🧮 algebra

1. **State the problem:** Solve the equation $-10x + 8y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation.

1. **State the problem:** Find the least common multiple (LCM) of 8, 6, and 3. 2. **Formula and rules:** The LCM of numbers is the smallest number that is a multiple of all the giv

1. **State the problem:** Simplify the expression $$(x^{\frac{1}{2}})^7 \times \sqrt{x^9}$$. 2. **Recall the rules:**

1. **State the problem:** Find the least common multiple (LCM) of 8, 6, and 3. 2. **Formula and rules:** The LCM of numbers is the smallest number that is a multiple of all the giv

1. **State the problem:** We have a line L given by the equation $$4y + 12 = 16x$$ and a line R that is perpendicular to L and passes through the point $(-1, 5)$. We need to:

1. **State the problem:** Solve for $x$ in the equation $2(x-3)+3(x+1)=4(x-2)$. 2. **Write down the equation:**

1. The problem is to find the first four terms of the sequence defined by the formula $a_n = 61 - 6(n - 1)$ for $n = 1, 2, 3, \ldots$. 2. The formula for the $n$-th term of the seq

1. **State the problem:** Solve for $x$ in the equation $2(x-3)+3(x+1)=4(x-2)$.\n\n2. **Write down the equation:** $$2(x-3)+3(x+1)=4(x-2)$$\n\n3. **Distribute the constants:** Mult

1. **Solve the equation** $\frac{x - 6}{4x} = \frac{1}{2}$. 2. Multiply both sides by $4x$ to eliminate the denominator:

1. **State the problem:** Simplify the expression $$(2\sqrt{3} - 5)(2\sqrt{3} + 5)$$. 2. **Formula used:** This is a product of conjugates, which follows the difference of squares

1. El problema nos pide evaluar las funciones $f(x) = 4x^2 - x$ y $g(x) = -4x + 2$ en valores específicos: $f(-2)$ y $g(5)$. 2. Para evaluar una función en un valor dado, sustituim

1. The problem is to find the value of $X$. 2. Since no equation or context is given, we cannot solve for $X$ directly.

1. **State the problem:** Solve for $X$ in the equation:

1. **State the problem:** Simplify the expression $$(4-\sqrt{10})(4+\sqrt{10})$$. 2. **Formula used:** This is a product of conjugates, which follows the formula $$(a-b)(a+b) = a^2

1. Stating the problem: Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy$. 2. Group terms to factor by grouping:

1. The problem is to simplify the expression $$(\sqrt{5}+3)(\sqrt{5}-3)$$. 2. This is a product of conjugates, which follows the formula $$(a+b)(a-b) = a^2 - b^2$$.

1. The problem asks: What percent of 70 is 3.5? 2. To find what percent one number is of another, use the formula:

1. **State the problem:** Factor the expression $$x^2y^2 - 5x^2y - 5xy^2 + xy^3$$. 2. **Recall the factoring technique:** Group terms to factor by grouping.

1. **State the problem:** Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy^3$. 2. **Identify common factors:** Group terms to factor by grouping:

1. Diketahui fungsi $f(x) = x + 3$. Kita diminta mencari fungsi inversnya, yaitu fungsi $f^{-1}(x)$ yang memenuhi $f(f^{-1}(x)) = x$. 2. Langkah pertama, ganti $f(x)$ dengan $y$, s

1. The problem asks: How many 35ths are equal to $\frac{4}{7}$? 2. We want to find a number $x$ such that $\frac{x}{35} = \frac{4}{7}$.