🧮 algebra

1. **State the problem:** We are given the cubic equation $$y=x^3 - 4x^2 + x + 8$$ and asked to find the values of $x$ when $$y=2$$. 2. **Set the equation equal to 2:**

1. The problem is to solve for the variable in the given expression or equation (please provide the expression or equation to solve). 2. Since the expression/equation to solve was

1. Statement of the problem: We want to find all real numbers $x$ satisfying the inequality $|x - 2| < 3$ and represent this set on a number line.

1. The problem is to understand the formula $U = qt\pi$ and possibly manipulate or evaluate it. 2. The formula relates three variables: $U$, $q$, and $t$, with the constant $\pi$ (

1. The problem states the equation $u=qt \pi$, where $u$ is expressed in terms of $q$, $t$, and $\pi$. 2. To understand it, recognize that $\pi$ is a constant approximately equal t

1. **Stating the problem:** Given the equation $$x^4 + 1 = \frac{5}{8} x^2$$, find the values of: - $$x + \frac{1}{x}$$

1. **State the problem:** We need to find 65% of 15. 2. **Convert percentage to decimal:** 65% means 65 out of 100, which is written as $0.65$.

1. **State the problem:** Given functions $f(x) = x^2 - 2x$ and $g(x) = 2x + 3$, and the equation $f \circ g^{-1}(x) = 3$, find the value of $x$. 2. **Find the inverse of $g$: **

1. Let's start by defining a piecewise function. A piecewise function is defined by different expressions over different intervals of the domain. 2. Consider this example of a piec

1. The problem gives two functions: $$g(x) = 2x+2$$ and $$f \circ g(x) = 8x+13$$. We need to find $$x$$ such that $$g \circ f(x) = 20$$. 2. First, understand the notation: $$f \cir

1. **State the problem:** Mr. Sanchez buys $4\frac{3}{4}$ kg of fish to make Spanish sardines. Each can contains $\frac{1}{12}$ kg of fish. Each can is sold for 25 pesos. We need t

1. The problem is to find how much money Mr. Sanchez will earn after selling all the cans of Spanish sardines he can make from 43/4 kg of fish. Each can contains 1/12 kg of fish an

1. State the problem: We are given the set $S = \{(x,y) \mid x,y \in \mathbb{R} \text{ and } y = 2x - 2\}$, which represents points $(x,y)$ in the real plane satisfying the linear

1. **Problem restatement:** We want to find the value of $a$ such that the line $2x - 3y = 6$ passes through points $(9,-4)$ and $(6,a)$. 2. **Substitute first point into the line

1. First, let's clarify what the "simple method" means in general terms: it's a straightforward approach to solving a problem without complicated steps. 2. For example, if you're s

1. Stating the problem: We have functions $f(x) = ax + 5$ and functions $f \circ g(x) = 8x + 13$, and are given that $g \circ f(5) = 8a$. We need to find the value of $a$. 2. Expre

1. The problem states that the cube root of $a$ equals the square root of 5, i.e., $\sqrt[3]{a} = \sqrt{5}$. 2. We want to find the value of $a$. To do this, we can cube both sides

1. The problem states: Given the function $y = 4x + 2$, find its characteristics and interpret its meaning. 2. This is a linear function where $y$ depends on $x$ with a slope of 4

1. Diberikan persamaan: $$2(2^x - 1)x^2 + (2x^2 - 2)x = 2^{x+1} - 2$$

1. **Aljafna (Equations)** - **Title:** Algebraic Equations

1. **State the problem:** We need to find two costs related to the garden: the cost of repairing the garden floor and the cost of constructing a wall around it. 2. **Given data:**