🧮 algebra

1. **State the problem:** We are given a set of data points representing the height $y$ of a rocket at different times $x$ in seconds. We need to write a quadratic regression equat

1. **State the problem:** We are given a quadratic function $f(x) = ax^2 + bx + c$ and some values of $f(x)$ at specific $x$ values. We need to find $f(1)$. 2. **Write down the giv

1. Énonçons le problème : Calculer la dérivée des fonctions g(t), h(x) et y données. 2. Rappel de la règle de dérivation d'un quotient :

1. The problem asks for the basic formula, but it is not specified which formula is needed. 2. In algebra, a common basic formula is the quadratic formula used to solve equations o

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. The problem asks to find the vertex, axis of symmetry, and y-intercept for given quadratic functions and verify your answers. 2. For #1, you wrote:

1. **Problem Statement:** Verify the horizontal asymptote, domain, continuity, holes, vertical asymptotes, and intercepts for the functions: - $f(x) = \frac{5x^2+125}{4x^3-8x^2-9x+

1. The problem is to determine if $a = 500$ given that $y = 500$ when $c = 0$. 2. Typically, in a linear equation of the form $y = ac + b$, when $c = 0$, $y$ equals the constant te

1. Let's clarify how to identify the answers $a$ and $b$ from the previous worksheet. 2. Typically, $a$ and $b$ represent variables or solutions to equations given in the problems.

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