🧮 algebra

1. Problems states: Find the value of $x$ such that $$\frac{x^2 - 5x + 6}{x - 3} = 0.$$\n\n2. A fraction equals zero when its numerator equals zero and denominator is not zero. So,

1. **Problem Statement:** Given the curve points A(0,2), B(1,0), C(4,4), D(6,0) for $y=f(x)$, find new points after transformations and explain effect on $y$. For the second part,

1. State the problem: We want to find the product of the expressions $(-8x + 7)$ and $(6x - 5)$. 2. Use the distributive property (FOIL method) to multiply:

1. **State the problem:** Solve the equation $-8x = 12$ for $x$. 2. **Isolate $x$:** To find $x$, divide both sides of the equation by $-8$ to get rid of the coefficient multiplyin

1. Problem: Find which equation is equivalent to $y - 34 = x(x - 12)$.\nStep 1: Expand the right side: $$y - 34 = x^2 - 12x$$\nStep 2: Add 34 to both sides: $$y = x^2 - 12x + 34$$\

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

1. **Problem 38:** Find which equation is equivalent to $y - 34 = x(x - 12)$.\nExpand the right side: $$y - 34 = x^2 - 12x \Rightarrow y = x^2 - 12x + 34.$$\nNow test each option:\

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

1. The problem gives two equations: $$5y - 15 = 2x$$

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

1. **State the problem:** A person buys 5 kg of meat at a price of 500 per gram with a tax of 6% per kg. We need to find the total price for 5 kg including tax. 2. **Convert kg to

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