🧮 algebra

1. The problem is to verify the factorization of the quadratic expression $$2x^2 - 13x + 20$$ given as $$(2x - 5)(x - 4)$$. 2. The formula for expanding two binomials is:

1. The problem is to simplify the expression where the first \(a\) is on the 2 and the second \(a\) is on the top with 3, which suggests the expression is \(a^{2a^3}\). 2. The expr

1. **State the problem:** Simplify the expression $$-\frac{1}{2}a + \frac{3}{2}a - 4$$. 2. **Identify like terms:** The terms $$-\frac{1}{2}a$$ and $$\frac{3}{2}a$$ are like terms

1. **State the problem:** Simplify the expression $\frac{5x}{5+x} + 17.5$. 2. **Understand the expression:** The expression consists of a rational term $\frac{5x}{5+x}$ and a const

1. The problem is to simplify the expression $\frac{5x}{5} + x + 17.5$. 2. Use the rule that $\frac{a \cdot b}{a} = b$ when $a \neq 0$.

1. **State the problem:** Find the value of $-32 \equiv ? \pmod{12}$. 2. **Recall the definition:** For integers $a$ and $m > 0$, $a \equiv r \pmod{m}$ means $r$ is the remainder w

1. **State the problem:** Find the equation of the line passing through points $(-8,7)$ and $(0,-1)$ in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ of a line throu

1. **Stating the problem:** Calculate the value of the expression $$\sqrt{16} \times 3 \times \sqrt{7} \times 1 \times \sqrt{25} \times 12 \times 7 \times \sqrt{36} \times 2 \times

1. Problema a resoldre: Calcula i simplifica l'expressió $$3 - 5 \times \frac{1}{4} - 2 \div 8$$. 2. Fórmules i regles importants:

1. The problem is to simplify the expression $+17 + (+1,7)$. 2. First, note that the expression contains a comma in $(+1,7)$ which is not standard notation for a number. Assuming i

1. The problem is to find the sum of $-8$ and $-27$. 2. We use the rule for adding integers with the same sign: add their absolute values and keep the common sign.

1. The problem is to find the sum of $-7$ and $-24$. 2. When adding two negative numbers, you add their absolute values and keep the negative sign.

1. The problem is to find the sum of $-5$ and $-61$. 2. We use the rule for adding integers: when adding two negative numbers, add their absolute values and keep the negative sign.

1. The problem is to find the sum of $-3$ and $-9$. 2. The formula for adding two numbers is simply $a + b$.

1. Diberikan pertidaksamaan: $$-3x - 5 \leq 7 + x$$ 2. Tujuan kita adalah mencari nilai $x$ yang memenuhi pertidaksamaan tersebut.

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **Problem statement:** Majed has two magic stones. When rubbed once, each stone produces one new stone, effectively doubling the number of stones. We need to find how many times

1. **State the problem:** We have a radioactive element with an initial amount of 800 grams. The amount remaining after $t$ years is given by the formula: $$A = 800 \left(\frac{1}{

1. **Stating the problem:** Majed starts with 2 magic stones. Each time the stones are rubbed once, each stone produces one new stone, effectively doubling the total number of ston

1. **State the problem:** We have a bacteria colony starting with 1,000 bacteria. The number of bacteria after $t$ hours is given by the formula: $$A = 1000 \times 35.6^{\frac{t}{1

1. **State the problem:** Find the intercepts, asymptotes, turning points, and intervals of increase/decrease for the rational function $$f(x) = \frac{5x+3}{2x-1}$$. 2. **Find the