🧮 algebra

1. The problem is to decrease 180 by 30 percent. 2. To decrease a number by a percentage, use the formula: $$\text{New value} = \text{Original value} - \left(\frac{\text{Percentage

1. **State the problem:** We are given a function $f(x) = 10x + 13$ and need to find the value of $x$ such that $f(x) = 40$. 2. **Write the equation:** Set the function equal to 40

1. The problem asks for the 4th and 5th terms of a sequence, but the sequence or formula is not provided. 2. To find specific terms in a sequence, we need the general term formula

1. Zadání: Potřebujete vzorec pro poměr, který lze použít v Desmosu. 2. Vzorec pro poměr dvou hodnot $a$ a $b$ je definován jako $$\text{poměr} = \frac{a}{b}$$ kde $b \neq 0$.

1. **State the problem:** Solve the equation $$ (\sqrt{2})^{4+x} + (\sqrt{2})^{2 - x} = 3\sqrt{2} $$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the quadratic equation $x^2 + 5x + 3 = 0$ and find solutions correct to 2 decimal places. 2. **Formula used:** The quadratic formula for solving $ax

1. **State the problem:** Solve the equation $$ (\sqrt{2})^{4+x} + (\sqrt{2})^{2-x} = 3\sqrt{2} $$ for $x$. 2. **Recall the properties of exponents:**

1. The problem asks to write each fraction in lowest terms. 2. To reduce a fraction to its lowest terms, divide the numerator and denominator by their greatest common divisor (GCD)

1. Stating the problem: Solve the quadratic equation $$3x^2 - 4x - 4 = 0$$. 2. Formula used: For a quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by the quadrati

1. **Problem Statement:** Rod is thinking of a polynomial in one variable with these characteristics: - Degree 4

1. The problem is to identify a polynomial that satisfies the following conditions: a. The polynomial has a degree of 4.

1. **State the problem:** We need to find the missing numbers in the equations: $$4 + \_ = 3 + 3$$

1. **Problem Statement:** Rod is thinking of a polynomial in one variable with these characteristics: - Degree 4

1. সমস্যাটি হলো: ৪, ৮ ১/২ , ২ এর চতুর্থ সমাপত্তি কোনটি? অর্থাৎ $4^{\frac{1}{4}}$, $8^{\frac{1}{2}}$, এবং $2^{\text{চতুর্থ সমাপত্তি}}$ এর মান নির্ণয় করতে হবে। 2. সূত্র ও নিয়ম:

1. The problem is to solve the equation $y = 2x + 3$ for $y$ given $x$. 2. The formula used here is the equation of a straight line in slope-intercept form: $$y = mx + b$$ where $m

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:** Solve the quadratic equation $x^2 - 5x + 6 = 0$ using the quadratic formula. 2. **Formula Used:** The quadratic formula to solve $ax^2 + bx + c = 0$ is:

1. **State the problem:** We are given the simultaneous equations:

1. The problem is to break an expression or equation into 3 pieces and then solve it. Since the exact expression is not provided, let's consider a general approach. 2. Suppose we h

1. The problem involves solving an equation or inequality by breaking it into cases based on the value of $x$ being greater than 0 or less than 0. 2. When dealing with piecewise co

1. **Problem Statement:** We have a piecewise function: