🧮 algebra

1. **Stating the problem:** A boy bought a bed on hire purchase terms. He paid a deposit of 2800 and six equally monthly instalments of 1500 each. We need to find the total hire pu

1. **Problem Statement:** A trader marks goods 80% above the cost price, gives successive discounts of 15% and 10%, and 5% of the goods are damaged and sold at a 40% loss. We need

1. **State the problem:** Yasuhiko has invested 21355 in equipment and machinery. Each hummingbird feeder costs 12.75 to make and sells for 21.75. We need to find how many feeders

1. **Problem:** Factorize the expression $$12x^4 + 72x^2y^2 + 108y^4$$. 2. **Step 1: Identify the greatest common factor (GCF).**

1. Problema: Calcolare gli asintoti delle funzioni date. 2. Formula e regole importanti:

1. **State the problem:** Solve the inequality $6 < 4x - 2 \ge 2$. 2. **Understand the compound inequality:** This means $6 < 4x - 2$ and $4x - 2 \ge 2$ must both be true.

1. **State the problem:** We need to find the value of $b$ in the equation $46 - b = 22$. 2. **Formula and rules:** To isolate $b$, we use the rule of equality which states that wh

1. Definiamo gli asintoti di una funzione razionale $y=\frac{P(x)}{Q(x)}$. 2. Gli asintoti verticali si trovano risolvendo $Q(x)=0$ dove la funzione non è definita.

1. **State the problem:** Solve the equation $$\frac{1}{3} + \frac{x + 2}{30} = \frac{x + 12}{10} - 2$$ for $x$ and express the answer as a decimal. 2. **Identify the goal:** We wa

1. The problem is to find the square root of 100. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the values of $m$ and $k$ given four pairs: $(m=1, k=-5)$, $(m=1, k=5)$, $(m=-5, k=1)$, and $(m=5, k=1)$. 2. Since the pairs are given explicitly, the val

1. **Statement of the problem:** We have two exercises involving functions and polynomials.

1. **State the problem:** We are given points $A(2,5)$, $B(-6,-3)$, and $C(a,1)$. We need to find the possible values of $a$ such that the length of $AB$ is twice the length of $AC

1. **State the problem:** We are given vectors $A = \left[\frac{3}{2}, 2\right]$, $B = \left[\frac{1}{2}, 4\right]$, and $C = \left[a, b, c\right]$ with the equation $2A - 3B = 4C$

1. Let's clarify the problem you are referring to and why the answer might be "1". 2. Often, when a teacher marks "1" as the answer, it could be related to solving an equation, sim

1. **State the problem:** Evaluate the expression $6x + 2y - 4$ when $x = 4$ and $y = -5$. 2. **Write the expression:**

1. The problem is to evaluate the expression $2x^2 + 5x - 2$ when $x = -3$. 2. The formula given is a quadratic expression: $2x^2 + 5x - 2$.

1. **Stating the problem:** We are given the system of equations: $$x + y = 25$$

1. **State the problem:** Evaluate the expression $6x + 10$ when $x = 5$. 2. **Formula and explanation:** The expression is a linear algebraic expression where $x$ is a variable. T

1. **State the problem:** We are given the equation $x + y = 24$ and need to understand its properties or solve for one variable in terms of the other. 2. **Formula and rules:** Th

1. **State the problem:** Solve the quadratic equation $x^2 + 24x - 48 = 0$. 2. **Formula used:** The quadratic formula is given by