🧮 algebra

1. We are given the quadratic equation $$2x^2 + 5x + 4k = 0$$ and told that its discriminant is zero. 2. Recall the discriminant formula: $$\Delta = b^2 - 4ac$$ where $a=2$, $b=5$,

1. لنحدد التعبير المعطى: $$\frac{1}{س} - 3 س$$. 2. لكي نجد قيمة التعبير، نحتاج إلى تبسيطه أو إيجاد علاقة بينه وبين الخيارات المعطاة.

1. The problem involves answering without any specific question, so I will provide a brief demonstration example involving algebra. 2. Let's solve the quadratic equation $$x^2 - 5x

1. بدأ السؤال بطلب حساب قيمة التعبير $$\frac{1}{3s} \quad ?$$ 2. الخيارات المعطاة هي كالتالي:

1. لنفهم السؤال، لدينا متغيرات ص و د مع المعطيات التالية: ص = 7.5 و ك د ص = 10. المطلوب إيجاد قيمة ك د ص معرفة ص. 2. من المعطى عند ص = 7.5، ونعلم أن ك د ص = 10.

1. The problem states we have the cubic polynomial $$f(x) = 2x^3 - 5x^2 + ax - 7$$ and that the value of $f(x)$ at $x=2$ is 11. 2. Substitute $x = 2$ into the polynomial to find $a

1. **Problem:** Determine whether the 12th term of the sequence $1+i, 2i, -2+2i, \dots$ is $10+12i$. 2. **Identify the type of sequence:** Observe the terms:

1. The problem is to find the 12th term of the geometric progression (GP) given the first three terms: $1+i$, $2i$, $-2+2i$. 2. Recall that the $n$-th term of a GP is given by $$a_

1. **State the problem:** Find the 12th term of the sequence: $1+i$, $2i$, $-2+2i$, ... 2. **Identify the pattern:** The given sequence terms are complex numbers: $a_1=1+i$, $a_2=2

1. **State the problem:** We have two points on a coordinate plane representing rides in a theme park: the Ferris wheel at $(-5, 4)$ and the roller coaster entrance at $(6, -8)$. W

1. مسئله: محاسبه مقدار عبارت $2a^2 - 3ab + b^2$ وقتی که $a=3$ و $b=-2$ است. 2. جایگزینی مقادیر داده شده در عبارت:

1. Problem 1: Complete the tables by finding missing values in each. **Table 1: Discounts and Sale Prices**

1. The problem asks us to find which of the points 9.5, 9.6, 9.7, 9.8, 9.9, or 10 is closest to $\sqrt{97}$. 2. First, calculate $\sqrt{97}$. Use a calculator or approximate:

1. সমস্যাটির বর্ণনা: ৪ বছরে মুনাফা-আসলে ৬০০০ টাকা এবং ৬ বছরে মুনাফা-আসলে ৬৫০০ টাকা হয়েছে। এখানে তিনটি প্রশ্ন রয়েছে: (ক) ৪ বছরের মুনাফা কত?

1. The request is to find the 12th number in a sequence. 2. Since the original sequence is not provided, please specify the sequence to find the 12th number.

1. The problem is to analyze the function $$g(x) = \frac{x}{x^2 - 25}$$ and understand its properties. 2. First, identify the domain. The denominator cannot be zero, so solve $$x^2

1. Stating the problem: Simplify the expression $(x+2)^2$. 2. Use the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. The problem is to understand Pascal's triangle and how to construct it. 2. Pascal's triangle is a triangular array where each number is the sum of the two numbers directly above

1. The problem asks to identify what a unit is from the given multiple choice options. 2. In mathematics, a "unit" typically refers to the multiplicative identity in a number syste

1. **Problem Statement:** Beatrice walks 1 km at 4 km/h and then 2 km at 4.5 km/h. Find her average speed for the whole journey. 2. **Step 1: Calculate the time taken for each part

1. Stating the problem: We want to resolve the expression $$\frac{2x^2 + 7x + 33}{x^3 + 0x^2 - 11x}$$. 2. Simplify the denominator: The denominator is $$x^3 + 0x^2 - 11x = x^3 - 11