🧮 algebra

1. **State the problem:** Given $x=2$, $y=3$, and $z=-4$, find the value of the expression $2xy + yz + 3x$. 2. **Write the expression:**

1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 13x + 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. **State the problem:** Given $x=2$, $y=3$, and $z=-4$, find the value of the expression $$2xy + y^2 + 3x$$. 2. **Write the formula:** The expression is $$2xy + y^2 + 3x$$.

1. **State the problem:** Simplify the expression $2x - 3(x+1)$. 2. **Use the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $6 - 6 \times \frac{1}{3}$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and s

1. **State the problem:** Solve for $x$ in the equation $12^{4} \times 4^{2} = 16^{x}$. 2. **Rewrite the bases in terms of prime factors:**

1. **State the problem:** Simplify the expression $\left(x - \frac{2}{3}\right) \ln x \ln x$. 2. **Rewrite the expression:** Notice that $\ln x \ln x = (\ln x)^2$. So the expressio

1. **State the problem:** We want to find the cost in cents of $p$ pencils if $k$ pencils cost $c$ cents. 2. **Formula and explanation:** The cost per pencil is the total cost divi

1. Planteamos el problema: calcular el resultado de la operación $$\frac{2a^3b^5}{3} \cdot \frac{-9a^6b}{4}$$. 2. Recordemos que para multiplicar fracciones se multiplican numerado

1. **Problem statement:** Ba số tự nhiên có một chữ số khác nhau được điền vào ba ô vuông dưới cùng: gọi lần lượt là $a$, $b$, $c$ với $a,b,c \in \{0,1,2,...,9\}$ và $a,b,c$ khác n

1. **Problem statement:** Determine the type of decimal representation of the fraction $$\frac{7}{3^{2023} \cdot 2^{2021}}$$. 2. **Recall the rule for decimal representations of fr

1. **Problem statement:** We have a square floor tiled exactly by smaller square tiles of the same size. The total number of tiles on the two diagonals is 45. We need to find the t

1. **Problem:** Test whether $(x - 2)$ is a factor of $f(x) = 2x^3 + 2x^2 - 17x + 10$ and factorize $f(x)$ if it is. 2. **Step 1: Use the Factor Theorem.**

1. **Problem statement:** We need to find the digit $P$ in a five-digit number $PQRST$ where each digit is from 1 to 5, used exactly once, and $P < Q$. 2. **Given conditions:**

1. **Stating the problem:** Given functions $f(x) = x + 3$ and $g(f(x)) = 2x + 5$, find the expressions for $f^{-1}(x)$, $g(x)$, $g(f^{-1}(x))$, and the value of $k$ such that $f(g

1. **Problem statement:** We need to find two consecutive natural numbers $n$ and $n+1$ such that the fractions $\frac{n}{7}$ and $\frac{n+1}{7}$ have the fraction $\frac{9}{11}$ l

1. **Problem statement:** We need to find the sum of three natural numbers given that the sum of their squares is 6525. The second number is \(\frac{2}{3}\) of the first and also \

1. المشكلة: حل معادلة باستخدام التعويضات المثلثية. 2. القاعدة الأساسية: التعويضات المثلثية تستخدم لتحويل تعبيرات تحتوي على جذور أو تعبيرات معقدة إلى تعبيرات مثلثية أبسط.

1. You asked for more questions to prepare for the TOLC test. 2. Since you did not specify a particular topic, here is a sample algebra question to practice:

1. Let's start by understanding the problem: we want to practice elementary operations (addition, subtraction, multiplication, division) and ordering (comparing sizes) between inte

1. **Stating the problem:** Solve the equation $$x^5 - x^4 - x^3 - x + 1 = 0$$ for $x$. 2. **Formula and approach:** This is a polynomial equation of degree 5. There is no general