🧮 algebra

1. The problem is to simplify the fraction $\frac{700}{8}$. 2. To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator.

1. **State the problem:** Solve the quadratic equation derived from the expression $(2 - y)^2 = -3y(2 - y)$. 2. **Rewrite the equation:** Expand both sides:

1. Let's start by understanding the problem: you want a detailed explanation of the steps leading up to step six in a solution process. 2. Since the original problem or context isn

1. Let's start by understanding the three topics: fractions, percentages, and standard form. 2. Fractions represent parts of a whole and are written as $\frac{a}{b}$ where $a$ is t

1. **State the problem:** Multiply the fractions $\frac{2}{7}$ and $\frac{14}{16}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators tog

1. Problema: Calculați rezultatul expresiei $$24 : (-9 + 5 \cdot 3)$$. 2. Formula și reguli: Ordinea operațiilor este importantă: mai întâi înmulțirea, apoi adunarea/scăderea, și î

1. **State the problem:** Fully factorise the expression $15p^2 + 24p$. 2. **Identify the greatest common factor (GCF):** The coefficients 15 and 24 have a GCF of 3, and both terms

1. **State the problem:** Fully factorise the expression $3k^2 + 9k$. 2. **Identify common factors:** Both terms have a common factor of 3 and $k$.

1. **Problem statement:** Show that the percentage error in approximating the sum to infinity of a geometric series by the sum of the first $n$ terms is given by

1. **State the problem:** Fully factorize the expression $x^2 + 12x$. 2. **Identify the common factor:** Both terms $x^2$ and $12x$ have a common factor of $x$.

1. **State the problem:** We are given a line passing through points approximately $(-9,5)$ and $(9,-5)$ and asked to find the slope of the line in simplest form. 2. **Formula for

1. **State the problem:** We need to find the slope of the line passing through the points $(-10,6)$ and $(0,-4)$ and express it in simplest form. 2. **Recall the slope formula:**

1. **State the problem:** Factorise the expression $8x - 6$. 2. **Identify the common factor:** Both terms $8x$ and $6$ have a common factor of $2$.

1. **State the problem:** We are given two functions:

1. **State the problem:** Factorise the expression $8x - 6$. 2. **Identify the common factor:** Both terms $8x$ and $6$ have a common factor of $2$.

1. **State the problem:** Factorise the expression $8x - 6$. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF) of all terms and fa

1. **State the problem:** We are given the profit function $$P(x) = 850x - 0.1x^2 - 4000$$ where $x$ is the number of units produced and sold.

1. **State the problem:** Solve the equation $$2000 \times (1.02)^x = 2500$$ for $x$. 2. **Isolate the exponential term:** Divide both sides by 2000 to get:

1. **State the problem:** Fully factorise the expression $8p + 12$. 2. **Identify the greatest common factor (GCF):** The coefficients are 8 and 12. The GCF of 8 and 12 is 4.

1. **Problem statement:** Given nonnegative real numbers $a,b,c$ satisfying $$(a + b)(b + c)(c + a) = 2,$$ prove that $$(a^2 + bc)(b^2 + ca)(c^2 + ab) + a^2 b^2 c^2 \leq 1.$$ 2. **

1. **State the problem:** We need to find the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ for the function $$f(x) = -x^2 + 6x + 3$$ where $$h \neq 0$$. 2. **Write the formula:**