🧮 algebra

1. Let's clarify the problem you solved and the expression you obtained: $4x^2 - x - 1$. 2. To understand why you got this result, we need to check the original problem or equation

1. **State the problem:** We need to subtract the polynomial \((5x^2 - 7x - 14)\) from \((9x^2 - 7x + 13)\). 2. **Write the expression:**

1. The problem is to simplify the expression $e \times -e^x$. 2. Recall that $e$ is the base of the natural logarithm, and $e^x$ is the exponential function.

1. **Decide if each statement is an equation, a formula, or an identity:** 1.a. $a^2 + b^2 = c^2$ is an **identity** (Pythagorean theorem, true for right triangles).

1. The problem is to simplify the expression $e \times -e^x$. 2. Recall that $e$ is the base of the natural logarithm, approximately equal to 2.718.

1. **State the problem:** Solve the equation $$\log_2 \frac{3x+1}{2x+7} = 3$$ for $x$. 2. **Rewrite the logarithmic equation in exponential form:**

1. The problem is to reduce the fraction $\frac{13}{26}$ to its lowest terms. 2. Find the greatest common divisor (GCD) of 13 and 26. Since 13 is a prime number and divides 26 exac

1. The problem is to simplify the expression $\text{Ex-ex}$. 2. Since $\text{Ex}$ and $\text{ex}$ are variables or terms, and subtraction is involved, we treat them as algebraic te

1. The problem is to understand the expression "No ex-e× × and x is the same" and clarify the meaning. 2. It seems the user is referring to the expression involving variables and e

1. The problem involves the equation $(\varepsilon + Kt) = 1 + (xt) t$ and the relation $-xt- = -et$ with $t (2)t t$ given. 2. First, clarify the expressions: assume $xt$ and $et$

1. مسئله را بیان می‌کنیم: چرا در تقسیم $$\frac{13}{26}$$ به $$\frac{1}{2}$$ رسیدیم؟ 2. ابتدا کسر $$\frac{13}{26}$$ را داریم. این کسر به معنای تقسیم عدد 13 بر عدد 26 است.

Problem: In a class of 40 students the number of students who study French is 10 more than the number of students who study history. If 8 students study both subjects, how many stu

1. Stating the problem: Decompose the expression $$\frac{x^2 + x - 3}{x(x-1)}$$ into simpler parts or partial fractions. 2. Factor the numerator if possible: The numerator is $$x^2

1. Reduce each numerical fraction to lowest terms: (a) $\frac{13}{26} = \frac{13 \div 13}{26 \div 13} = \frac{1}{2}$

1. **State the problem:** We are given the equation

1. The problem is to solve the equation using properties of equality or algebraic properties. 2. Since the user did not specify the exact equation, let's consider a general example

1. Let's first state the problem: We want to know if the numbers 7, 8, and 9 can be related or solved using the properties called componendo, alternendo, and invertendo. 2. These p

1. نبدأ بكتابة العدد المعطى: $\frac{6\sqrt{}}{42\sqrt{}}$. 2. نلاحظ أن المقام هو عدد ناطق، أي يمكن كتابته على شكل كسر بسيط.

1. **Problem 6:** The polynomial is $3x^3 + 8x^2 - 15x + k$ and $(x - 1)$ is a factor. Find $k$ and factorise the polynomial completely. Step 1: Since $(x - 1)$ is a factor, substi

1. The problem is to expand and simplify the expression $ (b + 5)(b - 10) $. 2. Use the distributive property (FOIL method) to expand:

1. The question asks if the interval for 3 is $(-\infty,0) \cup \{0\} \cup (0,+\infty)$. 2. This notation means all real numbers except possibly how 0 is treated (open or closed).