🧮 algebra

1. **State the problem:** Simplify the expression $$100^{-\frac{1}{2}}$$ step-by-step. 2. **Recall the rule:** For any positive number $a$ and rational exponent $m/n$, $$a^{\frac{m

1. **State the problem:** Simplify the expression $7^{-2}$ and express it as a fraction. 2. **Recall the negative exponent rule:** For any nonzero number $a$ and integer $n$, $a^{-

1. **Problem:** The curve $y = \sin x$ is transformed to $y = 4 \sin \left( \frac{1}{2} x - 30^\circ \right)$. Describe fully the sequence of transformations. 2. **Formula and rule

1. **State the problem:** Find the constant term in the expansion of $$\left(x - \frac{2}{x}\right)^4 \left(x^2 + \frac{2}{x}\right)^3.$$\n\n2. **Recall the binomial expansion form

1. The problem asks to write the slope-intercept form equation of the line passing through the point $(-2, -1)$ with slope $\frac{1}{2}$. 2. Recall the slope-intercept form of a li

1. The problem asks for the slope-intercept form equation of the line passing through the point (4, -3) with slope $m = -2$. 2. Recall the slope-intercept form of a line is given b

1. Vamos analisar a matriz $$A=\begin{bmatrix}-1 & 0 & 1 \\ 3 & 1 & -2 \\ 2 & 2 & a+1\end{bmatrix}$$ e o vetor $$b=\begin{bmatrix}2 \\ -1 \\ a+9\end{bmatrix}$$. 2. Para determinar

1. **State the problem:** Solve for $v$ in the equation $$\frac{5v}{7} = -25$$. 2. **Formula and rules:** To isolate $v$, multiply both sides of the equation by 7 to cancel the den

1. **State the problem:** Solve for $v$ in the equation $$-6v = - \frac{12}{7}$$. 2. **Isolate $v$:** To solve for $v$, divide both sides of the equation by $-6$.

1. **Problem Statement:** We are given a polynomial function $f(x)$ with the following features: - Degree is even

1. **State the problem:** We know 6 pears cost 3 dollars, and we want to find the cost of 16 pears using the scale factor. 2. **Set up the ratio:** The price per pear is constant,

1. The problem asks for the equation of a line in slope-intercept form, which is given by the formula: $$y = mx + b$$

1. The problem is to express the inequality $x \leq -3$ OR $x > 4$ using interval notation. 2. Recall that the union of intervals represents "OR" conditions, while the intersection

1. **State the problem:** We need to find the correct interval notation for the highlighted segment on the number line.

1. The problem asks to identify the set expression $x \leq -4 \cup x \geq 3$ as either an intersection, union, or no intersection of two sets. 2. The symbol $\cup$ denotes the unio

1. **State the problem:** Identify the inequality that matches the graph with open circles at -3 and 0, and arrows extending left from -3 and right from 0.

1. The problem is to convert the exponential equation $3^x = 81$ into its equivalent logarithmic form. 2. Recall the definition of logarithms: If $a^x = b$, then the logarithmic fo

1. **Énoncé du problème :** Calculer les inverses et puissances des nombres donnés, puis écrire une expression sous forme d'une puissance.

1. **State the problem:** A human and a turtle compete in a 1 km race. The turtle moves at a constant speed of 0.2 km/h and receives a 980 m head start. The human runs at a speed 1

1. **State the problem:** Solve the equation $$2(x+3) = 5 - (1 - x)$$ for $x$. 2. **Apply the distributive property:** Multiply 2 by each term inside the parentheses on the left si

1. The problem is to solve the equation given by the user. Since the user did not specify the equation, I will explain the general approach to solving algebraic equations step by s