🧮 algebra

1. **Stating the problem:** We are given the system of equations:

1. **State the problem:** We have a line $l$ with equation $2x - 3y = 12$.

1. **Problem statement:** Sketch the graph of the quadratic function $$y = - (x-1)(x+6)$$. 2. **Formula and rules:** This is a quadratic function in factored form. The x-intercepts

1. Problem: Simplify the expression $$\frac{2x^{4/3} \cdot x^{2/3}}{x^2}$$. 2. Formula and rules: When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a

1. Problemet är att lösa ekvationen $$x^{\frac{1}{3}} = 2$$. 2. Formeln för att lösa en ekvation med en rot är att upphöja båda sidor till den inversa potensen: $$\left(x^{\frac{1}

1. **State the problem:** Simplify or factor the quadratic expression $y^2 + 8y + 16$. 2. **Recall the formula:** A quadratic expression $ay^2 + by + c$ can be factored if it can b

1. **State the problem:** Factor the expression $$9a^2x^3 - 16x^3$$.

1. **State the problem:** Simplify the fraction $\frac{144}{56}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common diviso

1. The problem is to find the value of $4 \frac{7}{8} \div \frac{1}{8}$. 2. First, convert the mixed number $4 \frac{7}{8}$ to an improper fraction. The formula is $a \frac{b}{c} =

1. **State the problem:** A catering company provided quiches, each cut into a certain number of pieces. After the luncheon, some pieces were left over. We need to find how many qu

1. **Problem statement:** Factor out the greatest common factor (GCF) from the term $2x^4 - x^3$. 2. **Identify the GCF:**

1. **State the problem:** Solve the equation $$\frac{2^x y}{2^x 5} + \frac{y}{2} \cdot \frac{x^5}{5} = 10$$ for $y$. 2. **Simplify the first term:** Since $2^x$ appears in both num

1. **State the problem:** We need to find the values of the square roots and cube roots without using a calculator. 2. **Recall the definitions:**

1. **State the problem:** Simplify the expression $$\frac{2x}{x-4} + \frac{3 \cdot 5}{2x-2}$$. 2. **Rewrite the expression:** The expression is $$\frac{2x}{x-4} + \frac{15}{2x-2}$$

1. **State the problem:** Simplify the expression $6x - 4$ if possible. 2. **Analyze the expression:** The expression $6x - 4$ is a linear expression with two terms: $6x$ and $-4$.

1. Problemet er at lægge brøkerne $\frac{10}{12}$ og $\frac{3}{12}$ sammen. 2. Når brøker har samme nævner, lægger vi blot tællerne sammen og beholder nævneren.

1. The problem is to find the product of $2y^2$ and $y^2$. 2. The formula for multiplying powers with the same base is $a^m \times a^n = a^{m+n}$.

1. **State the problem:** Multiply $2y^2$ by $2y^2$. 2. **Write the expression:**

1. **State the problem:** We need to find the values of voltages $U_1$, $U_2$, $U_3$, and $U_4$ given the system of equations: $$

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-6 \leq x \leq -2$. 2. **Recall the formula:** The average rate of chan

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-6 \leq x \leq -2$. 2. **Recall the formula:** The average rate of chan