🧮 algebra

1. **Problem statement:** We are asked to determine the truth value of several statements about a function $f$ given only its variation table: $$\begin{array}{c|ccccc}

1. **State the problem:** Find the coefficient of $x$ in the expansion of $\left(5x - 3\right)\left(2x^2 - 3x + 1\right)$.\n\n2. **Write the expression to expand:** \n$$\left(5x -

1. **State the problem:** Evaluate the expression $$-5^2 - \left[1 - \frac{12}{(-2)^2}\right] + (-1)^3$$. 2. **Recall order of operations:** Exponents first, then multiplication/di

1. **State the problem:** Solve the inequality $\frac{2}{3x+6} < 0$. 2. **Rewrite the inequality:** The denominator is $3x+6$. The fraction is negative when numerator and denominat

1. **Problem statement:** Given the functions $f(x) = 5x + 1$ and $g(x) = \frac{x - 4}{2}$, find the value of $x$ if $fg(x) = 11$. 2. **Recall the composition of functions:**

1. Problem: Calculate $\frac{4}{5} + \frac{5}{6}$ and write the answer as a mixed number if appropriate. 2. Formula: To add fractions, find a common denominator, then add the numer

1. **Stating the problem:** We are given the quadratic equation $$16x^2 - 8x - 47 = 0$$ and told its roots are $$\frac{1}{4} + \sqrt{5}$$ and $$\frac{1}{4} - \sqrt{5}$$. We need to

1. **Илэрхийллийн утгыг олоорой:** $$9105 - 7865 + (2456 + 4895 - 3067) - 398$$ 2. **Тоо бодох үйлдлийг дараалалтай гүйцэтгэнэ:**

1. **Stating the problem:** Evaluate the summation $$\sum_{k=1}^5 (1 + k^3)$$. 2. **Recall the summation properties:** The sum of a sum is the sum of the sums, so

1. **State the problem:** Solve the equation $x + 2xy - y^2 = 2$ for $x$ in terms of $y$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $x + 2xy - y^2 = 2$ for $x$ in terms of $y$. 2. **Rewrite the equation:** The equation is $x + 2xy - y^2 = 2$.

1. **State the problem:** Simplify the function $f(x) = \frac{x^5 - 2x^3 - 8x^2}{x}$. 2. **Recall the rule:** When dividing a polynomial by $x$, divide each term in the numerator b

1. **State the problem:** Given the arithmetic sequence terms $a_2, a_6, a_{10}, a_{14}$ and the equation $$3(a_2 + a_6) + 2(a_6 + a_{10} + a_{14}) = 24,$$ find the sum of the firs

1. **Stating the problem:** We have a sequence $\{a_n\}$ with the first term $a_1 = 2$ and the recurrence relation $$a_{n+1} = \frac{a_n}{2} + \frac{1}{2n - 1}.$$ We need to find $

1. **State the problem:** Simplify the expression $$2\sqrt{3} - 5 - \frac{11}{\sqrt{12} - 1}$$. 2. **Recall the formula and rule:** To simplify expressions with radicals in the den

1. Let's start by stating the problem: Understanding every type of algebraic fraction. 2. An algebraic fraction is a fraction where the numerator and/or denominator are algebraic e

1. **State the problem:** We are given the system of equations: $$5x + 14y = 45$$

1. **State the problem:** We need to find which system of linear equations corresponds to the two lines shown on the graph. 2. **Analyze the graph:**

1. **State the problem:** Expand and simplify the expression $t(7t - 2) + 3t(4t - 5)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor

1. **State the problem:** Expand and simplify the expression $x(4x - 2) + x(5x + 6)$. 2. **Use the distributive property:** Multiply $x$ by each term inside the parentheses.

1. **State the problem:** Match each function description to the correct graph type. 2. **Analyze each function:**