🧮 algebra

1. The problem is to simplify the function $f(x) = x^2 + 2x3$. 2. Notice that $2x3$ means $2 \times 3$, which equals 6.

1. **State the problem:** Find the inverse function of $h(x) = 5x - \frac{1}{3}$.\n\n2. **Rewrite the function:** Let $y = 5x - \frac{1}{3}$.\n\n3. **Swap variables:** To find the

1. Stating the problem: Solve the equation $X - 6 = 3$ for $X$. 2. To isolate $X$, add 6 to both sides of the equation:

1. **Solve the quadratic equation** $x^2 + x - 12 = 0$. Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=1$, $c=-12$.

1. Solve $5 + \frac{x}{3} = 7$. Subtract 5 from both sides:

1. The problem is to understand the concept of a function in mathematics. 2. A function is a relation between a set of inputs and a set of possible outputs where each input is rela

1. We are given two natural numbers where the difference between the larger and smaller number is 1. 2. Let the smaller number be $s$. Then the larger number is $s+1$.

1. The problem states the quadratic equation $$ax^2 + c = 11x$$ has two distinct roots and the sum of the roots is $$11$$. 2. Rewrite the equation in standard form: $$ax^2 - 11x +

1. **State the problem:** We are given the quadratic equation $$4x^2 + c = 8x$$ and told it has two distinct roots. We need to find the sum of these roots. 2. **Rewrite the equatio

1. **Comparer $5\sqrt{2}$ et $7\sqrt{3}$** Calculons approximativement :

1. **State the problem:** Solve the simultaneous equations: $$5x - 2y = 23$$

1. **Problem:** Use the graph to answer questions about values of $x$ and $y$. (a) For what values of $x$ is $y=1$?

1. **State the problem:** Solve the equation $$21 - 3p = -27$$ and check the solution. 2. **Isolate the variable term:** Subtract 21 from both sides to get

1. **State the problem:** We have a rectangular tank with length 10 m and width 5 m. It is initially 45% filled with juice. After adding 75 m³ of water, the tank becomes \( \frac{3

1. The problem gives a system of equations: $$+k = x + 26$$

1. **State the problem:** We are given three pairs of values $(x, y)$ involving a constant $s$ and told there is a linear relationship between $x$ and $y$. We need to find which eq

1. **State the problem:** A rectangular tank is 10 m long and 5 m wide. It is initially 45% filled with juice. After adding 75 m^3 of water, the tank becomes 3/5 (or 60%) full. We

1. Bài toán yêu cầu xác định chiều rộng là $12 - x - y$. 2. Đây là biểu thức đại số mô tả chiều rộng dựa trên các biến $x$ và $y$.

1. **State the problem:** We are given values of an exponential function $g(x)$ at specific points $x = -1, 0, 1, 2$ and need to find the equation that defines $g(x)$. 2. **Analyze

1. The problem asks to find the slope of the line of best fit shown on the scatter plot. 2. The line passes near the points approximately at $(1, 2)$ and $(7, 14)$.

1. Let's clarify the step where you multiply 6 on the left side of the equation. 2. Suppose the original expression was $6 \times \frac{2x}{3} = 4v$.