🧮 algebra

1. Problema: Rasti funkcijos $f(x) = e^{4x+7}$ pirmykštę. 2. Naudojama formulė: Jei $f(x) = e^{g(x)}$, tai pirmykštė yra $$F(x) = \frac{1}{g'(x)} e^{g(x)} + C,$$ kur $g'(x)$ yra $g

1. **State the problem:** Evaluate the sum $$\frac{3}{4} + \frac{5}{6}$$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least common den

1. **Stating the problem:** Raheem takes $\frac{21}{4}$ hours to make a basket and $\frac{11}{2}$ hours to make a mat. He works a maximum of 22.5 hours per week. We need to show th

1. Let's state the problem: Determine when a system of linear equations has one solution, no solution, or infinitely many solutions. 2. Consider a system of two linear equations in

1. **State the problem:** Solve the system of linear equations: $$x+(b-1)y-z=4$$

1. **State the problem:** Prove the identity $$2\cosh(3x)\cosh(x) = \cosh(4x) + \cosh(2x)$$. 2. **Recall the formula for hyperbolic cosine product:**

1. **State the problem:** Solve the inequality $3x + 4 < 7x + 24$. 2. **Write down the inequality:**

1. **State the problem:** Solve the inequality $|2b - 1| \leq 3$. 2. **Recall the definition of absolute value inequality:** For any expression $x$, $|x| \leq a$ means $-a \leq x \

1. **State the problem:** We need to find a possible value of $x$ such that the point $(x, 53)$ satisfies the system of inequalities: $$y > 14$$

1. **State the problem:** Solve the quadratic equation $2x^2 + 3x - 2 = 0$ for $x$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Solve the system of equations using diagonal methods (Cramer's Rule): $$\begin{cases} x + y + z = 0 \\ x - 2y + 2z = 4 \\ x + 2y - z = 2 \end{cases}$$

1. **State the problem:** Find the equation of the line passing through the points $(-1, -3)$ and $(1, 11)$. 2. **Formula used:** The slope $m$ of a line through two points $(x_1,

1. **State the problem:** Find the equation of a line with slope $m=\frac{5}{4}$ that passes through the point $(-8,3)$.\n\n2. **Formula used:** The point-slope form of a line is g

1. **State the problem:** Simplify the expression $$\frac{a^{-1} b^{-2} c^{-6}}{4}$$ and express it as a single fraction with positive exponents. 2. **Recall the rule for negative

1. The problem asks whether the decimal representations of the fractions $\frac{2}{5}$, $\frac{15}{20}$, and $\frac{6}{16}$ will repeat or terminate. 2. A fraction in simplest form

1. **State the problem:** Solve the system of equations using diagonal methods (diagonalization or matrix methods): $$\begin{cases} x + y + z = 0 \\ x - 2y + 2z = 4 \\ x + 2y - z =

1. **State the problem:** We want to verify or solve the equation:

1. **State the problem:** We know that three-fifths of the Grade 8 class are in the band.

1. **State the problem:** We know that three-fifths of the Grade 8 class are in the band.

1. **Problem:** Determine if the function $f(x) = 3$ is even, odd, or neither. 2. **Recall definitions:**

1. **State the problem:** We need to solve the simultaneous equations: $$y = -2x + 11$$