🧮 algebra

1. We are asked to express the relationship between time spent on a job and the fee charged by a carpenter. 2. Let $t$ be the time in hours and $F(t)$ be the fee charged in euros.

1. Stating the problem: We have the function $$f(x)=\frac{2x-1}{x-1}$$ and we want to express it as a division of two functions $$u(x)$$ and $$v(x)$$ such that $$f(x) = \frac{u(x)}

1. The problem is to divide the function $$f(x)=\frac{2x-1}{x-1}$$ into two functions $$u(x)$$ and $$v(x)$$ such that $$f(x) = \frac{u(x)}{v(x)}$$. 2. Observe the given function $$

1. **Problem Statement:** Factorize the given polynomials. 2. **viii.** Factorize $-6x^2 - x + 2$.

1. Stating the problem: Solve the linear equation $1x+\frac{130}{180}-3x=\frac{31}{27}$.\n\n2. Simplify the fractions where possible:\n$\frac{130}{180} = \frac{13}{18}$.\nSo equati

1. The problem is to identify and analyze the graph of a function described with points and behavior. 2. The graph passes through the point (1, 2). This means that the function's v

1. The problem is to find the function describing the situation. 2. Since no specific problem details were given, I will explain how to approach defining a function from a problem

1. The problem involves analyzing a curve that passes through points and describes a specific behavior between those points. 2. Key points given are approximately at $x=-1$, $y\les

1. The problem is to explain how to draw the graph of $f_2(x) = -\sqrt{|x| + 1}$ starting from the graph of $f(x) = \sqrt{x + 1}$.\n\n2. First, understand the graph of $f(x)$. This

1. **State the problem:** We want to prove that for the function $t(x) = (x-1)^2$, the equality $t(2-x) = t(x)$ holds. 2. **Evaluate $t(2-x)$:** Substitute $2-x$ into the function

1. **State the problem:** We need to prove that $t(2-x) = t(x)$, where the function $t(x) = (x-1)^2$.

1. The problem is to simplify the expression \( \sqrt[6]{c^6} \). 2. Recall that the sixth root of a number \( x \) is written as \( \sqrt[6]{x} = x^{\frac{1}{6}} \).

1. The problem is to factorize the given polynomials: i. \(3y^2 + 12y\)

1. Problem: Solve each inequality below, then match to the graph that represents its solution set. 1. Solve $x + 11 > 16$:

1. The problem is to simplify the expression $|x-1| + 1$. 2. Recall that the absolute value function $|x-1|$ outputs the distance between $x$ and $1$ regardless of direction. It is

1. We are asked to analyze the expression $|x-1| + 1$. 2. The absolute value function $|x-1|$ represents the distance between $x$ and $1$ on the number line.

1. Stating the problem: We want to simplify the product $ (5 - x)(6 - 5x)(2 - x) $. 2. First, multiply the first two binomials:

1. The problem refers to "26 from same picture," which likely involves solving an algebraic or geometric expression labeled 26 in a referenced image. 2. Since the picture is not pr

1. **State the problem:** Simplify the expression $ (5x + 3)(x - 1)(3x - 2) $. 2. **Multiply the first two binomials:**

1. **Stating the problem:** The inequality given is $1 + 3x \neq 1 + 3x$. 2. **Analyzing the inequality:** Both sides of the inequality are the same expression: $1 + 3x$.

1. Stating the problem: Expand and simplify the product $$ (x^3 - 2x^2 + 5x - 7)(2x - 3) $$ 2. Distribute each term in the second polynomial to every term in the first polynomial: