🧮 algebra

1. Let's clarify the question: "Is Z negative?" This depends on the context or the definition of Z in your problem. 2. If Z is a variable or a value, you need to check its value or

1. **Problem statement:** We are given the function $$f(x) = \frac{x^3 - 16x}{-4x^2 + 4x + 24}$$ and asked to analyze it, including graphing the curve and its asymptotes. 2. **Simp

1. **Problem statement:** We are given the function $$f(x) = \frac{x^3 - 16x}{-4x^2 + 4x + 24}$$ and asked to analyze and graph it, including its oblique (slant) asymptotes. 2. **S

1. **State the problem:** Simplify the expression $$\frac{x^4 - y^4}{x^2 - 2xy + y^2} \times \frac{x - y}{x(x + y)} \div \frac{x^2 + y^2}{x}$$. 2. **Rewrite the division as multipl

1. **Expand** $(x + 2)^4$ using the binomial theorem. The binomial theorem states:

1. The problem asks to solve the equations graphically: 10. $|x - 1| = 2$

1. The problem is to understand the expression $\frac{a}{b}$, which represents a fraction where $a$ is the numerator and $b$ is the denominator. 2. This fraction means that $a$ is

1. The problem gives two equations: $y=3m+4$ and $x=5m-6$. 2. These equations express $y$ and $x$ in terms of the parameter $m$.

1. **Check the consistency and solve the system:** Given:

1. **State the problem:** We have the cryptarithm (alphametic puzzle): $$\begin{array}{cccc}

1. The problem is to find the expression for $2 \times A$ where $A$ is a variable or a given quantity. 2. Multiplying a variable by 2 means doubling its value.

1. Problem: Find the inverse function $f^{-1}(x)$ for $f(x) = \frac{2x+1}{x-1}$, $x>1$. 2. To find $f^{-1}(x)$, start by setting $y = \frac{2x+1}{x-1}$.

1. Problem: Find the inverse function $f^{-1}(x)$ for $f(x)=\frac{2x+1}{x-1}$, $x>1$. 2. To find $f^{-1}(x)$, start by setting $y=f(x)$:

1. **Stating the problem:** We are given a function $د(س) = س^2$ and asked several questions about its symmetry axis, zeros, and limits.

1. Muammo: 25 ta ketma-ket natural sonning yig'indisi 1000 ga teng. Bu sonlarning eng kichigi nechaga teng? 2. Ketma-ket sonlar: $x, x+1, x+2, \dots, x+24$.

1. The problem asks to find the sum of the numbers in the sequence starting from 10, 11, 12, 13, 14, 15, 16, ... up to 10 terms. 2. This is an arithmetic progression where the firs

1. The problem is to show that $$\sinh 2x = 2 \sinh x \cosh x$$. 2. Recall the definitions of hyperbolic sine and cosine:

1. The problem is to show that the parametric equations $x = a \cos \theta$ and $y = b \sin \theta$ represent the ellipse given by the equation $$\frac{x^2}{a^2} + \frac{y^2}{b^2}

1. The substitution method is used to solve a system of equations by expressing one variable in terms of the other and substituting it into the second equation. 2. Suppose the syst

1. The problem is to analyze the equation of the form $3x^2 + 2y^2 = 11$. 2. This is an equation of an ellipse because it is a sum of squared terms equal to a constant.

1. The problem asks to express the perimeter $P$ of a square as a function of its area $A$. 2. Let the side length of the square be $s$.