🧮 algebra

1. The problem is to solve an equation or expression, but since the exact problem is not specified, let's consider a common example: solve the quadratic equation $x^2 - 5x + 6 = 0$

1. **Plot the graphs of the functions:** a) The function is $y=3x^2-7$.

1. Stating the problem: We need to find the determinant of the 3x3 matrix $$\begin{bmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{bmatrix}$$. 2. Recall the formula for the deter

1. The problem is to find the determinant of the 2x2 matrix \(\begin{bmatrix} x & 3 \\ 7 & ? \end{bmatrix}\). However, the matrix is incomplete as the bottom right element is missi

1. **State the problem:** We are given the line equation $y = 4x - 1$ and the conic equation $x^2 + 2x + y^2 = k$. We want to analyze the relationship between these two equations.

1. **Problem (a): Solve the system by substitution:** Given:

1. **Problem statement:** We have two pairs of sequences. For each pair, the second sequence is formed from the first by adding, subtracting, or multiplying by a number. We need to

1. The problem gives two sequences: - First sequence: 7, 10, 13, 16, ... with nth term $3n + 4$

1. The problem states that the exchange rate graph is a straight line passing through points (0,0), (5,600), (10,1200), (15,1800), and (20,2400). 2. Since the graph is linear and p

1. The problem states that the exchange rate graph shows the relationship between pounds (£) and Japanese yen (¥). 2. From the graph, the line passes through points (5, 750), (10,

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 $$-3$$: