🧮 algebra

1. **State the problem:** Calculate $-\frac{3}{7} \div -\frac{18}{35}$.\n\n2. **Recall division of fractions rule:** Dividing by a fraction is the same as multiplying by its recipr

1. **State the problem:** We need to divide $\frac{3}{5}$ by $\frac{3}{15}$.\n\n2. **Rewrite division as multiplication:** Dividing by a fraction is the same as multiplying by its

1. The problem is to multiply $-24$ by $\frac{1}{3}$. 2. We write the multiplication as:

1. State the problem: Calculate the product of $-1 \frac{1}{2}$ and $\frac{8}{15}$. 2. Convert the mixed number to an improper fraction: $-1 \frac{1}{2} = -\left(1 + \frac{1}{2}\ri

1. Problem 8: Find the number halfway between 3000 and 4000. To find the halfway point, calculate the average of 3000 and 4000.

1. The problem states that 55% of 500 pupils are girls. 2. To find the percentage of boys, we need to calculate what remains after the girls' percentage.

1. We are given four triangular diagrams each divided into four smaller triangles with sets of numbers and a circled number on the side. 2. The numbers appear to be part of a patte

1. State the problem: Solve the equation $\log_{3}(2-3x)=\log_{9}(6x^{2}-19x+2)$.\n\n2. Express both sides with the same base: Notice that $9=3^{2}$, so rewrite the right side loga

1. The problem is to find the domain and range of the function $$y = x^2 - 8x - 10$$. 2. **Domain:** Since this is a quadratic function (a polynomial), its domain is all real numbe

1. **Problem Statement:** Given a rectangular land plot of dimensions 8 m by 7 m divided into four parts labeled (1), (2), (3), and (4) with the following sizes:

1. We start with the equation of the graph to draw: $$2xy+1=0$$. 2. To understand the graph, we isolate $y$ in terms of $x$: $$2xy = -1 \implies y = \frac{-1}{2x}$$.

1. Mathematical induction is a proof technique used to show that a statement is true for all natural numbers $n \geq k$, where $k$ is a starting point, usually 1. 2. It has two mai

**Problem:** Simplify the expression $$\sqrt{x}^{\frac{1}{2}} \cdot (yz)^{-\frac{1}{2}} \cdot \sqrt{z}^3 \cdot y^{\frac{1}{2}} \cdot (x^{\frac{1}{4}})^3$$. 1. Rewrite all radicals

1. The problem is to simplify the expression $t^2 + \frac{2}{t^2} + 0 \times t + 1$. 2. Notice that $0 \times t = 0$, so it can be removed from the expression.

1. State the problem: Simplify the expression $t \times 2$. 2. Understand that multiplying a variable by a number means doubling that variable.

1. The problem states that the ratio (common ratio) of a geometric progression (G.P.) is given as \(\frac{25}{49}\). We have the second term as \(x + 5\). 2. Let's denote the first

1. The problem presents rows of numbers with two unknown values labeled as $X$ and $Y$. Our goal is to find a relationship or rule to determine $X$ and $Y$ for each row. 2. Let's a

1. Please provide the full problem or expression you'd like me to calculate so I can assist you accurately.

1. The problem involves calculating the price per year given two variables: Cost per kg and Price per year as indicated in the last column. 2. The equation based on the problem sta

1. The problem asks to calculate the price per year for each raw material by multiplying the cost per kg by the amount per year (in kg). 2. The formula to use is:

1. The problem is to find the prime factorization of the numbers represented in the diagram: 2, 5, 45, 1, 3, and 15. 2. Prime factorization means expressing each number as a produc