🧮 algebra

1. Stating the problem: Solve the equation $$\frac{x}{9} = 6$$ for $x$. 2. To isolate $x$, multiply both sides of the equation by 9 to cancel the denominator:

1. Stating the problem: Solve for $x$ in the equation $$10 = \frac{4}{5} (7x + 15)$$. 2. Eliminate the fraction by multiplying both sides by 5:

1. The problem states that a cooking workshop started at 10:00 and ended at 13:00. 2. We need to find how many sessions of length $\frac{3}{4}$ hours fit into the total duration.

1. The original point is given as $(8, 2)$. This means $x=8$ and $y=2$ where $y=f(x)$. 2. The transformation is $y = -3f(-4x)$. We need to find the new coordinates after applying t

1. The problem is to simplify the expression given by the user. 2. Since no specific expression was provided, please provide the expression you want to simplify.

1. **State the problem:** Simplify and verify the equality: $$1 - \frac{1}{\sqrt{8}} = \left(\frac{1}{4} + \frac{1}{\sqrt{8}}\right) - 1$$

1. We are asked to find between which two consecutive integers the value of $x$ lies when $2^x = 14$. 2. To solve for $x$, take the logarithm base 2 of both sides:

1. \textbf{הבעיה:} יש לנו שלוש טבלאות עם פרמטרים $a_k$, $b_k$, ו-$c_k$ עבור $k=1,2,3$. הנוסחה הכללית עבור הערך במקום $(m,n)$ בטבלה $k$ היא: $$a_k + c_k (m-1) + \left(b_k + 30(m-1)\

1. The problem is to simplify the expression $8y^2 - 4y$. 2. Identify the common factor in both terms. Both terms have a factor of $4y$.

1. The problem is to simplify the expression $\frac{8y^2 - 4y}{4y}$.\n\n2. First, factor the numerator: $8y^2 - 4y = 4y(2y - 1)$.\n\n3. Rewrite the expression using the factorizati

1. The problem involves analyzing the relationship between project price and project duration for three clients: Responsive, Bright Crowd, and The Pink Frog Company. 2. The data gi

1. **State the problem:** We need to plot the functions $y = x^2$, $y = -x^2$, $y = x^3$, and $y = -x^3$ and answer questions about symmetry, origin passage, and the effect of chan

1. **State the problem:** Simplify the expression $\sqrt{8} - \sqrt{15}$. 2. **Simplify each square root if possible:**

1. The problem is to simplify the expression $$\sqrt{\wedge} - \sqrt{15}$$. 2. The symbol \(\wedge\) is not a standard numeric value or variable in mathematics, so it cannot be sim

1. Das Wort "kürze" bedeutet in der Mathematik oft, einen Bruch zu vereinfachen, indem man Zähler und Nenner durch ihren größten gemeinsamen Teiler (ggT) teilt. 2. "Fasse zusammen"

1. Stating the problem: Simplify the expression $$\frac{a - b}{a + b} + \frac{a + b}{a - b}$$. 2. Find a common denominator: The denominators are $a + b$ and $a - b$. The common de

1. The problem is to simplify the expression $\sqrt{8} - \sqrt{15}$.\n\n2. First, simplify $\sqrt{8}$. Since $8 = 4 \times 2$, we have:\n$$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \

1. Masalah: Gambarkan daerah penyelesaian dari sistem pertidaksamaan \(3x + 7y \leq 21\) dan \(2x - 2y > 4\). 2. Pertama, kita ubah pertidaksamaan menjadi bentuk garis batas untuk

1. The problem is to analyze the system of inequalities: $$3x + 7y \leq 21$$

1. **State the problem:** We need to determine the slope of the line shown on the Cartesian coordinate system. 2. **Identify two points on the line:** From the description, the lin

1. The problem asks to find the slope of the line from the first graph with points approximately (-4,0) and (4,4). 2. The slope formula is $$m=\frac{y_2-y_1}{x_2-x_1}$$.