🧮 algebra

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 \((2x + 5)(2 - 3x)\):

1. The problem is to solve the equation $|3x-1| = -1$. 2. Recall that the absolute value of any real number is always non-negative, meaning $|a| \geq 0$ for any $a$.

1. The problem is to solve the equation $|3x-1|=0$. 2. Recall that the absolute value of a number is zero only if the number itself is zero.

1. Pomnoži: a) Izračunajmo proizvod $(2x + 5)(2 - 3x)$. \begin{align*}

1. The problem is to solve the inequality $|3X+2| < 4$. 2. Recall that $|A| < B$ means $-B < A < B$ for any real numbers $A$ and $B > 0$.

1. Stating the problem: Solve the equation $2X + X = 0$ for $X$. 2. Combine like terms on the left side: $2X + X = 3X$.

1. **State the problem:** We need to prove that if $$y = \frac{\log_a x}{\log_a b}$$ where $a$ and $b$ are constants, then $$y = \frac{\log_{10} x}{\log_{10} b}$$ can be expressed

1. **Problem a:** Solve $2 \log_9(\sqrt{x}) - \log_9(6x - 1) = 0$. Step 1: Use the property $\log_b(a^c) = c \log_b(a)$ to rewrite $2 \log_9(\sqrt{x})$ as $2 \times \frac{1}{2} \lo

1. نبدأ بتبسيط العبارة الأولى (n - 9)(n + 7). 2. نستخدم خاصية التوزيع (توزيع الحد الأول على الثاني):

1. **نبدأ بكتابة المعطى:** $$\left(\frac{24x}{6x^2} \cdot \frac{y^4}{y^2}\right)^{-3}$$