🧮 algebra

1. The problem asks how we know that $a$ and $b$ are the answers. 2. In algebra, $a$ and $b$ typically represent solutions to an equation or variables found by solving.

1. **State the problem:** We are given the function rule $g(h) = 500 \cdot 4^h$ representing the number of bacteria after $h$ hours. We need to find: a. How many bacteria were ther

1. The problem asks: What are the values of $a$ and $b$ in an exponential function of the form $$y = a \cdot b^x$$? 2. The general form of an exponential function is $$y = a \cdot

1. **State the problem:** We need to find a function rule that relates the number of minutes $m$ to the number of bacteria $b(m)$ in the population. 2. **Analyze the data points:**

1. **State the problem:** We know that 26 dogs were adopted this spring, which is 130% of the number adopted last spring. We need to find how many dogs were adopted last spring. 2.

1. **State the problem:** Solve the equation $x^2 + y^2 + z^2 = 3xyz$ for real numbers $x, y, z$. 2. **Recognize the form:** This is a symmetric equation in three variables. One co

1. **Stating the problem:** We have the compound interest formula:

1. **State the problem:** We want to find the dimensions of a rectangular field that maximize the enclosed area given a total fencing cost of 700. 2. **Define variables:** Let $x$

1. **Problem:** Simplify the expression $2 \ln(a^3 b^4) - 3 \ln a - 3 \ln(ab^2)$ as simply as possible. 2. **Recall logarithm rules:**

1. **State the problem:** Fill out the table by converting numbers to whole numbers or decimals and write them in standard form.

1. **Stating the problem:** We need to simplify the expressions using the rules of exponents. 2. **Recall the exponent rules:**

1. **State the problem:** We need to solve the equation $$30 = \frac{5}{9}(F - 32)$$ for the temperature $F$ in degrees Fahrenheit. 2. **Recall the formula:** The equation relates

1. **State the problem:** Solve the equation $$\frac{2R_T - 1}{3} = \frac{3R_T + 1}{6}$$ for $R_T$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides

1. **State the problem:** We are given the proportion \( \frac{5000}{1500} = \frac{V_p}{800} \) and need to find the value of \( V_p \). 2. **Formula used:** To solve for \( V_p \)

1. **State the problem:** We have an initial number of users $P_0 = 330$ on a website, growing exponentially at an annual rate of 51%. We want to write a function $P(t)$ representi

1. **State the problem:** Solve the equation $$\frac{N_p}{1200} = \frac{1600}{1000}$$ for $N_p$. 2. **Formula and rules:** To solve for $N_p$, multiply both sides of the equation b

1. **State the problem:** Solve for the temperature in Fahrenheit ($F$) given the Celsius temperature is 40 using the formula relating Celsius and Fahrenheit. 2. **Formula:** The c

1. **State the problem:** Solve the linear equation $$\frac{5}{6} - 6w = \frac{1}{3}$$ for $w$. 2. **Isolate the term with $w$:** Subtract $\frac{5}{6}$ from both sides:

1. **State the problem:** Simplify the expression $$(b^2 + 1)(-b) + (-b + 1)(1 - b^2).$$ 2. **Recall distributive property:** To simplify, we will expand each product using the dis

1. **State the problem:** Simplify the expression $ (x^2y + x)(xy - 1) - 2x(x^2y^2 - 1) $. 2. **Use distributive property:** Expand each product.

1. **State the problem:** Calculate the value of the expression $$\left(\sqrt{0.25 \times 10^4}\right)\left(4 \times 10^3\right)^2$$. 2. **Recall formulas and rules:**