🧮 algebra

1. **Problem statement:** Find the first 4 terms and the 50th term of the sequences: a) $a_n = n + 10$

1. The problem is to evaluate the expression $$(3x^2 - y^2)^3$$ for given values or to understand its form. 2. Since no specific values for $x$ and $y$ are provided, we consider th

1. **State the problem:** We are given a system of inequalities: $$x + 2y \leq 24$$

1. State the problem: Solve the equation $$\frac{x - 7}{3} = 5$$ for $x$. 2. To isolate $x$, multiply both sides of the equation by 3 to eliminate the denominator:

1. The problem asks to find the first 4 terms and the 10th term of two sequences defined by formulas. 2. For sequence (a) defined by $a_n = n + 5$:

1. **Résoudre l'équation $x^2 - x - 1 = 0$** Utilisons la formule quadratique $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ avec $a=1$, $b=-1$, $c=-1$.

1. The problem gives a linear cost function for hiring a scooter: $$C = 0.15t + 22$$ where $C$ is the cost and $t$ is the time in minutes. 2. The graph shows the cost starts near 1

1. **State the problem:** A vendor sold a total of 224 sodas and hot dogs combined. The number of sodas sold was three times the number of hot dogs sold. 2. **Define variables:** L

1. **State the problem:** Solve the quadratic equation by factorization: $$6y^2 - 149y - 120 = 0$$ 2. **Multiply the coefficient of $y^2$ and the constant term:**

1. **State the problem:** Solve the linear equation $$\frac{-2v}{5} = -10$$ for $$v$$. 2. **Isolate the variable:** To eliminate the fraction, multiply both sides of the equation b

1. **State the problem:** Solve the equation $$-3w = \frac{9}{5}$$ for the variable $$w$$. 2. **Isolate $$w$$:** To solve for $$w$$, divide both sides of the equation by $$-3$$:

1. **State the problem:** Solve for $y$ in the equation $$12 = - \frac{4}{5} y$$. 2. **Isolate $y$:** To solve for $y$, divide both sides of the equation by $-\frac{4}{5}$.

1. **State the problem:** We need to find the slope and y-intercept of the line given by the equation $$y = 4 - 7x$$. 2. **Rewrite the equation in slope-intercept form:** The slope

1. **State the problem:** We are given the quadratic function $$y = x^2 - 9x + 14$$ and need to find the x-coordinate of the turning point using symmetry. 2. **Recall the symmetry

1. **State the problem:** Given the function $f(x) = -x^2 + 2x + 3$, find points $A$, $B$, and $C$ where the graph cuts the axes, then find the area of triangle $\Delta ABC$, and f

1. **State the problem:** We need to graph the solution set of the system of inequalities:

1. **State the problem:** Solve the equation for $t$ given by

1. The problem states that the sequence starts at 14 and increases by 8 each time. This is an arithmetic sequence with first term $a_1=14$ and common difference $d=8$. 2. The $n$th

1. The problem is to find the next number in the sequence: 13, 10, 6, 8, 9, 5, 2, ... 2. Let's analyze the differences between consecutive terms:

1. The problem is to find the next number in the sequence: 31, 18, 47, 65, 113, 178, 291, ... 2. First, calculate the differences between consecutive terms:

1. The problem states that we will not put brackets around variables in expressions. 2. This means when writing algebraic expressions, variables like x, y, or z will be written pla