🧮 algebra

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:

1. We are asked to determine if the functions $h(x)=\frac{x-3}{\sqrt{x+1}+2}$ and $k(x)=\sqrt{x+1}-2$ are equal. 2. Start by simplifying $h(x)$. Notice that $h(x)$ is a fraction wi

1. Stating the problem: Simplify the expression $$x^2 (x - y) y^2 (x + 2y)$$. 2. Rewrite the expression grouping terms:

1. We start with the problem: Simplify the expression $$x^2 (x - y) y^2 (x + 2y)$$. 2. First, observe the terms and group the factors for clarity:

1. The problem is to find the value or expression related to "X" but the user did not provide any specific details or equation involving X. 2. To help with math problems, please pr

1. Given the equation $2x - 20y + xy - 190 = 0$, we want to analyze or simplify it. 2. Group the terms involving $x$ and $y$:

1. The problem is to find the square root of 1225. 2. Recall that the square root of a number $x$, denoted $\sqrt{x}$, is a value that when multiplied by itself gives $x$.

1. The problem asks for the square root of 81. 2. The square root of a number $x$ is the number $y$ such that $y^2 = x$.

1. The problem asks to find $K_\infty$ and $\beta$ given the expression: $$K_\infty = \frac{(2.00 - 1 - u) + \beta (2.00^2 - 1 - u^2)}{5}$$