:** The function is given by

1. El problema es completar los denominadores faltantes en una expresión o ecuación con fracciones. 2. Para resolver problemas con fracciones, recordamos que cada término debe tene

1. Das Problem lautet: Schreibe die Lösungsschritte für eine algebraische Aufgabe auf Deutsch. 2. Zuerst wird das Problem klar formuliert, z.B. eine Gleichung lösen oder einen Ausd

1. **Planteamiento del problema:** Calcular las coordenadas del vector \(\overrightarrow{AB}\), su módulo y argumento dados los puntos \(A(4,-1)\) y \(B(2,-2)\).

1. The problem asks to write given sets in set builder notation. 2. Set builder notation describes a set by a property that its members satisfy.

1. **Problem statement:** Simplify the expression

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d