🧮 algebra

1. **State the problem:** We want to find an equation relating the amount of water $W$ in the pond to the time $T$ in minutes, given that water is added at a rate of 25 liters per

1. **State the problem:** Solve the equation $$4(3x-1)=8$$ for $$x$$. 2. **Use the distributive property:** Multiply $$4$$ by each term inside the parentheses:

1. **State the problem:** Solve the equation $$\frac{4}{7} (x + 14) = \frac{2}{3} (x - 7)$$. 2. **Use the distributive property:** Multiply each fraction by the terms inside the pa

1. **State the problem:** Solve the linear equation $$\frac{3}{5} (x - 15) = \frac{1}{2} (x + 20)$$. 2. **Distribute the fractions:**

1. **State the problem:** Solve the equation $$5(2x + 6) - 3(4x - 3) = 9$$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the linear equation $$7(3x + 4) = 4(3x - 1) + 23$$. 2. **Apply the distributive property:** Multiply out the parentheses.

1. **State the problem:** Solve the inequality $$\frac{1}{3} (3x - 9) \geq 6 - 2(-2x)$$ for $x$. 2. **Apply distributive property:** Multiply inside the parentheses on the left and

1. **State the problem:** Rationalise the denominator of the expression $$\frac{15 + \sqrt{5}}{6\sqrt{5}}$$ and simplify the result. 2. **Recall the rule:** To rationalise a denomi

1. **State the problem:** We need to calculate the sum of squares of the differences between each number and $0.15$: $$\sum (x_i - 0.15)^2$$

1. **State the problem:** Calculate the sum of squared differences from $0.90$ for the given values: $9.0, 8.0, 7.0, 2.0, 3.0, 6.0, 19.0, 15.0, 53.0, 4.0, 0.0, 0.0, -4.0, -33.0, -3

1. **Problem a:** Write the number 0.000 049 24 in standard form. 2. **Step 1:** Identify the decimal number: 0.00004924.

1. **State the problem:** Calculate the value of $$2\sqrt{3333}$$. 2. **Recall the formula:** The expression involves a constant multiplied by a square root, so the value is $$2 \t

1. **State the problem:** We need to solve the inequality $$\frac{1}{2}x - 16 > 17$$ and express the solution in interval notation. 2. **Add 16 to both sides:**

1. **State the problem:** Simplify the expression $$\frac{x^2+4x}{x^2+3x-54}-\frac{4}{x-6}$$. 2. **Factor the denominator of the first fraction:**

1. The problem states the expression $\frac{y}{4}$. 2. This is a fraction where $y$ is the numerator and $4$ is the denominator.

1. **State the problem:** Solve the system of linear equations: $$\frac{x}{3} + \frac{y}{2} = 2$$

1. **State the problem:** Simplify the expression $$(x-4)\times(2x^2+3x-2)$$. 2. **Formula and rules:** Use the distributive property (also called FOIL for binomials) to multiply e

1. **State the problem:** Simplify the expression $$(x-4)\times(2x^2+3x-2)$$. 2. **Formula and rules:** Use the distributive property (also called FOIL for binomials) to multiply e

1. **State the problem:** Find the term independent of $x$ in the expansion of $$\left(x-\frac{2}{x}\right)^6$$. 2. **Formula used:** Use the Binomial Theorem:

1. **State the problem:** We are given the equation $$y - 3.5 = -2(x + 1)$$ and asked to analyze or work with it. 2. **Rewrite the equation in slope-intercept form:** The slope-int

1. 問題は数列の和 $S = \sum_{k=1}^n \frac{1}{(2k-1)(2k+1)}$ を求めることです。 2. 第$k$項は分母が積の形 $ (2k-1)(2k+1) $ になっているので、部分分数分解を使います。