🧮 algebra

1. **Nêu bài toán:** Tìm và biểu diễn hình học tất cả các nghiệm của phương trình $$5(x+y)=2x+4y-1$$. 2. **Viết lại phương trình:**

1. **Stel het probleem vast:** We willen het snijpunt van de grafiek van de functie $$g(x) = 4 - 8 \cdot \left(\frac{1}{2}\right)^x$$ met de x-as bepalen. 2. **Formule voor snijpun

1. **State the problem:** Find all complex solutions of the quadratic equation $$3x^2 - x + 4 = 0.$$\n\n2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0,$$

1. **State the problem:** Simplify the expressions $$\frac{\sqrt{-48}}{\sqrt{-16}}$$ and $$\sqrt{-6} \cdot \sqrt{-10}$$ with no negative numbers under radicals and no radicals in d

1. **State the problem:** Find the equation of line D in the form $y = mx + c$ given it crosses the y-axis at 2 and passes through points approximately $(1, 3.5)$ and $(4, 8)$. 2.

1. The problem asks to identify where Emilio made a mistake while factoring the trinomial $x^2 - x - 12$. 2. In Part A, Emilio rewrites the expression as $x^2 - 4x + 3x - 12$ to re

1. **State the problem:** Factor the quadratic expression $s^2 + 6s + 5$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, th

1. The problem is to solve the formula for the area of a trapezoid, given by $$A = \frac{1}{2} h (x + y)$$, for the height $h$. 2. The formula relates the area $A$, the height $h$,

1. **State the problem:** Solve the equation $$2x - y = 18$$ first for $$x$$, then for $$y$$. 2. **Solve for $$x$$:**

1. We are asked to find the equation of the tangent line $t$ to the graph of the function $f(x) = x^2$ at the point $P(-3, 9)$. 2. The formula for the tangent line to a function $f

1. **Stel het probleem vast:** We hebben twee getallen die zich verhouden als 5 : 4. Dit betekent dat de verhouding van het eerste getal tot het tweede getal 5 tot 4 is. 2. **Formu

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the denominato

1. **Problem:** Identify if the given statements about the rational number system are True or False, and correct the false ones. 2. **Formula/Rules:**

1. **Planteamiento del problema:** Encontrar la ecuación de la recta que pasa por el punto $(1,7)$ y tiene pendiente $\frac{2}{3}$. 2. **Fórmula a usar:** La ecuación punto-pendien

1. **State the problem:** Divide and reduce to lowest terms the mixed numbers: $$1 \frac{1}{3} \div 2 \frac{5}{6}$$ 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Multiply $1000000000000000000000$ by $10000000000000000$. 2. **Use the multiplication rule for powers of 10:** Each number is a power of 10. We can write

1. **State the problem:** Solve the equation $$\frac{2x - 3}{x^2 - 4} + \frac{x + 1}{x^2 - x - 2} = \frac{4}{x - 2}$$ for $x$. 2. **Factor denominators:**

1. **State the problem:** Simplify the expression $$\frac{3x}{5} + \frac{4x+7}{5}$$. 2. **Formula and rules:** When adding fractions with the same denominator, add the numerators a

1. **State the problem:** We are given the equation of a circle: $$x^2 + y^2 - 14x + 10y + 49 = 0$$

1. **State the problem:** We need to find Karen's mother's present age given the equation formed by the problem statement. 2. **Translate the problem into an equation:** Let $x$ be

1. **State the problem:** Add the fractions $\frac{1}{2}$, $\frac{2}{5}$, and $\frac{9}{10}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find