🧮 algebra

1. The user provided several expressions: $32\pi$, $64$, $64\pi$, and $16$. 2. We will analyze these numbers to find their relationships or simplify them.

1. Solve $d = rt$ for $r$. Start with the equation:

1. Problem: Determine if $4xy + 2y = 9$ is a linear equation. Step 1: A linear equation in two variables $x$ and $y$ must be of the form $Ax + By = C$ where $A$, $B$, and $C$ are c

1. Find the x- and y-intercepts for the linear equations given. 2. For equation 7: \(y-4=0\)

1. The problem states an irregular polygon with sides labeled as $x-2$, $x$, $x-7$, $x-1$, and $x-3$, and the total perimeter is 52 inches. 2. To find $x$, we set up an equation: t

1. The problem asks to analyze and graph the line given by the equation $y = 3x - 6$. 2. First, identify the slope and the y-intercept.

1. **State the problem:** Simplify the expression $$\frac{1 + \sin\theta + i \cos\theta}{1 + \sin\theta - i \cos\theta}$$. 2. **Multiply numerator and denominator by the conjugate

1. Stating the problem: We have the function $$f(x) = \frac{1 + x^{8}}{5x}$$ and we want to understand its properties and simplify it if possible. 2. Simplify the function: The num

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 $