🧮 algebra

1. The problem asks to evaluate $f(-2)$ for the given piecewise function. 2. From the graph description, the function has a horizontal line segment from $x=-2$ to $x=2$ at $y=-4$,

1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} 9x - 6, & x < 0 \\ 9x - 12, & x \geq 0 \end{cases}$$

1. The problem is to rewrite the number 0.00711 in scientific notation. 2. Scientific notation expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer.

1. The problem asks to rewrite the number $2.09 \times 10^2$ as a whole number or decimal. 2. The expression $2.09 \times 10^2$ means $2.09$ multiplied by $10$ raised to the power

1. **State the problem:** Simplify the expression $$\frac{-8y^7 z^2}{24 y^2}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$12 - \frac{8y^{7}z^{2}}{24y^{2}}$$. 2. **Identify the formula and rules:** When simplifying expressions with fractions, divide n

1. **State the problem:** Solve the system of equations: $$y = -2x^2 + 4x - 1$$

1. **Solve for y in the equation** $-10 = \frac{y}{9}$. 2. To isolate $y$, multiply both sides by 9:

1. **Stating the problem:** We have two rectangular bar models representing fractions or division expressions.

1. The problem is to understand and analyze the exponential function $y=4^x$ and compare it with other exponential functions like $y=2^x$ and $y=2 \cdot 2^x$. 2. The general form o

1. **State the problem:** Solve for $y$ in the equation $6 = 11 - y$. 2. **Isolate the variable $y$:** To solve for $y$, we want to get $y$ alone on one side of the equation. Start

1. **State the problem:** Multiply the rational expressions $$\frac{4x - 7y}{3x^{5} y^{7}} \cdot \frac{18x^{4} y^{9}}{12x - 21y}$$ and simplify the result. 2. **Rewrite the express

1. **State the problem:** We need to find the number of child tickets sold at the movie theatre given that child tickets cost $6.30, adult tickets cost $9.40, three times as many a

1. The problem is to understand how to use the remainder fraction in polynomial division or related contexts. 2. The remainder fraction is the part of the division that remains aft

1. **State the problem:** Multiply the expressions \( \frac{3m^5 n^6}{8m - 6n} \) and \( \frac{24m - 18n}{27m^2 n^{10}} \) and simplify. 2. **Write the multiplication:**

1. **State the problem:** Divide the polynomial $4x^3 - 4x^2 - 16x + 7$ by the product $(x+1)(x-2)$ using long division, then express the result as partial fractions.

1. The problem asks for the domain of the function $r(x) = \sqrt{1 - x}$.\n\n2. The domain of a square root function includes all $x$ values for which the expression inside the squ

1. The problem asks for the domain of the function $f(x) = \frac{48}{7x - 24}$. The domain is all real numbers except where the denominator is zero. 2. To find where the denominato

1. **Stating the problem:** We are asked to perform a complete study of the function represented by the first graph (a) and then use it as an example to analyze the other six graph

1. **Problem Statement:** Verify that the sequence $$u_n = \frac{14}{3} \left(\frac{1}{2}\right)^n + l$$ satisfies both the initial condition and the recurrence relation given in t

1. **State the problem:** Simplify the expression $$(32x^{20}y^{30})^{-\frac{3}{5}}$$ to its simplest form using only positive exponents. 2. **Recall the rule for fractional expone