🧮 algebra

1. **State the problem:** A human and a turtle compete in a 1 km race. The turtle moves at a constant speed of 0.2 km/h and receives a 980 m head start. The human runs at a speed 1

1. **State the problem:** Solve the equation $$2(x+3) = 5 - (1 - x)$$ for $x$. 2. **Apply the distributive property:** Multiply 2 by each term inside the parentheses on the left si

1. The problem is to solve the equation given by the user. Since the user did not specify the equation, I will explain the general approach to solving algebraic equations step by s

1. المشكلة: حل المعادلة لإيجاد مجموعة الحل. 2. القاعدة العامة: لحل المعادلة، نحتاج إلى عزل المتغير (عادة x) على أحد جانبي المعادلة.

1. نبدأ بكتابة المعادلة المعطاة: $\log_5 x + 6 \log_5 5 = 5$ 2. نعلم أن $\log_5 5 = 1$ لأن الأساس والعدد متساويان.

1. Énoncé du problème : Calculer les expressions données dans la première question. 2. Formules et règles importantes :

1. **Problem (a):** Saima buys a fridge and a freezer during a 15% off sale. The total amount paid is 57120. The freezer's original price is 40000. Find the fridge's original price

1. **Énoncé du problème :** On considère la suite numérique $(U_n)$ définie par $U_n = (n+2)(n-1)$ pour tout $n \in \mathbb{N}$.

1. **State the problem:** We need to find and simplify the expression $$\frac{f(a+h)-f(a)}{h}$$ where $$f(x) = 4x + 7$$. 2. **Recall the formula:** This expression represents the d

1. Let's start by understanding the problem: You want to know the vertex form, standard form, and factored form of a quadratic equation, which is a key topic in Grade 10 algebra. 2

1. **State the problem:** Given the quadratic equation $x^2 - 2x - 1 = 0$ with roots $\alpha$ and $\beta$, find the equation whose roots are $2\alpha + \frac{1}{\beta}$ and $-2\alp

1. The problem is to evaluate the expression $\frac{3}{8} + \frac{1}{8} - \frac{1}{6} + \frac{1}{4}$.\n\n2. To add and subtract fractions, we need a common denominator. The denomin

1. **State the problem:** Solve the system of equations using matrices: $$\begin{cases} x + 3y + z = 3 \\ x + 5y + 5z = 1 \\ 2x + 6y + 3z = 8 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$5x + 6y = 70$$

1. **State the problem:** We have two lines, L and M. Line L passes through points $(4, -1)$ and $(6, 4)$. Line M is perpendicular to L and crosses the y-axis at $(0, 8)$. We need

1. The problem asks to find the number of x-intercepts of the graph of the function $y = x^2 + 5x - 1$. 2. To find x-intercepts, we set $y=0$ and solve the quadratic equation:

1. **State the problem:** We have two equations: $x = a + b$ and $y = a - b$, with $a = 3$. We want to understand the relationship between $x$ and $y$ and how they relate to the po

1. The problem is to solve the equation given in the image: $$\frac{2x+3}{x-1} = 4$$. 2. The formula used here is to solve rational equations by eliminating the denominator: multip

1. **State the problem:** Given $a=5+2\sqrt{5}$ and $b=\frac{1}{a}$, find $a^2+b^2$. 2. **Recall the formula:** We want to find $a^2 + b^2$. Since $b=\frac{1}{a}$, this becomes $a^

1. **State the problem:** Given $a=5+2\sqrt{5}$ and $b=\frac{1}{a}$, find $a^2 + b^2$. 2. **Recall the formula:** We want to find $a^2 + b^2$. Since $b=\frac{1}{a}$, we can write $

1. **Problem 8:** You subtract two integers and the difference is -8. Find two pairs of integers that work. - First pair: both minuend and subtrahend are negative.