🧮 algebra

1. **State the problem:** Kwame spends fractions of his monthly salary on food, rent, and sweets, and after these expenses, he has 90 left. We need to find his total salary, and ho

1. সমীকরণটি হলো $12x^3 - x^2 - 5x - 2 = 0$। মূলরাশির সমষ্টি নির্ণয় করতে আমরা কিউবিক সমীকরণের মূলরাশির সূত্র ব্যবহার করব। 2. একটি কিউবিক সমীকরণের সাধারণ রূপ $ax^3 + bx^2 + cx + d =

1. The problem is to understand and analyze the equation $y^2 + 2xy = C$. 2. This is an implicit equation involving variables $x$ and $y$ and a constant $C$.

1. The problem is to find the square root of 144. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Factorize the quadratic equation $$6x^2 - x - 5 = 0$$. 2. **Formula and rules:** To factorize a quadratic equation of the form $$ax^2 + bx + c = 0$$, we l

1. **Problem statement:** Jack's and Angie's savings are in the ratio 21 : 8, and Angie's and Hazel's savings are in the ratio 4 : 9. The total savings of Jack, Angie, and Hazel is

1. **Problem statement:** The ratio of Mary's beads to Jane's beads is 4 : 7. The ratio of Jane's beads to Pauline's beads is 5 : 2. Mary has 6 more beads than Pauline. We need to

1. **State the problem:** Solve the equation $x - 5.7 = 0.8$ for $x$. 2. **Formula and rule:** To isolate $x$, add $5.7$ to both sides of the equation. This uses the addition prope

1. **State the problem:** Solve the equation $$\frac{(N-2)180}{N} = 150$$ for $N$. 2. **Understand the formula:** This equation often appears in polygon interior angle problems, wh

1. The problem asks which method eliminates one of the variables in the system of equations: Equation A: $5x + 9y = 12$

1. **State the problem:** Determine which pair of equations could not be used to solve the system: $$4x + 2y = 22$$

1. **State the problem:** We need to find two consecutive integers such that twice the smaller integer plus half the larger integer equals 33. 2. **Define variables:** Let the smal

1. The problem is to simplify the expression $$\sqrt{18x^{4}}$$. 2. Recall the property of square roots: $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ and that $$\sqrt{x^{2}} = |x

1. **State the problem:** Simplify the expression $$\left(\dfrac{x^6 y^3}{z^9}\right)^{\frac{1}{3}}$$ where all variables are positive real numbers. 2. **Recall the power of a quot

1. The problem is to simplify the expression $$\frac{2 \pm \sqrt{(-2)^2 + 4(1)(1)}}{2}$$. 2. First, calculate the value inside the square root (the discriminant): $$(-2)^2 + 4(1)(1

1. **Problem Statement:** We are given four linear functions defined on the domain $-4 \leq x \leq 6$:

1. **State the problem:** We need to show algebraically that the curve $C$ with equation $y = x^2 + 3x - 3$ and the line $L$ with equation $y = 5x - 5$ have exactly one point in co

1. **Problem:** Find the x- and y-intercepts of line "A" which has slope 0 and passes through (-5,12). 2. **Understanding the problem:** A line with slope 0 is horizontal. The equa

1. Problema: Rasti geometrinės progresijos 8-tąjį narį $b_8$, kai žinoma, kad $b_{10} \cdot b_6 = 18$ ir visi nariai yra teigiami. 2. Geometrinės progresijos nariai apibrėžiami for

1. Problema: Turime geometrinės progresijos sumos formulę $$S_n = \frac{8}{5} (1 - 6^n)$$ ir norime rasti vardiklį $r$. 2. Geometrinės progresijos suma yra apskaičiuojama pagal for

1. **Problem:** Find the coordinates of the centre and the radius of the circle given by the equation $$9x^2 + 9y^2 + 6x - 24y + 8 = 0$$. 2. **Step 1: Simplify the equation.** Divi