🧮 algebra

1. The problem asks to simplify the expression $$8^{-1} \div 8^{2}$$ and leave the answer in terms of indices (exponents). 2. Recall the rule for division of powers with the same b

1. **State the problem:** Solve the simultaneous equations: $$2x^2 + 3y^2 = 11$$

1. We are asked to simplify the expression $$8^{-1} / 8^{2}$$ and leave the answer in indices (exponents). 2. Recall the law of exponents for division: $$\frac{a^{m}}{a^{n}} = a^{m

1. The problem is to simplify the expression $\frac{2^{10}}{2^{4}}$ and leave the answer in indices. 2. Recall the property of exponents: when dividing powers with the same base, s

1. Stated problem: Calculate $5^3 \div 5^3$. 2. Use the quotient rule for exponents: $a^m \div a^n = a^{m-n}$. Here, $a=5$, $m=3$, and $n=3$.

1. The problem asks to simplify the expression $2^5 \times 2$ and leave the answer in indices form. 2. Recall the index law for multiplication with the same base: $a^m \times a^n =

1. The problem is to evaluate the expression $2^{5} \times 2$. 2. According to the order of operations, first evaluate the exponentiation: $2^{5} = 2 \times 2 \times 2 \times 2 \ti

1. **Stating the problem:** Solve the quadratic equation $$2x^2 + 5x + 2 = 0$$ using the sum and product method. 2. **Identify coefficients:** For the quadratic equation $$ax^2 + b

1. The problem asks to solve a quadratic equation using the sum and product of roots method. 2. Suppose the quadratic equation is $ax^2 + bx + c = 0$.

1. **State the problem:** Solve the quadratic equation $$2x^2 + 5x + 2 = 0$$. 2. **Identify coefficients:** Here, $$a = 2$$, $$b = 5$$, $$c = 2$$.

1. **State the problem:** Calculate the value of $(-2)^3$. 2. **Understand the exponent:** Raising a number to the power of 3 means multiplying the number by itself three times.

1. **State the problem:** We are given ratios of animals in a zoo and need to solve two problems: (a) Write the number of antelope as a percentage of the number of zebra.

1. **State the problem:** We want to find the multiplicative inverse of the expression $$2 + \frac{y}{S}$$ and show that it can be written in the form $$c + d \frac{y}{3}$$ where $

1. Let's start by specifying the problem clearly: solving a typical Class 9 math problem which might involve algebra, geometry, or arithmetic concepts. 2. Since the user didn't spe

1. **Problem statement:** Evaluate the expressions: $$F = -23 - [2 - 5 \times (3 + (-6) \div 2)]$$

1. The problem is to solve the equation $(t + 1)(t + 2) = 0$. 2. According to the zero product property, if a product of two factors equals zero, then at least one of the factors m

1. The problem is to show that the lines $L_1$ and $L_2$ are parallel. 2. The equation of line $L_1$ is given as $$y = 5x + 1,$$ which is in slope-intercept form $y = mx + b$ where

1. The problem involves understanding the graphs described and their equations. 2. We are given two lines related to a variable $x$ and a parameter $\beta t.i-1$:

1. **Problem i:** Solve the system $$\begin{cases} x_1 - 5x_2 = -85 \\ 2x_1 + 4x_2 = 40 \end{cases}$$

1. Solve $0.2x = 7$. Divide both sides by $0.2$: $$x = \frac{7}{0.2} = 35$$

1. The problem is to solve the equation $$(-1 - m)^2 = 12 - m^2 + 1^2$$ for $m$. 2. Start by expanding $(-1 - m)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$: