🧮 algebra

1. The problem is to understand and simplify, if possible, the expression $$\frac{2x}{2x - 3y}$$. 2. The numerator is $$2x$$, and the denominator is $$2x - 3y$$.

1. The problem asks to write the expression \(\log(8x^3) + \log(2x)\) as a single logarithm. 2. Recall the logarithm property: \(\log(a) + \log(b) = \log(ab)\).

1. Dado o problema: $$\frac{1}{a-3} + \frac{a+1}{a+3} = \frac{1-a}{9 - a^2}$$ 2. Observe que o denominador $$9 - a^2$$ pode ser fatorado como $$9 - a^2 = (3 - a)(3 + a)$$.

1. Problem A: Simplify the expression $$(3^2 - 8) + \frac{2^2}{2} \cdot 3 - 3$$ using order of operations. 2. Calculate powers and parentheses first:

1. The problem states that the cost of hiring a car in 2018 is 264 rupees, which is 20% more than the cost in 2013. 2. Let the cost in 2013 be $x$ rupees.

1. **Stating the problem:** We have the quadratic equation $$2x^2 + kx + 5k = 0$$ and multiple choice options for the value of $k$. To solve for $k$, we use the fact that the quadr

1. The problem consists of finding the distance between two points in the coordinate plane: $(-x,1)$ and $(-5,7)$. 2. Use the distance formula between two points $(x_1,y_1)$ and $(

1. **State the problem:** We need to find the equation of a line that passes through the point $(2, 3)$ and has a slope of $-3$. 2. **Recall the point-slope form of a line:** The p

1. Determine the equation of the line passing through point (2, 3) with slope $m = -3$. Use the point-slope form of the line equation: $$y - y_1 = m(x - x_1)$$

1. **State the problem:** Simplify the expression $$\frac{2x}{2x + 3y} + \frac{4x}{2x - 3y} - \frac{8x^2}{4x^2 - 9y^2}$$. 2. **Identify common denominators:** Notice that the denom

1. The problem asks to find the equation of a line passing through a given point (which is missing). 2. To determine the equation of a line, we need at least two things: a point on

1. Problema 60: Simplifique a expressão $$\frac{x - x^3}{x^2 + 4x + 4} - \frac{8x}{2x + 4}$$. Primeiro, fatoramos denominadores e numeradores relevantes:

1. The problem states: Rewrite the logarithmic equation $$91 = \log_5 y$$ as an exponential equation. 2. Recall that the logarithmic equation $$\log_b a = c$$ can be rewritten as t

1. Stated problem: Simplify the expression $c^1 \times \sqrt[3]{c^3}$.\n\n2. Break down the expression: $c^1$ is simply $c$. The term $\sqrt[3]{c^3}$ means the cube root of $c^3$.\

1. **State the problem:** Simplify the expression $$rs - 3 ( r - s )^2 + 4s^2$$ and verify the right side $$rs - 3 ( r - s ) ( r - s ) + 4s^2$$. 2. **Expand the squared term:** Sin

1. **State the problem:** We are given a total of 175 teachers to be apportioned among five high schools based on their student populations using Webster's method. 2. **List the po

1. Problem 38: Find which equation is equivalent to $y - 34 = x(x - 12)$. Expand the right side:

1. The problem is to show that the function defined by $f(x) = 12$ has no maximum. 2. Note that $f(x) = 12$ is a constant function, meaning it has the same value for every $x$.

1. We are given the polynomial equation $$6x^6-25x^5+31x^4-31x^2+25x-6=0$$ and asked to solve it using synthetic division. 2. First, try to find rational roots using the Rational R

1. **State the problem:** Given mappings from numbers on the left to numbers on the right, find the unknown output, especially for inputs 9 and 19. 2. **Analyze the first set:** 4

1. The problem presents three circles each with four numbers around and asks to find the missing value in the third circle (J).\n\n2. Let's observe the numbers around each circle a