🧮 algebra

1. **Problem:** Löse die quadratische Gleichung grafisch mit Hilfe der Normalparabel und einer Geraden. **a)** Gegeben: $x^2 - 0{,}5x - 0{,}5 = 0$ oder umgeformt $x^2 = 0{,}5x + 0{

1. **State the problem:** Find the angle between the two lines given by the symmetric equations: $$\frac{x}{2} = -(y+1) = \frac{z+1}{-2}$$

1. **State the problem:** We are given the vector equation of a line: $$(x, y, z) = (3, -1, 2) + r(3, 2, -4)$$

1. Diberikan ekspresi \( \frac{9 \times 8 \times 7 \times 6}{2 \times 1} \). Kita diminta menuliskan notasi faktorisasi dari ekspresi ini. 2. Perhatikan bahwa \(9 \times 8 \times 7

1. Masalah: Diberikan parabola $y = x^2 - 3$ dan mengalami dilatasi terhadap titik pusat $O$ dengan faktor skala 2. Kita diminta mencari persamaan bayangan parabola setelah dilatas

1. **Problem:** Find the domain and range of the function $f(x) = 2 - |x - 5|$. 2. **Formula and rules:** The domain of a function is the set of all possible input values ($x$) for

1. **State the problem:** Solve the equation $q - 12 = 3q + 6$ for $q$. 2. **Write down the equation:**

1. Stating the problem: Solve the linear equation $2x + 3 = 11$ for $x$. 2. Formula and rules: To solve for $x$, isolate the variable by performing inverse operations. Subtract 3 f

1. **Problem Statement:** We need to determine which polynomial matches the graph described. The graph has:

1. **State the problem:** We have the function $y=2^x$ (solid line) and a dilation from the y-axis by a factor $a$ (dotted line). We need to determine if $a$ is greater than 1, les

1. The problem asks whether the dilation factor $a$ from the x-axis applied to the graph $y=2^x$ is greater than or less than 1. 2. A dilation from the x-axis by a factor $a$ means

1. **State the problem:** Solve the inequality $2x - 3 > 1$. 2. **Write the inequality:**

1. **Problem:** Determine the domain and range of the function shown in the first graph, which is a line segment from $(-3,-3)$ (not included) to $(1,4)$ (included). 2. **Formula a

1. The problem is to find the internal ratio of the parts 2 : 3 : 5. 2. The internal ratio means dividing a whole into parts proportional to 2, 3, and 5.

1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and need to understand its behavior. 2. **Formula and rules:** The function involves an absolute value, which

1. The problem asks for the domain and range of a function, but the function itself is not specified. 2. The domain of a function is the set of all possible input values (x-values)

1. The problem is to find the domain and range of a function. 2. The domain of a function is the set of all possible input values (x-values) for which the function is defined.

1. **State the problem:** We are given the function $$h(x) = -4|x - 5|$$ and need to identify the value of $$a$$ and the vertex of the graph. 2. **Formula and explanation:** The ge

1. The problem is to solve a system of 2 simultaneous inequalities. 2. A system of inequalities involves finding the set of values that satisfy both inequalities at the same time.

1. **Problem Statement:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula and Rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we use the q

1. **State the problem:** We are given the function $h(x) = -4|x - 5|$ and asked to understand its graph and properties. 2. **Formula and explanation:** The function involves the a