🧮 algebra

1. The problem states that the function $f(x) = \frac{1}{6} \left(\frac{2}{5}\right)^x$ is reflected across the y-axis to create the function $g(x)$. We need to find which ordered

1. **Problem statement:** Reflect the function $f(x) = \frac{1}{10} \cdot 10^x$ across the y-axis. 2. **Reflection rule:** Reflecting a function across the y-axis means replacing $

1. The problem asks for the domain of the function $$f(x) = - \frac{5}{6} \left( \frac{3}{5} \right)^x$$. 2. The domain of an exponential function $$a^x$$, where $$a > 0$$ and $$a

1. **Énoncé du problème :** Simplifier la fraction $\frac{28}{12}$. 2. **Formule et règles importantes :** Pour simplifier une fraction, on divise le numérateur et le dénominateur

1. The problem states that the function $g(x) = 8(4^x)$ is reflected across the x-axis to create $f(x)$. We need to find the equation of $f(x)$. 2. Reflection across the x-axis mea

1. **Stating the problem:** We are asked to express the given algebraic expressions using inverse operations or to expand and simplify algebraic expressions using appropriate prope

1. The problem asks to expand and simplify the given algebraic expressions using notable identities. 2. Important identities to use:

1. The problem is to understand and compare the percentages and the number 4.4 million given: 5%, 35%, 43%, 47%, and 4.4 million. 2. Percentages represent parts per hundred, so 5%

1. **State the problem:** Solve the equation $$3 - 2x = \frac{3}{4}(x + 3)$$. 2. **Distribute the right side:** Apply the distributive property to expand $$\frac{3}{4}(x + 3)$$:

1. **State the problem:** Solve and simplify the expression $$(1-x)^2 + 2x(1-x)$$. 2. **Recall formulas and rules:**

1. **State the problem:** Solve the equation $$\frac{5(2w + 1)}{3} = 11$$ for $w$. 2. **Understand the formula and rules:** This is a linear equation with a fraction. To solve, we

1. Problem statement: We are asked to find the value of $f^{-1}(3)$, which means we want to find the input $x$ such that $f(x) = 3$. 2. Important rule: The inverse function $f^{-1}

1. **State the problem:** We know Amsterdam had 882 thousand inhabitants at the beginning of 2022, which is 5% of the total population of The Netherlands, and that Amsterdam's popu

1. **State the problem:** Simplify the expression $$\frac{(-6a^{2}b)^{2}}{(3ab)^{2}} - (2a)^{3} : (-a) + 6 \left[-(-a^{2}b)^{2}\right]^{3} : (a^{5}b^{3})^{2}$$. 2. **Recall the rul

1. **State the problem:** Find the value of $a$ in the equation $$2 = \frac{26}{2a}$$. 2. **Write down the formula and rules:** We want to solve for $a$. The equation involves a fr

1. **State the problem:** Solve the equation $$20 - \frac{t}{3} = 14$$ for $t$. 2. **Isolate the term with $t$:** Subtract 20 from both sides:

1. **State the problem:** Solve the equation $$\frac{54}{h - 1} = 3$$ for $h$. 2. **Use the formula:** To solve for $h$, multiply both sides of the equation by the denominator $(h

1. **State the problem:** Simplify the expression $$(-9x^2 + 2) \cdot 4x^2 + 2x^2 (5x^2 - 8) - (-7x^4 + 5x^2) \cdot 4$$. 2. **Apply the distributive property:** Multiply each term

1. Problem (a): Simplify the expression $2a(-4a^2 + 3a - 2) - 5(4a - a^2 - 2a^3)$. 2. Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Solve for $x$ when $f(x) = 0$ given the function $f(x) = -\frac{1}{30}(x+3)(x-27)$. 2. **Formula and rules:** To find the roots of a function, set the fun

1. **State the problem:** We are given the function $f(x) = -\frac{1}{30}(x+3)(x-27)$ and want to understand its properties. 2. **Formula and rules:** This is a quadratic function