🧮 algebra

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

1. **Problem statement:** Find the zeros (Nullstellen) of the function given in factor form: $$f(x) = x(x-2)(x+3)$$ 2. **Formula and rules:** The zeros of a function in factor form

1. We are asked to graph the function $f(x) = x^4 - 3x^2 + 2$. 2. The function is a polynomial, so it is continuous and smooth everywhere.

1. Let's start by stating the problem: You want to understand how to apply the difference of squares to simplify a denominator. 2. The difference of squares formula is: $$a^2 - b^2

1. The problem is to understand how to perform the third difference of squares. 2. The difference of squares formula is $a^2 - b^2 = (a-b)(a+b)$.

1. Let's start by stating the problem: You want to understand how to factor expressions using the difference of squares method. 2. The difference of squares formula is:

1. **State the problem:** Simplify the expression $$6^3 \times \frac{1}{9^2}$$. 2. **Recall the formulas and rules:**

1. **State the problem:** Simplify the rational expression $$\frac{4r^2 + 24r + 32}{16r^2 - 16r - 96}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Factor the expressions $t^2 - 49$ and $t^2 - 14t + 49$. 2. **Recall formulas:**