🧮 algebra

1. **Problem 2:** Solve for $x$ in the equation $$\ln(x - 2) + \ln(2x - 3) = 2 \ln x.$$ 2. **Formula and rules:** Use the logarithm property $$\ln a + \ln b = \ln(ab)$$ and the pow

1. **State the problem:** Solve for $x$ in the equation $\log_3(2x-5) = 2$. 2. **Recall the logarithm definition:** $\log_b(a) = c$ means $b^c = a$.

1. **State the problem:** Simplify the expression $$\frac{20x^{-3}c}{4x^{4}-5}$$. 2. **Recall the rules:** When simplifying expressions with exponents, remember that $x^{-n} = \fra

1. **State the problem:** Simplify the expression $$\frac{(-3b^4)^3}{3b^8h^{-9}}$$. 2. **Apply the power to the numerator:** Use the rule $$(ab)^n = a^n b^n$$ to expand the numerat

1. **Problem:** Solve the equation $10 - 6v = -104$ for $v$. 2. **Formula and rules:** To solve for $v$, isolate $v$ by moving constants to the other side and dividing by the coeff

1. **State the problem:** Solve the equation $$6^{x-1} = 2^{3x+1}$$ and express the solution in the form $$\frac{\ln a}{\ln b}$$. 2. **Recall the formula and rules:** To solve equa

1. **Stel het probleem vast:** We moeten de totale kosten berekenen voor 6 grondzeilen, elk met een afmeting van 3,5 m bij 4 m, waarbij de prijs € 10 per m² is. 2. **Formule voor o

1. **State the problem:** We need to find the equation of the trend line (line of best fit) passing through the two given points (4, 7) and (6, 0). 2. **Formula used:** The slope-i

1. **State the problem:** We need to find the equation of the trend line (line of best fit) passing through the two yellow points on the scatter plot. 2. **Identify the points:** T

1. **State the problem:** Simplify the radical expression $\sqrt{486a^4b}$.\n\n2. **Recall the formula and rules:** The square root of a product is the product of the square roots:

1. Énonçons le problème : On a une suite $U_n$ définie par $U_0=2$ et la relation de récurrence $$U_{n+1} = \frac{1}{4} - U_n - 3.$$ 2. On définit une nouvelle suite $V_n$ telle qu

1. Énonçons le problème : On a une suite $U_n$ définie par $U_0=2$ et la relation de récurrence $$U_{n+1} = \frac{1}{4} - U_n - 3.$$ 2. Simplifions la relation de récurrence :

1. **Problem:** Determine which store charges a higher cost per pair of jeans by finding the unit rate (constant of proportionality) for Jenny's Jean Store and Jean Warehouse. 2. *

1. **State the problem:** Find the product of the binomials $$(4x + 3)(4x - 3)$$. 2. **Formula used:** This is a difference of squares pattern, which states:

1. **State the problem:** We need to square the binomial $\left(8y - 5\right)^2$. 2. **Formula used:** The square of a binomial $\left(a - b\right)^2$ is given by:

1. مسئله: شکل داده شده دو مستطیل است که هر کدام به ۵ قسمت عمودی تقسیم شده‌اند و یک خط افقی در وسط دارد. مستطیل سمت چپ ۳ قسمت از ۵ قسمت به رنگ صورتی سایه‌دار شده و مستطیل سمت راست ۲

1. **State the problem:** We are given that the speed $v$ of a tsunami in metres per second is equal to the square root of ten times the depth $d$ of the water in metres.

1. The problem asks to draw lines representing the "rise" and "run" of a line and to state the slope in simplest form. 2. The slope $m$ of a line is defined as the ratio of the ris

1. **Problem statement:** We will solve the first subproblems of 2.224 and 2.225 by adding or subtracting the given rational expressions using the main denominator and simplifying

1. **Problem 2.224 a)** Simplify \( \frac{3a^2 + 2}{5a + 5} + \frac{1 - a}{10} \). 2. Factor the denominator in the first fraction: \(5a + 5 = 5(a + 1)\).

1. **Problem 2.224 a)**: Add \( \frac{3a^2 + 2}{5a + 5} + \frac{1 - a}{10} \) 2. **Rewrite denominators:**