🧮 algebra

1. The problem shows a pattern with three numbers and a circled number in the middle, producing a result on the right side of the arrow. 2. Given the example: $2\ (4)\ 9 \to 40$, w

1. State the problem: Calculate the value of the expression $3 \cdot (73) - 0.2 \cdot (19)$.\n\n2. Multiply the numbers inside the parentheses by their coefficients:\n$$3 \cdot 73

1. **State the problem:** Solve the absolute value equation $$|x - 5| = 7$$. 2. **Understand the absolute value:** The equation $$|x - 5| = 7$$ means the distance between $$x$$ and

1. **State the problem:** Solve the absolute value equation $$|2x - 4| + 3 = 15$$ for $x$. 2. **Isolate the absolute value:** Subtract 3 from both sides:

1. The problem is to simplify the expression $\frac{3}{ }$, which appears incomplete. 2. Since the denominator is missing, we cannot perform any division or simplification.

1. **State the problem:** Solve the absolute value equation $$|4x - 12| = 16$$. 2. **Understand absolute value:** The equation $$|A| = B$$ means $$A = B$$ or $$A = -B$$, where $$B

1. **Problem Statement:** For each quadratic function, find the vertex, axis of symmetry, range, maximum or minimum, intervals of increasing and decreasing, and intercepts. ---

1. **State the problem:** Solve the compound inequality $$18r + 6 < 24 \text{ OR } 7r - 9 > 12.$$\n\n2. **Solve the first inequality:** $$18r + 6 < 24.$$\nSubtract 6 from both side

1. **State the problem:** Solve the compound inequality $$-5 < \frac{x - 4}{2} \leq 1$$ and express the solution in the form $$a < x \leq b$$. 2. **Isolate the variable:** Multiply

1. **State the problem:** Solve the compound inequality $$16y - 18 > 46 \text{ OR } 14y + 6 < 20.$$ 2. **Solve the first inequality:** $$16y - 18 > 46.$$

1. **State the problem:** Solve the compound inequality \(3m + 2 < 5\) or \(\frac{m + 1}{2} > 4\). 2. **Solve the first inequality:**

1. **Problemstellung:** Wir haben drei Taxiunternehmen mit unterschiedlichen Preisstrukturen und sollen die Fahrpreise als Terme angeben, Werte berechnen, Schaubilder zeichnen, ver

1. The problem asks to determine the interval where the parabola is decreasing. 2. The parabola opens upwards and has its vertex at approximately $(3, -7)$.

1. **State the problem:** Calculate the value of $5^3 \times 6^6$. 2. **Calculate each power separately:**

1. The problem is to analyze the function $f(x) = e^{[x]}$ where $[x]$ is the greatest integer function (floor function) and $x \in [-4, 2]$. 2. The greatest integer function $[x]$

1. The problem is to analyze the function $f(x) = e^x$ for $x \in [-4, 2]$. 2. The function $f(x) = e^x$ is an exponential function where the base $e$ is approximately 2.718.

1. **Stating the problem:** Lisa’s Quick Stop sells milk at a price 2% below the main grocery store. We are given Lisa’s prices for 8 weeks and want to find the corresponding main

1. The problem is to solve the equation fully. Since no specific equation is given, let's consider a general approach to solving algebraic equations. 2. Identify the type of equati

1. **State the problem:** Solve for the roots of the equation $$x^4 + 5x = 7$$ in closed form. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Calculate the value of $2^{10} \times 5^{10} \times 10^{15}$. 2. **Rewrite the expression:** Notice that $10 = 2 \times 5$, so $10^{15} = (2 \times 5)^{15

1. The problem is to graph the line and write the function for $y = 3x + 2$. 2. This is a linear function where the slope is 3 and the y-intercept is 2.