🧮 algebra

1. The problem is to divide the mixed number $1 \frac{5}{6}$ by the fraction $\frac{5}{6}$.\n2. First, convert the mixed number to an improper fraction.\n\n$$1 \frac{5}{6} = \frac{

1. **State the problem:** We want to find which expression is equivalent to the polynomial $$x^3 + 3x^2 + x + 3$$. 2. **Recall the distributive property and factoring:** To check e

1. **State the problem:** We have a function $f(x) = 155 + 125x$ representing the total cost to rent a car, where $x$ is the number of days rented and $f(x)$ is the total charge. 2

1. Il problema chiede di semplificare o manipolare l'espressione $\sqrt{12-k}$.\n\n2. La radice quadrata $\sqrt{x}$ è definita solo per $x \geq 0$, quindi è importante ricordare ch

1. **Problem:** Factor completely the polynomial $$y^6 + 10y^5 - 24y^4$$. 2. **Formula and rules:** To factor a polynomial, first look for the greatest common factor (GCF) among al

1. **State the problem:** Solve the inequality $$-22 \leq x + 8$$ for $x$. 2. **Isolate $x$:** To solve for $x$, subtract 8 from both sides of the inequality.

1. **State the problem:** Solve the inequality $$-8 > 11 + x$$ and find the range of values for $$x$$. 2. **Isolate $$x$$:** To solve for $$x$$, subtract 11 from both sides:

1. **State the problem:** We have a function $f(x) = (x + 3)^2 + 5$ and need to find $f(0)$ and rewrite $f(x)$ in standard quadratic form. Then solve the quadratic equation $3x^2 -

1. **State the problem:** (a) A color printer prints 20 pages in 7 minutes. We need to find how many pages it prints per minute.

1. **State the problem:** Solve the system of equations using Cramer's Rule: $$\begin{cases} x - y + 4z = 0 \\ x - 2y = 1 \\ 2x - 5y - 4z = 2 \end{cases}$$

1. **Problem statement:** (a) Jose bought 14 pounds of sugar for 6 dollars. We need to find how many dollars he paid per pound of sugar.

1. **State the problem:** Simplify the expression $$\frac{-40p^4 - 15p^3}{-5p^2}$$. 2. **Recall the rule:** When dividing terms with the same base, subtract the exponents: $$\frac{

1. **State the problem:** We need to find the quotient of the polynomial $$-25z^4 - 5z^3$$ divided by the monomial $$-5z^2$$. 2. **Write the division expression:**

1. **State the problem:** We have a cubic function $$f(x) = 2x^3 + px^2 - 11x + q$$ where $$p, q \in \mathbb{Z}$$.

1. **State the problem:** Solve the inequality $$-4 \leq \frac{3x + 5}{2x - 3}$$ where $$x \in \mathbb{R}$$ and $$x \neq \frac{3}{2}$$ because the denominator cannot be zero. 2. **

1. Problemet: Vi skal løse ligningen $$2x + 3 = 11$$. 2. Formel og regler: For at løse en lineær ligning isolerer vi variablen $x$ ved at udføre inverse operationer på begge sider

1. **Problem statement:** We have golf irons numbered 1 to 9 with corresponding angle measures in degrees: 12°, 16°, 20°, 24°, 28°, 32°, 36°, 40°, 44°. We want to find the equation

1. The problem is unclear as it asks "How can I calculate it without using more numbers?" but does not specify what "it" refers to. 2. To help you effectively, please provide the s

1. Vamos analisar o polinómio dado: $7x^2$. 2. Um polinómio é uma expressão algébrica que pode ser escrita como a soma de termos, cada um consistindo de um coeficiente multiplicado

1. **State the problem:** We need to find all values that are part of the range of the given function based on the plotted points. 2. **Recall the definition of range:** The range

1. The problem asks for the domain of the relation given by the set of ordered pairs $\{(4, -1), (-5, 2), (-9, 4), (0, 3)\}$. 2. The domain of a relation is the set of all first el