🧮 algebra

1. Stating the problem: We are given the equation $27x = 9y$ and need to find the value of $\frac{x}{y}$. 2. Start by dividing both sides of the equation by $9y$ to isolate $\frac{

1. The problem is to solve the equation or expression given, but no equation was provided by the user. 2. To solve a math problem, please provide the specific equation or expressio

1. Stating the problem: You want to know formulas and steps to change the subject of a formula involving square roots and squares. 2. When the formula involves a square root, e.g.,

1. The expression given is $$\frac{\log(m)\sqrt[p]{3-n}}{mn^{2}}$$. 2. We note that $$\sqrt[p]{3-n}$$ means the $$p$$-th root of $$3-n$$, which can be written as $$(3-n)^{\frac{1}{

1. **State the problem:** We need to find the value of $y^2$ given the equation $$9x^2 - 9y^2 = 4.$$\n\n2. **Isolate the term involving $y^2$:** Subtract $9x^2$ from both sides to

1. **Stating the problem:** Solve the given algebraic expressions, simplify fractions, evaluate equations, and solve for variables. 2. **Simplify fractions:**

1. **Rational numbers equalities and simplifications:** - Given equalities like $\frac{-8}{14} = \frac{-4}{3.5} = \frac{16}{-2.1}$,... we check if the fractions simplify to the sam

1. The problem is to understand and work with the equation $x + y = 5$. 2. This is a linear equation representing a line in the coordinate plane.

1. State the problem: Find the gradient (slope) of the line passing through points A(1,3) and B(-2,5). 2. Use the slope formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$:

1. **Stating the problem:** Solve the equation $\frac{k+k}{k} = 6$ for $k$. 2. **Simplify the numerator:** $k+k = 2k$, so the equation becomes $\frac{2k}{k} = 6$.

1. **Stating the problem:** We explore 5 functions focusing on aids in graph sketching: domain and range, intercepts, symmetries, asymptotes, and real-life applications. 2. **Funct

1. Represent 7/5 and 4/5 on the number line. - The fractions 7/5 and 4/5 are represented as points on the number line between 1 and 2.

1. The problem asks for the equation of a line passing through point B(-1, 3) that is parallel to the line given by the equation $$y=4x+2$$. 2. Since the line we want is parallel t

1. Soal: Cari himpunan penyelesaian dari $\frac{x+2}{4-2x} \geq 1 - x$. Langkah-langkah:

1. The problem asks us to find the retail price of a smartphone with a 20% markup on the production cost of 8,000 rubles (excluding VAT). 2. First, calculate the amount of the mark

1. Stating the problem: Given a geometric sequence with first four terms 418.5, 279, 186, 124, find the common ratio $r$, the 5th term $u_5$, the smallest integer term, and the sum

1. Given the PIN code formula: $$\text{Pin Code} = \frac{5_0'(3x^3 - 2x^2 + x - 4) \times 4^2}{\sqrt{x^2 - 3x + 24}}$$

1. The given function is $S(p) = \sqrt{500 - 2p} + 5$. 2. For the square root to be defined for real numbers, the radicand (expression inside the square root) must be non-negative:

1. The problem is to find the value of $\log (0.25 \times 0.025)$.\n\n2. First, multiply the numbers inside the logarithm: $$0.25 \times 0.025 = 0.00625.$$\n\n3. So the problem red

1. **State the problem:** We are given two equations: $$x + y = 4$$

1. **Question 21: Geometric Sequence** - *Problem:* Given the first four terms of a geometric sequence: 418.5, 279, 186, 124, ..., find the common ratio $r$, the 5th term $u_5$, th