🧮 algebra

1. The problem involves solving the equation $1 - \frac{1}{2} = 2a$ for $a$. 2. First, simplify the left side:

1. El problema ens diu que cada dècim val 20 i volem comprar un dècim per a cada nombre que acaba en 395. 2. Primer, hem d'entendre quants nombres acaben en 395 dins d'un interval

1. **State the problem:** Mdm Grace's shop sells plates and cups. The price ratio of a plate to a cup is 3:2, and the price difference is 3. In the first month, 4/7 of the items we

1. **State the problem:** Simplify the expression $$\frac{8y}{2 - 3y} - \frac{4}{-3y^2 + 2y} + \frac{3y + 2}{y}$$. 2. **Rewrite the expression and factor denominators:** Note that

1. **State the problem:** Solve for $y$ in the equation $$\ln(y - 3) = 2t + t^2.$$\n\n2. **Recall the formula and rules:** The natural logarithm function $\ln(x)$ is the inverse of

1. **Stating the problem:** Given points A(-2,1), B(2,3), and C(-1,-2), find: a) The equation of the line BC.

1. **State the problem:** Solve the quadratic equation $2x^2 + x - e^2 = 0$ for $x$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are giv

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eli

1. **Stating the problem:** We have a total sum of 6727 with 29 factors listed, some repeated and some decimal values. We need to divide these factors into two separate sums such t

1. Il problema chiede di risolvere l'espressione $$\left(\frac{9}{12} a^{2} b\right)^2$$. 2. La regola per elevare un prodotto a una potenza è elevare ogni fattore alla potenza: $$

1. **State the problem:** We are given the sequence 4, 7, 12, 19, 28, 39 and need to find a formula for the nth term, $a_n$. 2. **Analyze the sequence:** Calculate the differences

1. **State the problem:** Find a formula for the nth term $a_n$ of the sequence: 4, 7, 12, 19, 28, 39. 2. **Analyze the sequence:** Calculate the differences between consecutive te

1. **State the problem:** Simplify or understand the expression $$\left(\frac{a - 3}{a + 2}\right)^{1 - \sqrt{2}}$$. 2. **Recall the exponent rule:** For any base $x$ and exponents

1. **State the problem:** Simplify or analyze the expression $$\frac{(a - 3)^{1 - \sqrt{2}}}{a + 2}$$ where $a$ is a variable. 2. **Recall the rules:**

1. Das Problem lautet: Löse die Gleichung $$2x + 3 = 7$$. 2. Die allgemeine Formel zum Lösen linearer Gleichungen ist: $$ax + b = c \Rightarrow x = \frac{c - b}{a}$$.

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x + 2y + z = 2 \\ 7y + 2z = 4 \\ -10z = 6 \end{cases}$$

1. The problem is to find the domain of the function $f(x)$ given the table and graph description. 2. From the table, $f(x)$ is undefined for $x = -5, -4, -3, -2$ and defined start

1. **Problem statement:** Sketch the graph of the piecewise function

1. **State the problem:** Given the function $f(x) = 4\sqrt{x} + 3$, solve for $x$ when $f(x) = 10$. 2. **Set up the equation:**

1. The problem presents a table with two rows: the first row contains the numbers 1, 2, 3, and 4, and the second row contains the values 178.39, 213.86, 257.14, and 307.95 respecti

1. **State the problem:** Solve the quadratic equation $$c t^2 + 15t = -36$$ for $t$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: