🧮 algebra

1. The problem is to solve the ratio $3\sqrt{3}$ is to $9\sqrt{2}$ is to what number? 2. We interpret this as a proportion: $\frac{3\sqrt{3}}{9\sqrt{2}} = \frac{9\sqrt{2}}{x}$ wher

1. The problem asks us to evaluate the sum $$\sum_{k=1}^{15} \frac{1}{k}$$ which means adding the reciprocals of all integers from 1 to 15. 2. The formula for this sum is the parti

1. The problem is to simplify the expression $6a - 3b$ using identities. 2. The expression $6a - 3b$ is a linear combination of terms and does not directly match common algebraic i

1. The problem is to simplify the expression $6a - 3b$ using identities. 2. This expression is a linear combination of terms and does not directly match common algebraic identities

1. Diberikan persamaan matriks: $$\begin{bmatrix}2 & 3 \\ 5 & -1\end{bmatrix} \begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}7 \\ -8\end{bmatrix}$$

1. The problem is to graph the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. The general form of an exponential function is $y = a^x$.

1. Énoncé du problème : On considère la fonction $f : \mathbb{R} \to \mathbb{N}$ définie par $f(x) = 4E^2(x) - 4E(x) + 2$ où $E(x)$ est la partie entière de $x$. Il s'agit d'écrire

1. **Problem:** Solve for real $x$ in the quadratic equation $$x^2 - 7x + 10 = 0.$$ 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the roots are given by the quadrat

1. The problem is to understand how to write fractions in a text format. 2. Fractions represent a part of a whole and are written as $\frac{numerator}{denominator}$ where the numer

1. **State the problem:** We are given the rational function $$f(x) = \frac{2x^2 - 5x + 3}{x^2 + 5x}$$ and need to find its horizontal and vertical asymptotes, and its domain. 2. *

1. **Problem Statement:** Given the function $$f(x) = \frac{2x^2 - 5x + 3}{x^2 + 5x}$$

1. **Énoncé du problème :** Nous avons une fonction quadratique modélisant le prix de clôture EUR/USD en fonction du temps $t$ et du momentum $m$ :

1. **Problem:** Solve the system of equations: $$2x + 3y = 7$$

1. The problem is to evaluate the expression: $$150 - (3 \cdot 3.25 + \frac{3}{4} \cdot 47.80 + 2.5 \cdot 11)$$ 2. We use the order of operations (PEMDAS/BODMAS): first calculate m

1. **Stating the problem:** A man invested a certain amount at 5% per annum interest. After 1 year, the total amount in the bank is 840000 cedis. We need to find the principal (the

1. **Problem:** Determine the slope and y-intercept of the linear function $f(x) = -3x + 6$. 2. **Formula:** A linear function is generally written as $y = mx + b$, where $m$ is th

1. **State the problem:** We have two rectangles, A and B. Rectangle A has length 15 and width $w$. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. We

1. **State the problem:** We are given the equation $A + B = \frac{9}{2}$. We want to understand or solve this equation. 2. **Formula and rules:** This is a simple linear equation

1. **State the problem:** Solve the equation $$\frac{6-x}{2x} = \frac{3}{x+1}$$ and rewrite it as a quadratic equation. 2. **Use the cross-multiplication rule:** For two fractions

1. **State the problem:** We want to find the maximum value of the objective function $$z = -200x^2 + 4y^2$$ subject to the constraint $$y = 5x - 10$$. 2. **Use substitution:** Sin

1. Stating the problem: Evaluate the expression $317.200 - (4.200.000 \times 0,032) \times 1,72$. 2. Note that the commas in numbers are decimal separators, so rewrite the expressi