🧮 algebra

1. **Stating the problem:** We are given a sequence of figures where the number of squares in each figure follows a pattern. The table shows figure number $x$ and number of squares

1. **Problem Statement:** Graph the polynomial function $f(x) = x^3 + x^2 - 4x - 4$ given that $(x+1)$ is a zero.

1. The problem is to identify the domain and range of the function $$y = \sqrt{x - 4}$$. 2. The domain of a square root function $$y = \sqrt{f(x)}$$ requires the expression inside

1. **State the problem:** Simplify the expression and solve the equation if possible. Given expressions:

1. Das Problem lautet: Soll man die Klammer in einem Ausdruck einfach weglassen oder ausmultiplizieren? 2. Die Regel lautet: Wenn vor der Klammer ein Pluszeichen steht, kann man di

1. Das Problem lautet: Löse die Gleichung $ (3x-4)-(x+1)-13=0 $. 2. Zuerst entfernen wir die Klammern und fassen ähnliche Terme zusammen:

1. Il problema richiede di disegnare o trovare l'equazione di una parabola. 2. La forma generale di una parabola con asse verticale è $$y = ax^2 + bx + c$$ dove $a$, $b$, e $c$ son

1. **State the problem:** We are given the function $f(x) = 9x^6 - 9 + 4x^4$ and want to understand it better. 2. **Rewrite the function in standard polynomial form:**

1. The problem asks to simplify expressions involving powers of $x$ and express the answers in exponential form. 2. The key formula to use is the laws of exponents:

1. **Stating the problem:** Vi ska skriva uttrycken som potenser och förenkla dem.

1. **State the problem:** Solve the equation $$j(x) = e^{2x} - 3e = 2e$$ for values of $x$. 2. **Rewrite the equation:** We want to find $x$ such that

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 0.05x + 0.04y + 0.045z = 0 \\ 0.05x + 0.04y + 1.045z + w = 0 \\ 1.05x + 1.04y = 0 \end{cases}$$

1. **State the problem:** Maria has a budget of 90 to rent a car from Katey's Kars, which charges 78 per day plus 0.43 per kilometer. We need to find the maximum distance Maria and

1. **State the problem:** We need to find the range of values of $x$ that satisfy the compound inequality $$5x - 7 \leq 9x - 1 < 8x + 1.$$\n\n2. **Break the compound inequality int

1. The problem asks: "Taylor's dad is building a terrarium for his lizards. The number of lizards will determine how many shelves the terrarium will have. What is the independent v

1. The problem asks: "Taylor's dad is building a terrarium for his lizards. The number of lizards will determine how many shelves the terrarium will have. What is the independent v

1. **State the problem:** Solve for $x$ in the equation $$f(x) = \frac{(e^x)^3}{e^2} = e^5.$$ 2. **Rewrite the function:** Using the property of exponents, $(e^x)^3 = e^{3x}$, so t

1. **State the problem:** Solve the equation $$(y - 7)^2 - 9 = (y - 10)(y - 4)$$ for $y$. 2. **Recall formulas and rules:**

1. **Problem Statement:** Analyze the polynomial function $$f(x) = 6x^4 - 23x^3 + 7x^2 + 27x - 9$$ including its zeros, intercepts, extrema, intervals of increase/decrease, and end

1. The problem asks which quadratic function has solutions at $1$ and $-\frac{3}{4}$. 2. Recall that if a quadratic function is factored as $(x - r_1)(x - r_2) = 0$, then the solut

1. **State the problem:** We have the function $$h(x) = 5 - 2 \cdot 3^{7-x}$$ and its inverse function $$k(x) = h^{-1}(x)$$. We want to find the value of $$x$$ such that $$k(x) = 5