🧮 algebra

1. The problem asks to write algebraic expressions for two descriptions. 2. For part (a), "The product of 15 and c" means multiply 15 by c.

1. **State the problem:** We need to substitute a value into an equation and solve for the variable, then interpret the result in the context of an app's user growth. 2. **Given:**

1. Problema: Rezolvați ecuația de gradul II $x^2 - 4 = 0$ în mulțimea numerelor reale. 2. Formula folosită: Pentru ecuația de forma $ax^2 + bx + c = 0$, soluțiile se găsesc cu form

1. **State the problem:** Solve the quadratic equation $x^2 + 3x - 5 = 0$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$:

1. Problema: Rezolvați ecuațiile de gradul II în mulțimea numerelor reale pentru primele trei ecuații din prima coloană: a) $x^2 - 4 = 0$

1. **State the problem:** We are given the function $$P(t) = 800(1.05)^t$$ and asked to find the value of $$t$$ when $$P(t) = 1000$$. 2. **Write the equation:** Set $$P(t) = 1000$$

1. **State the problem:** Find the equation of the straight line passing through points $(0,2)$ and $(9,-1)$ in the form $ax + by = c$ where $a$, $b$, and $c$ are integers in lowes

1. **State the problem:** Simplify the expression $5x^2 + 8x + 3x^2$. 2. **Combine like terms:** Like terms are terms that have the same variable raised to the same power. Here, $5

1. **State the problem:** Find the line of symmetry for the quadratic function $f(x) = x^2 + 10x + 9$ given the vertex $(-5, -16)$. 2. **Recall the formula:** The line of symmetry

1. **State the problem:** Find the vertex of the parabola given by the quadratic function $f(x) = x^2 + 10x + 9$. 2. **Formula for vertex:** The vertex of a parabola $f(x) = ax^2 +

1. **State the problem:** We need to find the number of network devices $n$ that minimizes the total cost $C$ given by the equation $$C = 8n^2 - 176n + 1800.$$ 2. **Formula and con

1. **State the problem:** Solve the inequality $|x + 29| - 1 < 7$. 2. **Isolate the absolute value:** Add 1 to both sides:

1. The problem states a phone plan charges an initial fee of 40 plus 0.40 per minute. 2. We want to write a function $f(x)$ where $x$ is the number of minutes used, and $f(x)$ is t

1. **State the problem:** We want to determine if the number of weeks $t$ is proportional to the number of vehicles made $v$ when a factory makes 50 vehicles per week. 2. **Recall

1. The problem states that two quantities, $x$ and $y$, are directly proportional. This means we can write the relationship as: $$y = kx$$

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:**