🧮 algebra

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

1. **State the problem:** Solve the system of equations: $$\frac{x+1}{3} - \frac{y-1}{2} = 1$$

1. Diberikan soal: Hitung nilai dari $\log_3 9 + \log_3 8 - \log_3 12$. 2. Kita gunakan sifat logaritma: $\log_b m + \log_b n = \log_b (mn)$ dan $\log_b m - \log_b n = \log_b \left

1. **State the problem:** Calculate the value of the expression $344 + 56(153 - 95)$.\n\n2. **Apply the order of operations:** According to the order of operations (PEMDAS/BODMAS),

1. **State the problem:** Ludek has two payment options for 8 days of work. Option 1 pays a fixed $40 per day. Option 2 pays doubling amounts starting at $2 on day 1, $4 on day 2,