🧮 algebra

1. The problem asks to simplify the expression $$\sqrt{7} - t + \sqrt{7} + t$$ and determine under what conditions the result is a natural number (belongs to $\mathbb{N}$). 2. Begi

1. The problem is to describe the function $y = x^3$. 2. This is a cubic function where each input $x$ is raised to the third power.

1. The problem is to simplify or solve an expression where the terms $-t$ and $t$ are inside a square root. 2. Let the expression inside the root be $-t + t$ or $t - t$; inside the

1. First, state the problem: Prove that $\sqrt{7} - t + \sqrt{7} + t \in \mathbb{N}$ where $t$ is a variable. 2. Simplify the expression inside the set membership:

1. The problem is to solve an algebraic expression or equation. 2. Since no specific problem was given, let's consider a general example: Solve for $x$ in the equation $$2x + 3 = 1

1. We are asked to determine certain key features of the quadratic function $f(x)$. 2. The vertex form of a quadratic function $f(x) = ax^2 + bx + c$ is given by the vertex coordin

1. The problem asks to construct tables of ordered pairs for four exponential functions and sketch their graphs. 2. For each function, calculate $y$ at several values of $x$ (e.g.,

1. The problem is to rewrite the quadratic function $f(x)=-2x^2+6x-1$ in the form $a(x+h)^2+k$ where $a$, $h$, and $k$ are constants. 2. Start by factoring out the coefficient of $

1. **State the problem:** Solve the system of equations graphically and verify the solution. Given:

1. Let's start by stating the problem: Calculate $\frac{1}{4}$ divided by 2. 2. Division by a number is equivalent to multiplication by its reciprocal. The reciprocal of 2 is $\fra

1. **Problem:** Solve the system of linear equations using Gauss Elimination and find expressions for $x$, $y$, and $z$. Given system:

1. The problem states that the salvage value $S(t)$ of the company jet after $t$ years is given by: $$S(t) = 700,000 \times (0.8)^t$$

1. Let's start by writing the expression given: $$x^2 + 3y + 3x - y^2$$. 2. Group the terms to see if we can simplify or rearrange: $$x^2 + 3x + 3y - y^2$$.

1. The problem is to understand the expression $X^2 + b^2$ and explore its components. 2. This expression is a sum of squares, where $X$ and $b$ are variables or constants.

1. **Stating the problem:** We are given the salvage value function $$S(t) = 700000(0.8)^t$$ which represents the value of the jet after $$t$$ years. 2. **Find the rate of deprecia

1. The problem involves converting various linear equations into slope-intercept form and finding intercepts or verifying points on lines. 2. For equation $7x + 3y = 21$:

1. Stating the problem: Simplify the expression 2(x + 3). 2. Apply the distributive property which states that $a(b + c) = ab + ac$.

1. The problem asks for the rate of depreciation in dollars per year after 10 years. 2. To find the rate of depreciation, we need a function or formula that models the value of the

1. Solve |x - 1| = 4 This means the expression inside the absolute value can be 4 or -4.

1. Problem: Find the rate of depreciation after 1 year for the salvage value of a company jet given by the formula $$S(t) = 500000(0.9)^t$$ where $S(t)$ is the salvage value in dol

1. State the problem: Solve the inequality $$\sqrt{5 - x} \geq x - 3$$. 2. Consider the domain: The expression inside the square root must be non-negative: