🧮 algebra

1. The problem is to find the value of $x$ in the equation $$5^x = 120$$. 2. To solve for $x$, we use logarithms. The key formula is:

1. **State the problem:** We need to find the value of $x$ in the equation $$5 \times 625^{3-x} = \left(\frac{1}{25}\right)^{3x}.$$\n\n2. **Rewrite the bases as powers of 5:** Note

1. **Stating the problem:** We are given that $A$ is partly constant and partly varies with $x$. We have values: when $x=16$, $A=13$; when $x=24$, $A=13$; and when $x=24$, $A=17$.

1. **State the problem:** Solve the equation $$\frac{1}{x+1} + \frac{9}{x+9} = 1$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator t

1. **State the problem:** Solve the simultaneous equations: $$y = 2 - x$$

1. The problem involves understanding how changes in the equation of a parabola $y = x^2$ affect its graph. 2. The general form of a parabola is $y = a(x-h)^2 + k$, where:

1. **State the problem:** Given $h(x) = f(x)g(x)$, with $f(x) = 2x + 5$ and $h(x) = -2x^2 - 5x$, find $g(x)$. 2. **Formula used:** Since $h(x) = f(x)g(x)$, we can find $g(x)$ by di

1. **State the problem:** Find the percent difference between 0.012 and -0.009. 2. **Formula:** Percent difference between two values $a$ and $b$ is given by:

1. **State the problem:** Joanne shears a certain number of sheep per day, and we want to find out how many sheep she can shear in 29 days if she continues at the same rate. 2. **I

1. **State the problem:** We need to find Joanne's shearing rate in sheep per day. 2. **Formula:** Rate is calculated as $$\text{Rate} = \frac{\text{Total sheep sheared}}{\text{Num

1. The problem asks us to complete the table by calculating the fuel efficiency in litres per kilometre (L/km) for each car. 2. The formula to calculate fuel efficiency is:

1. **State the problem:** We are given the first five terms of a quadratic sequence: 4, -3, -16, -35, -60. We need to find an expression for the nth term of the sequence in terms o

1. **State the problem:** We are given the first five terms of a quadratic sequence: 1, 6, 13, 22, 33. We need to find an expression for the nth term of the sequence. 2. **Recall t

1. **Problem Statement:** Find the formula for the nth term of the sequence: 3, 12, 27, 48, 75, ... 2. **Identify the pattern:** Let's denote the nth term by $a_n$. We want to find

1. **Problem statement:** Solve for $x$ in the equation $\log_x 32 = \frac{9}{7}$.

1. **State the problem:** We need to find how many whole numbers from 1 to 100 are multiples of 5 or 7. 2. **Formula and rules:** To find the count of numbers divisible by 5 or 7,

1. **State the problem:** There are 20 rows with 25 seats each, and 450 people attend a movie. We want to find the minimum number of rows that must have the same number of people s

1. **State the problem:** Alina walks to a bookstore 1200 m away at 60 m/min. Her friend cycles at 160 m/min and gives her a ride after some walking. The total time to reach the bo

1. Énoncé du problème : Résoudre dans $\mathbb{R}$ l'inéquation $$ (x^4 - 3)(x^3 + 3) \geq 0 $$. 2. Formule et règles importantes : Pour résoudre une inéquation produit $A \times B

1. **State the problem:** Simplify the expression $\frac{-x}{2x}$. 2. **Recall the rule:** When simplifying fractions, you can cancel common factors in the numerator and denominato

1. **State the problem:** Solve the equation $ (3x+7)! = 1 $ for $x$. 2. **Recall the factorial definition:** The factorial of a non-negative integer $n$, denoted $n!$, is the prod