🧮 algebra

1. **State the problem:** We are given two functions $f(x) = 4x$ and $g(x) = 8x^2 + 5$. We need to evaluate the compositions: (a) $(f \circ g)(4)$ means $f(g(4))$

1. **State the problem:** We need to evaluate the composite functions $(g \circ f)(x)$ and $(f \circ g)(x)$ at given values of $x$. This means: - $(g \circ f)(x) = g(f(x))$

1. **State the problem:** We need to evaluate composite functions such as $(f \circ g)(1)$, $(f \circ g)(-1)$, $(g \circ f)(-1)$, $(g \circ f)(0)$, $(g \circ g)(-2)$, and $(f \circ

1. **State the problem:** We need to find the domain of the function $$f(x) = \frac{x^2 - 25}{x^2 - 16}$$. 2. **Recall the domain rule for rational functions:** The domain includes

1. **State the problem:** We are given a table of temperatures in Fahrenheit ($F$) and Celsius ($C$) below freezing and asked to complete the equation in standard form relating $F$

1. **State the problem:** We are given the line equation $$y - 11 = -\frac{4}{3} (x + 7)$$ and need to find which of the given equations represent the same line. 2. **Start by dist

1. **Problem 46:** Evaluate $0.64^{\frac{7}{2}}$ and $0.64^5$. 2. **Step 1:** Express $0.64$ as a fraction: $0.64 = \frac{64}{100} = \frac{16}{25}$.

1. **State the problem:** Solve the inequality $$3^{1 - x^2} - \frac{1}{9} < 0$$. 2. **Rewrite the inequality:** Move $$\frac{1}{9}$$ to the other side:

1. **State the problem:** Solve the inequality $$5^{x+2} + 5^{x+1} < 5^{2x} + 125$$. 2. **Rewrite the terms using properties of exponents:**

1. **State the problem:** Solve the equation $b = 12b + 1$ for $b$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $b = \frac{12}{b} + 1$ for $b$. 2. **Rewrite the equation:**

1. **State the problem:** Calculate the value of $99999999\sqrt{9292929922929}$.\n\n2. **Recall the formula:** The expression involves a multiplication of a number and the square r

1. **State the problem:** Find the square root of 1919282872737. 2. **Recall the formula:** The square root of a number $x$ is a value $y$ such that $$y^2 = x.$$

1. **State the problem:** We have a train with adults and children at Station X, Y, and Z with given ratios and changes. We want to find:

1. The problem is to evaluate the expression $$2^^5$$, which represents tetration, a power tower of 2's of height 5. 2. Tetration is defined as repeated exponentiation. For example

1. The problem is to evaluate the expression $$2^^2$$, which represents tetration, a power tower of 2s of height 2. 2. Tetration $$a^^n$$ means $$a$$ raised to the power of $$a$$ r

1. **State the problem:** Simplify the ratio $9 : 81$. 2. **Formula and rules:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).

1. **Problem 11:** Find the missing number in the proportion $$6/\boxed{x} = 12/32$$ given $$96 = 12/32$$. Since $$12/32$$ is a fraction, the equality $$96 = 12/32$$ is likely a ty

1. **Problem statement:** Fill in the missing numbers (boxes) in the equivalent fractions for problems 12, 13, and 14. 2. **Recall the rule for equivalent fractions:** Two fraction

1. **State the problem:** We have five symbols representing numbers: ❄️, 🌎, ⚡, 🔥, 🌱, ☀️, and 🌀. We are given five equations involving these symbols and need to find the values of e

1. (a) (i) Calculate the exact value of $$(5.8^2 + 1.02) \times 2.5$$. Step 1: Calculate $5.8^2$.