🧮 algebra

1. **State the problem:** Solve for $x$ in the equation $$x = 200000 + 70000 + \frac{2139}{100} \times x.$$\n\n2. **Rewrite the equation:** Combine the constants on the right side:

1. **State the problem:** We need to find the values of $m$ (slope) and $c$ (y-intercept) for the line $Q$ given its equation in the form $y = mx + c$. 2. **Identify points on the

1. **State the problem:** Simplify the expression $x - (-3)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. Formally, $a - (

1. **Problem statement:** Simplify and arrange the polynomial $P(x) = 3x^3 + 5x - 12 - x^2 + x^3 - 6x^2 - 2x$ in ascending powers of $x$. 2. **Combine like terms:**

1. **Problem statement:** Given two polynomials: $$P(x) = 3x^3 + 5x - 12 - x^2 + x^3 - 6x^2 - 2x$$

1. Bài toán yêu cầu rút gọn biểu thức phân số $$\frac{2x^3 - 7x^2 - 12x + 45}{3x^3 - 19x^2 + 33x - 9}$$. 2. Công thức rút gọn phân số đại số là phân tích tử số và mẫu số thành các

1. The problem states that the function $f$ is composed of two pieces: a polynomial piece and an exponential piece. 2. The graph shows the polynomial piece on the left side for $x

1. **State the problem:** Solve the quadratic equation $$64x^2 + 5x + 25 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Solve the system of linear equations: $$5(x + 1) - 2(y - 3) = 21$$

1. **State the problem:** Simplify the expression $-5 - 5 + 6$. 2. **Apply the rules of addition and subtraction:** When adding and subtracting integers, combine the numbers step-b

1. The problem is to evaluate the expression $6 - 5 \times 3 - 2$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication must be done before addition and subtract

1. **State the problem:** Simplify the expression $$\frac{8}{9} - \frac{4}{5} + \frac{1}{6}$$. 2. **Find a common denominator:** The denominators are 9, 5, and 6. The least common

1. **State the problem:** Simplify the expression $$\frac{7}{8} - \frac{1}{4} - \frac{2}{5}$$. 2. **Find a common denominator:** The denominators are 8, 4, and 5. The least common

1. **Problema:** Resolver la expresión $$\frac{1}{2} - \left[\frac{3}{4} \times 5 + 2 \times \left(-\frac{3}{4} \times 2 + 5\right)\right] + \frac{5}{2}$$. 2. **Fórmulas y reglas:*

1. **Problema:** resolver los siguientes cálculos en $\mathbb{R}$. **a)** $$\frac{1}{2}-4+\left(\frac{3}{5}+\frac{1}{2}\right)^2$$

1. **State the problem:** Solve the quadratic equation $X \times x + 9 = 0$. 2. **Rewrite the equation:** The equation can be written as $Xx + 9 = 0$.

1. **Problem 1: Evaluate $\frac{3ac}{b}$ given $a=4$, $b=-2$, and $c=-3$.** 2. Use the formula:

1. **Problem:** Given that $a = 4$, $b = -2$, and $c = -3$, evaluate $\frac{3ac}{b}$. 2. **Formula:** The expression is $\frac{3ac}{b}$. We substitute the values of $a$, $b$, and $

1. El problema nos pide hallar dos cosas: (a) el valor de $f(-4)$ y (b) un valor de $x$ tal que $f(x) = -5$. 2. Observando el gráfico, la función $f$ es una parábola con vértice ap

1. The problem asks for the slope of a line perpendicular to the line given by the equation $$y = 4x + \frac{3}{2}$$. 2. Recall that the slope-intercept form of a line is $$y = mx

1. **State the problem:** David can plant 300 flowers in the same time Sarah plants 240 flowers. David plants 10 more flowers per hour than Sarah. We want to find Sarah's planting