🧮 algebra

1. **State the problem:** We need to find the slope of the line passing through the points $(-2, -2)$ and $(1, 3)$ and determine if the slope is positive or negative. 2. **Formula

1. **State the problem:** We are given a function $f$ with points on its graph and asked to find values and solve equations involving $f$ and its inverse $f^{-1}$.

1. The problem asks to express the product $10 \cdot 10^7$ as a single power of 10 with a simplified exponent. 2. Recall the rule for multiplying powers with the same base: $$a^m \

1. **State the problem:** Calculate the value of $10 \cdot 10^7$. 2. **Recall the rule for multiplication with powers of 10:** When multiplying powers of 10, you add the exponents

1. **Problem:** Given the base function $y=\frac{1}{x}$, it is transformed by reflecting along the x-axis, vertically stretching by a factor of 3, horizontally stretching by a fact

1. **State the problem:** Calculate the value of $\frac{44}{46}$. 2. **Write the fraction:** $\frac{44}{46}$.

1. **State the problem:** Estimate the value of $$\frac{0.482 \times 61.2^2}{\sqrt{98.01}}$$ using approximations to 1 significant figure. 2. **Approximate each value to 1 signific

1. The problem is to simplify the expression $(-9)^0$. 2. Recall the rule: Any nonzero number raised to the power 0 equals 1, i.e., $a^0 = 1$ for $a \neq 0$.

1. The problem asks to sketch a graph of a bike ride as a function of distance traveled over time. 2. To model this, we use a piecewise function $f(t)$ where $t$ is time and $f(t)$

1. **State the problem:** Find the function $(g - h)(x)$ where $g(x) = 2x - 3$ and $h(x) = x^3 - 2x^2 + 2x$. 2. **Recall the formula:** The difference of two functions is given by

1. **Problem:** Perform the indicated operation for the first problem. Given functions:

1. The problem asks to simplify the expression $$\frac{\sqrt{252}}{3}$$ in simplest radical form. 2. First, factorize 252 to find perfect squares inside the square root:

1. **Problem Statement:** We have a piecewise function describing the distance $f(x)$ in kilometers Michelle and Rashid travel after $x$ hours of biking:

1. **State the problem:** We know a 162 pound man can have 1016 mg of a medicine in a day. We want to find how much medicine a 161 pound woman can have, assuming the dosage is prop

1. The problem is to simplify the radical expression $\sqrt{160}$. 2. Recall the rule for simplifying radicals: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.

1. **State the problem:** We need to find the unit price (price per ounce) for each bottle of dish soap and determine which is the better deal. 2. **Formula:** The unit price is ca

1. **State the problem:** We need to find the weighted average of points A, B, and C on a number line where point B weighs twice as much as point A, and point C weighs twice as muc

1. **State the problem:** Solve the equation $4 = \frac{r}{7 - 3}$ for $r$. 2. **Understand the equation:** The right side is a fraction with numerator $r$ and denominator $7 - 3$.

1. **State the problem:** Solve the equation $3r - 4 = 8$ for $r$. 2. **Write down the equation:**

1. The problem is to expand and simplify the perfect square polynomial $ (c - 2)^2 $. 2. Recall the formula for the square of a binomial:

1. The problem asks to find the value of $x$ in the equation $$\frac{3x+1}{2} = 7.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$.\n\n3. F