🧮 algebra

1. The problem asks for the domain of the function $$f(x) = \sqrt{x^2 - 1}$$. 2. The expression inside the square root, called the radicand, must be non-negative for the function t

1. The problem asks to identify the false statement among the given options about absolute values and square roots. 2. Let's analyze each statement:

1. **State the problem:** Given that $a > 0$ and $b < 0$, determine which of the following expressions is always negative: (a) $|ab|$

1. **State the problem:** We need to find which value among $-1$, $0$, $3$, and $4$ does not satisfy the equation $$|x - 3| + |x + 1| = 4.$$ 2. **Analyze the absolute value express

1. The problem is to solve a system of linear equations. 2. A linear system typically looks like:

1. The problem involves matching algebraic expressions and logarithmic equations to their corresponding graphs and solving exponential and logarithmic equations. 2. For the algebra

1. **State the problem:** Solve the equation $4x = 5y - 140$ for $x$ in terms of $y$. 2. **Isolate $x$:** To express $x$ in terms of $y$, add $140$ to both sides and then divide bo

1. The problem involves adding and subtracting fractions with different denominators. 2. First, convert all fractions to have a common denominator where necessary.

1. **State the problem:** We need to write an inequality involving pixels per inch (ppi) that relates the lab's average finger width in pixels to the manufacturers' widths. 2. **Gi

1. **State the problem:** We need to order the following values from least to greatest: $$\sum_{i=5}^7 i, \sqrt{15}, \log_4(9), 7!, \infty, \frac{13}{17}, e^3, \int_2^9 x \, dx, \f

1. The problem involves analyzing the points and piecewise function shown on the graphs. 2. From the left graph, the points are (-2, 1), (0, 0), and (2, -2).

1. **Problem:** Find the approximate average annual growth rate of Calgary's population from 1971 to 2016. Step 1: Identify variables.

1. The problem is to analyze the function $x(t) = (t - 6)^2 - 9$ which represents profit over time. 2. This is a quadratic function in vertex form, where the vertex is at $(6, -9)$

1. **State the problem:** We need to find the equation of the parabola representing Jillian's first bounce, which starts at (0,0), reaches a vertex at (2,6), and ends at (6,0). 2.

1. **State the problem:** Sort the following values from least to greatest: Top-left: $\log_4(26)$

1. **State the problem:** Simplify the expression $$-\sqrt[4]{36x^4b^4} + \frac{1}{2}\sqrt{32x^6b} - \frac{4}{5xb}\sqrt{18x^8b^3} + \frac{2}{3}\sqrt{486x^2b^2}$$

1. The problem asks to compare the graph of the second function $$y=\frac{1}{7}4^{-2x-10}-3$$ to the graph of the first function $$y=4^x$$. 2. Start with the first function $$y=4^x

1. **Problem Statement:** Prove that the right-hand side equals the left-hand side.

1. **Énoncé du problème** : Étudier la parallélisme des expressions suivantes en fonction de $n$ : $$a = 4n + 6$$

1. Pomnoži (Multiply): a) Izračunaj proizvod \((2x + 5)(2 - 3x)\):

1. Zadatak 12: Pomnoži a) Pomnožimo izraze \((2x + 5)(2 - 3x)\):