🧮 algebra

1. **Problem statement:** Simplify and solve the system of equations for part (a): $$\frac{x}{y} = \frac{7}{5}$$

1. **State the problem:** Simplify the expression $\left(2^2 \cdot 5^2\right)^{\frac{1}{2}} \cdot 8^{\frac{1}{3}} \div \frac{1}{2} - 11$. 2. **Use the properties of exponents:**

1. The problem asks for the smallest possible answer to the multiplication $20 \times 300$ given that Isaac estimated it by rounding each number to 1 significant figure. 2. Isaac's

1. **State the problem:** We are given the cubic function $$f(x) = -0.3x^3 - 0.3x^2 + 1.8x$$ and want to analyze its behavior including intercepts and extrema. 2. **Formula and rul

1. Il problema chiede di trovare quanto ha speso Marta in pizzeria sapendo che insieme hanno speso 31 e che Luca ha speso 5 in più di Marta. 2. Definiamo le variabili:

1. **State the problem:** We are given three points on a number line: R, M, and S, with M = $\sqrt{270}$. We need to find the values of R and S to one decimal place, knowing that R

1. The problem is to simplify the expression $$\frac{3^{-2}}{5^{-2}}$$ and verify the equivalence to $$\frac{5^2}{3^2}$$. 2. Recall the rule for negative exponents: $$a^{-n} = \fra

1. **State the problem:** Find the equation of the line passing through the points (0,4) and (1,6) in slope-intercept form $y=mx+b$. 2. **Formula and rules:** The slope $m$ is calc

1. **State the problem:** You sold hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. The total money made is 78.50, and the total number of items sold (hot do

1. The problem is to graph the equation $$y = |x + 2| - 2$$. 2. This is an absolute value function shifted horizontally and vertically.

1. The problem is to graph the equation $$y = |x + 3| + 4$$. 2. This is an absolute value function, which creates a V-shaped graph.

1. **State the problem:** Calculate the summation $$\sum_{i=1}^4 i$$ which means adding all integers from 1 to 4. 2. **Formula used:** The sum of the first $n$ natural numbers is g

1. Il problema chiede di trovare l'equazione della parabola sapendo che il vertice è $V(0;3)$ e passa per il punto $P(1;2)$. 2. L'equazione generale di una parabola con vertice in

1. **State the problem:** Graph the equation $y = |x - 2| - 4$. 2. **Recall the absolute value function:** The graph of $y = |x|$ is a V-shaped graph with vertex at the origin $(0,

1. **Stating the problem:** We need to solve the expression $\frac{3}{-4} - \left(-\frac{2}{5}\right)$ and the product $\frac{3}{-4} \cdot \left(-\frac{2}{5}\right)$.

1. **Stel het probleem vast:** We moeten de uitdrukking $3\sqrt{3} \cdot \sqrt{12} \cdot 2\sqrt{8}$ herleiden. 2. **Gebruik de regels voor wortels en vermenigvuldiging:**

1. **State the problem:** We need to solve for $n(t)$ in the equation:

1. The problem asks to express each fraction as a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{Decimal} = \frac

1. **State the problem:** We are given that 730 ml of water is used for 950 grams of flour. We need to find how much water is used for 1000 grams of flour. 2. **Formula used:** Thi

1. Il problema chiede di trovare l'intersezione con l'asse x di una funzione, cioè i punti in cui la funzione si annulla (y=0). 2. La formula generale per trovare l'intersezione co

1. The problem is to convert the equation $y = -\frac{3}{4}x - 3$ into the form $3x + 4y = 4$ and verify the solution. 2. Start with the given equation: