🧮 algebra

1. Let's first clarify the problem: we need to determine the equation of line $l_2$. 2. Usually, the equation of a line can be expressed as $y=mx+b$, where $m$ is the slope and $b$

1. The problem states we have a line $l_1$ with equation $x + 2y = 4$. 2. We need to find line $l_2$ perpendicular to $l_1$ and passing through the origin.

1. تمّ إعطاء السؤال: حساب حاصل ضرب 480 في 5. 2. نستخدم قاعدة الضرب المباشر للأعداد الصحيحة: 480 \times 5.

1. **Stating the problem:** We need to factor common terms from the expression $$y'=(4x+3)^3(x+1) - 4\left[16(x+1) - 3(4x+3)\right].$$

1. Stating the problem: Three businessmen Njoroge, Chatles, and Omondi contributed a total of 329000 to start a business. We know the ratio of Njoroge's to Chatles's contribution i

1. Let's understand what a common factor is: it is a number or expression that divides two or more terms without leaving a remainder. 2. To find a common factor in step 6, identify

1. **State the problem:** Solve for $x$ in the equation $$\frac{125^{4x}}{5^{2x}} = 3125.$$\n\n2. **Express all terms with the same base:** Note that $125 = 5^3$ and $3125 = 5^5$.

1. نبدأ بفهم المطلوب: 300 قسمة خمس تعني 300 ÷ 5. 2. نكتب العملية الحسابية:

1. The problem asks how to find the unit rate given a fraction or ratio in the form $\frac{\text{numerator}}{\text{denominator}}$. 2. The unit rate is the value corresponding to "p

1. Problem statement: - A parish agricultural officer has 450 kilograms of fertilisers and 120 litres of anti-tick vaccine to distribute equally among farmers. We need to find the

1. Let's define the problem clearly: we need to solve the given math problem step-by-step. 2. Since no specific problem was given, I will provide a generic algebra example: Solve f

1. The problem is to solve for $x$ in the equation $2x + 3 = 11$. 2. Start by isolating the variable term: subtract 3 from both sides to get $2x = 11 - 3$.

1. **State the problem:** We are given an initial road length 13 years ago, $L_0 = 1350$ km.

1. **Evaluate and simplify each expression:** 2. Simplify $\frac{8x^{2}y^{2}}{12x+y}$ as is, since no further factorization is possible without more information.

1. **State the problem:** We need to find consecutive positive integers whose sum is 2024 and determine the largest integer in such a sum. There must be at least 2 terms. 2. Let th

1. Problem a: Find total future profits of a tool with a net return decreasing by 10% annually and a current gain of 400. 2. Since net return decreases by 10% annually, the common

1. The question "when do we half the number" relates to situations where a quantity is reduced to half its original value. 2. This commonly appears in problems involving exponentia

1. The problem: Find the equation of an ellipse given its vertices. 2. Recall the standard form of the ellipse equation centered at the origin with horizontal major axis:

1. **Problem 20:** Given height equation $$h = -16t^2 + 96t$$ , find $$t$$ when $$h = 144$$ feet. 2. Substitute $$h = 144$$:

1. 問題陳述：已知 $x,y,z$ 均為正實數，且滿足條件 $$x^{2}+y^{2}+z^{2}=1$$ 求表達式 $$\sqrt{2}xy + yz$$ 的最大值。

1. Problem statement: Evaluate $y$ for the linear function $y = -\frac{1}{3}x - \frac{2}{5}$ at $x = 0$, and describe the graph. 2. Substitute $x = 0$ into the formula to get $y =