🧮 algebra

1. **Problem:** Expand each logarithm using logarithm properties. 2. **Step 1:** $\log_6 \left(\frac{u}{v}\right)$

1. The problem asks for the average rate of change of the function $f(x)$ on the interval $3 \leq x \leq 4$. 2. The average rate of change of a function on an interval $[a,b]$ is g

1. The problem asks to sketch the graph of the transformed function $$-f(x)-1$$ given the original graph of $$f(x)$$. 2. The original graph is a V-shaped graph centered at the orig

1. Stating the problem: Simplify the polynomial expression $$5x^4 + 6y^4 - 12xy + 2x^3 - 4y^4 + 20xy$$. 2. Group like terms:

1. The problem states that the carpet costs 20 per square metre. 2. To find the total cost of carpeting a room, you need to know the area of the room in square metres.

1. The problem is to calculate the cost of carpet needed to cover the floor of a square room with side length 5 metres. 2. First, calculate the area of the square floor using the f

1. Problem 8: Given $f(x) = |x|$ and $g(x) = x^3 - 7$, find the composite function $f \circ g$ and its domain. 2. To find $f \circ g$, we substitute $g(x)$ into $f$:

1. The problem is to determine if the fractions $\frac{21}{14}$ and $\frac{12}{8}$ are equal. 2. Simplify each fraction by dividing numerator and denominator by their greatest comm

1. **State the problem:** We need to find the cost of the plastic sheet that will cover the bottom of a rectangular swimming pool. 2. **Identify the dimensions:** The pool is 4 met

1. **State the problem:** A cyclist rode 154.8 kilometers in 4 hours at a steady speed. We need to find the speed in kilometers per hour. 2. **Recall the formula for speed:** Speed

1. The problem states: A cyclist rode 15 kilometers. We need more information to solve a specific question related to this distance. Since the problem is incomplete, please provide

1. **State the problem:** Simplify and solve the expression $$-4\left(\frac{1}{4}x - \frac{1}{2}\right) - 10(-x - 10)$$. 2. **Distribute the constants inside the parentheses:**

1. **Énoncé du problème :** Soit $k(x) = 2x + \sqrt{x} + 3$. Montrer que l'équation $k(x) = 17$ admet une unique solution $\alpha \in [6;7]$.

1. **Problem statement:** Evaluate the following without a calculator: a) $1 \frac{3}{4} + 2 \frac{11}{12}$

1. **State the problem:** Find the slope and y-intercept of the line given by the equation $$y = \frac{3}{2}x - \frac{4}{3}$$. 2. **Identify the slope:** The equation is in slope-i

1. The problem asks us to graph the line with slope $-\frac{1}{2}$ and y-intercept $-3$ on a Cartesian coordinate plane. 2. Recall the slope-intercept form of a line is given by:

1. The problem is to analyze the linear equation $-3x + y = -6$ and express it in slope-intercept form. 2. Start by isolating $y$ on one side:

1. The problem is to graph the line with slope $-\frac{2}{3}$ passing through the point $(3, -1)$. 2. Recall the point-slope form of a line: $$y - y_1 = m(x - x_1)$$ where $m$ is t

1. **Problem (a):** Find the slope of the line passing through the points $(-5, -8)$ and $(6, -8)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)

1. The problem asks to factor the polynomial $1 - 8c^3$. 2. Recognize this as a difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

1. **State the problem:** Simplify the expression $$\log_7(98) - \log_9(30) + \log_7(15)$$. 2. **Rewrite the logarithms with the same base where possible:** Notice that $$\log_7(98