🧮 algebra

1. We are given the equation $$\frac{x^{28}}{x^w} = x^7$$ and need to find the value of $w$. 2. Recall the law of exponents for division: $$\frac{x^a}{x^b} = x^{a-b}$$.

1. The problem is to fully simplify the expression $7 \times v^2 - 4v \times v$. 2. First, rewrite the expression using standard algebraic notation: $$7v^2 - 4v \cdot v$$.

1. The problem shows a number pyramid with algebraic expressions. The top brick is $6h^2 + 9h + 4$. 2. The second row has two bricks: left is $3h^2 + 5h$, right is unknown (empty).

1. **State the problem:** Simplify the expression $9d + 5n - 6d - 2n + 11 - 11 - 3d$. 2. **Group like terms:** Group the terms with $d$, $n$, and constants separately:

1. The problem is to rearrange the formula $h = a v$ to make $a$ the subject. 2. Start with the equation:

1. **State the problem:** We are given a parabola with vertex at $(3,1)$ and need to find the x-intercepts $p$ and $q$ of the parabola. 2. **Identify the vertex form of the parabol

1. **State the problem:** Make $h$ the subject of the equation $h + p = w$. 2. **Isolate $h$:** To make $h$ the subject, we need to get $h$ alone on one side of the equation.

1. The problem is to factor the quadratic expression $x^2 + 5x + 6$. 2. We look for two numbers that multiply to the constant term 6 and add up to the coefficient of $x$, which is

1. **State the problem:** Solve the equation $$\frac{x}{-3} + 5 = 10$$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides:

1. The problem appears to involve the expression $\frac{a}{b}$ followed by multiple mapping arrows $\mapsto\mapsto\mapsto$. 2. Typically, $\frac{a}{b}$ represents a fraction or rat

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. **State the problem:** We have an increasing function $f$ on its domain. We want to determine which of the given functions is not necessarily increasing on its domain. 2. **Anal

1. The problem states that the graph of the function $g(x) = mx^2$ is a parabola with vertex at the origin $(0,0)$ and passes through the point $(-2, 20)$. We need to find the valu

1. The problem asks us to determine the interval(s) where the function $f(x) = -4$ is negative. 2. The function $f(x) = -4$ is a constant function, meaning it has the same value fo

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. **Problem 5.4:** Show that \(\left(3 - \frac{1}{\sqrt{5}}\right) \left(9 + \frac{3}{\sqrt{5}} + \frac{1}{5}\right)\) can be expressed as \(a - \frac{1}{25} \sqrt{b}\) where \(a,

1. **State the problem:** (a) Two variables $x$ and $y$ are such that the rate of change of $y$ with respect to $x$ is proportional to $y$. We need to state a model for $y$ in term

1. The problem is to solve the equation $5.5$. 2. Since $5.5$ is a constant number and not an equation, it is already simplified.

1. **State the problem:** We are given the function $$y=1-2e^{\frac{1}{2}x+1}$$ and asked to identify the basic function, sketch it over the interval $$0 \leq x \leq 1$$, identify

1. **State the problem:** Find the domain of the function $$k(x) = \frac{1}{\sqrt{4 - x}}$$. 2. **Analyze the function:** The function involves a square root in the denominator. Fo

1. **State the problem:** Show that \( (3 - \frac{1}{\sqrt{5}})(9 + \frac{3}{\sqrt{5}} + \frac{1}{5}) \) can be expressed as \( a - \frac{1}{25} \sqrt{b} \) where \( a, b \in \math