🧮 algebra

1. **Stating the problem:** We are given the function $f(x) = \sqrt[3]{x - 8}$ and want to understand its properties. 2. **Formula and rules:** The cube root function $\sqrt[3]{x}$

1. **State the problem:** Oscar thinks of a number $r$. He squares it to get $r^2$, multiplies by 4 to get $4r^2$, divides by 3 to get $\frac{4r^2}{3}$, then adds 7 to get 55. We n

1. **State the problem:** We have a rectangle and a square with the same perimeter. The rectangle has width $x+7$ cm and height 7 cm. The square has side length $x+5$ cm. We need t

1. **State the problem:** Solve for the two possible values of $p$ in the equation $$\frac{78 - 3p^2}{5} = 6.$$\n\n2. **Use the formula and rules:** To solve for $p$, first elimina

1. **State the problem:** Find the least common multiple (LCM) of the numbers 20, 66, 77, 88, and 99. 2. **Formula and rules:** The LCM of several numbers is the smallest positive

1. **State the problem:** We need to find the equation of a line $L$ that passes through the point $(3, -2)$ and is inclined at an angle of $60^\circ$ to the line $\sqrt{3}x + y =

1. **Problem statement:** Given the quadratic equation $x^2 - bx + c = 0$ with roots $\alpha$ and $\beta$, we need to form a new quadratic equation whose roots are $\alpha + \frac{

1. **State the problem:** Find the least common multiple (LCM) of the single number 123456789. 2. **Understand the concept:** The LCM of a single number is the number itself becaus

1. Let's start by stating the problem: We want to find the sum and product of the roots of a quadratic equation and express the roots \(\alpha\) and \(\beta\) as the subject. 2. Co

1. The problem is to make $\alpha$ and $\beta$ the subject of an equation. However, the original equation involving $\alpha$ and $\beta$ is not provided. 2. To make a variable the

1. The problem describes points on a horizontal number line with their corresponding numerical values: B = 0, D = 0.17, C = 0.5, A = 1.5. 2. We are asked to understand or analyze t

1. Let's start by stating the problem: We want to find the sum and product of the roots of a quadratic equation. 2. A quadratic equation is generally written as $$ax^2 + bx + c = 0

1. **Stating the problem:** We need to write an equation for the cost $c$ of hiring a bicycle in pounds in terms of the number of days $d$ it is hired for.

1. **State the problem:** We are given the equation of a line: $$5y = 35 + 6x$$ and need to find the coordinates of its y-intercept. 2. **Recall the y-intercept definition:** The y

1. **State the problem:** Simplify the expression $\frac{18}{3}(4+2)-5$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. لنبدأ بحل السؤال الأول من تمرين 01: 𝑥 عدد حقيقي حيث 𝑥 ≤ ٢ يكافي 5 − 3𝑥 ≤ −١. 2. نكتب المتباينة: $$5 - 3x \leq -1$$

1. المشكلة هي إيجاد تعبير عام للحدود $a_n$ بدلالة $n$ والحدود الابتدائية $a_0$, $a_1$, $a_2$ بدون وجود حدود سابقة مثل $a_{n-1}$ أو $a_{n-2}$. 2. عادةً، المتتاليات التي تعتمد على حد

1. **State the problem:** We are given the quadratic sequence defined by the formula $a_n = n^2 + 6n - 10$. 2. **List the first 5 terms:** To find the first 5 terms, substitute $n=

1. نبدأ بكتابة المعادلة المعطاة: عدد حقيقي حيث $x \le 2x$. 2. نطرح $x$ من كلا الطرفين للحصول على:

1. **Problem statement:** We are given two opposite vertices of a rectangle: $(1,3)$ and $(5,1)$. The other two vertices lie on the line $y = 2x + c$. We need to find the value of

1. **State the problem:** Solve the equation $$0 = 24x + 2x^2 - 95$$ for $x$ and round the solutions to the nearest integer. 2. **Rewrite the equation:** The equation is a quadrati