🧮 algebra

1. نبدأ بذكر المشكلة: نريد حساب ميل المستقيم الذي يمر بالنقطتين (7,4) و (-2,1). 2. صيغة ميل المستقيم بين نقطتين \((x_1,y_1)\) و \((x_2,y_2)\) هي:

1. समस्या: एक गोलाकार गुब्बारे की त्रिज्या $r$ समय $t$ के साथ स्थिर गति से बदल रही है। आरंभ में $r=3$ ईकाई और 3 सेकंड बाद $r=6$ ईकाई है। $t$ सेकंड बाद त्रिज्या ज्ञात करें। 2. सूत्र

1. The problem is to understand how to multiply fractions and decimals, as shown in the example $\frac{3}{8} = 3 \times \frac{1}{8} = 3 \times \frac{1}{2} \times \frac{1}{4} = 3 \t

1. The problem is to find the proportion of 45 out of 50 and then express it as a percentage of 100. 2. The formula for proportion is $\text{Proportion} = \frac{\text{Part}}{\text{

1. **Stating the problem:** We have a sequence defined by

1. **State the problem:** We are given the equation $$Q = 250000 - 500P - 1.5M - 240P_R$$ and values $$P=200$$, $$M=60000$$, and $$P_R=100$$.

1. The problem is not explicitly stated, but since the user requested "calculation only," I will provide a sample algebraic calculation. 2. Consider solving the quadratic equation

1. The problem is to understand what \( \lambda^{1/2} \) means. 2. In mathematics, \( \lambda^{1/2} \) represents the square root of \( \lambda \).

1. **State the problem:** We need to evaluate compositions of functions $f$ and $g$ using the given table values for $x = \{-2, -1, 0, 1, 2\}$. The functions are defined as: $$\beg

1. **Problem:** A 10m length of string weighs 350g. How long is a string that weighs 875g? 2. **Formula:** Weight is directly proportional to length, so \( \frac{weight_1}{length_1

1. **Stating the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cance

1. **State the problem:** Solve for $Y$ in the equation $(1.50Y+4)(0.50Y-4)=140$. 2. **Use the distributive property (FOIL) to expand:**

1. The problem is to analyze the function $$f(x) = \frac{x^3 + x^2 - 4x - 4}{x^3 - x^2 - 8x + 12}$$ and then construct its graph. 2. First, factor numerator and denominator to simp

1. **State the problem:** We are given the logarithmic function $$y = 2 \log_3 (x - 1) + 4$$ and need to find its domain, range, vertical asymptote, and compare it with the base gr

1. **Problem:** Solve the inequality $$\frac{2x + 3}{2} > \frac{x - 4}{3}$$. 2. **Formula and rules:** To solve inequalities involving fractions, first find a common denominator or

1. **State the problem:** We need to create a sequence of multiples of 2 starting from 2 (i.e., 2, 4, 6, ...) such that the sum of these numbers equals 15000. 2. **Formula used:**

1. The problem asks to create a table of numbers that are multiples of 2 and whose total sum is 15000. 2. We know multiples of 2 are numbers like 2, 4, 6, 8, ...

1. Verilmiş funksiyanı yazırıq: $$f(x, y) = x^2 + y^2 - 2xy$$ 2. İndi $f(1, 2)$ qiymətini tapırıq:

1. Problem: Given the function $f(x,y) = x^2 + y^2 - 2xy$ and $k = 1.30$, find the value of $k \cdot f(1,2)$. 2. First, calculate $f(1,2)$ by substituting $x=1$ and $y=2$ into the

1. **Problem:** Evaluate $7.2 \times (3.75 - 1.25)^2$ without a calculator. 2. **Step 1:** Calculate the expression inside the parentheses:

1. **State the problem:** Simplify the expression $-hk + hq + hq$. 2. **Identify like terms:** The terms $hq$ and $hq$ are like terms because they have the same variables.