🧮 algebra

1. **Stating the problem:** We are given discrete points: $(-3,9)$, $(-3,5)$, $(-1,2)$, $(0,2)$, $(1,1)$, $(3,1)$ and asked to identify the function type they represent. 2. **Under

1. **State the problem:** Find the next two terms in the sequence 19, 20, 22, 25, 29. 2. **Analyze the pattern:** Calculate the differences between consecutive terms:

1. **Problem Statement:** Identify the polynomial equation from the given options based on the graph's behavior at its roots. 2. **Given Information:** The graph has roots at $x=1$

1. **State the problem:** Solve the equation $$16 \cdot 64^{3 - 2r} = \left(\frac{1}{4}\right)^{3r}$$ for $r$. 2. **Rewrite bases as powers of 2:**

1. The problem asks to find 5 ordered pairs that satisfy the relation $y = x + 4$. 2. The formula given is $y = x + 4$, which means for any value of $x$, $y$ is that value plus 4.

1. **State the problem:** Solve the equation $3(E-2)+4E=36$ for $E$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $x^2 - 49 = 0$ for $x$. 2. **Recall the formula:** This is a difference of squares equation, which can be factored using the identity $

1. The problem is to find the rationalizing factor for an expression involving a radical. 2. The rationalizing factor is used to eliminate the square root or radical from the denom

1. The problem is to find the cube root of 49, written as $\sqrt[3]{49}$. 2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.

1. The problem asks to find the domain of a function, but the function is not specified in the question. 2. The domain of a function is the set of all possible input values (usuall

1. The problem asks whether the graph of the equation $y^2 = 8x$ represents a function. 2. Recall the definition of a function: for every input $x$, there must be exactly one outpu

1. **Problem 4:** Given a quadratic function graph with vertex, zeros, minimum value, and axis of symmetry to find. 2. The vertex of a quadratic function in standard form $y = ax^2

1. **State the problem:** Find the solutions to the system of equations where a parabola and a line intersect. 2. **Given equations:** Assume the parabola is $y = -a(x - 4)^2 + b$

1. **State the problem:** We want to graph the linear equation $y = 2x + 5$. 2. **Understand the formula:** This is a linear equation in slope-intercept form $y = mx + b$, where $m

1. **Énoncé du problème :** Nous avons une fonction logarithmique $N(t) = \log_c b(t+2)$ qui donne le nombre de personnes guéries en fonction du temps $t$ (en années) depuis l'admi

1. **State the problem:** We need to find the solutions to the system of equations represented by the two curves: a concave down parabola and a straight line with negative slope. 2

1. Let's state the problem: You have a quadratic function with a variable $k$ in the constant term, and you want to find the value of $k$. 2. The general form of a quadratic functi

1. **Énoncé du problème :** Des élèves veulent louer une limousine pour 600. Le coût par élève dépend du nombre d'élèves (de 1 à 8) partageant ce coût.

1. Énoncé du problème : Hélène et David ont chacun une voiture avec un odomètre indiquant respectivement 25000 km et 20000 km au début de l'année.

1. **State the problem:** We are given a table of values for a function $k(r)$ at points $r = 1, 3, 5, 7, 9$ and need to determine if the function is linear, quadratic, or neither.

1. **State the problem:** Ashley is installing two granite countertops. One is 3 feet long and 2 feet wide, and the other is 4 feet long and 2 feet wide. The granite costs 10 per s