🧮 algebra

1. The problem is to evaluate each mathematical expression and then list the results from lowest to greatest. 2. Evaluate each expression step-by-step:

1. Let's clarify the problem: it seems you want to solve an equation or expression involving a logarithm. 2. Recall the main properties of logarithms: for example, $\log_b(xy) = \l

1. **Stating the problem:** We are given several mathematical expressions and asked to list them from lowest value to greatest value. 2. **Evaluate each expression:**

1. **State the problem:** We are given a 3x3 grid of expressions: \[\sum_{i=2}^3 i, \quad e^3, \quad 6! \\

1. The problem is to list a set of numbers from least to greatest. 2. However, the specific numbers to sort have not been provided.

1. The problem asks to select all the squares that contain values which are perfect squares, and then order these values from least to greatest. 2. First, evaluate each expression:

1. Problem: Analyze the polynomial $f(x) = (x + 1)(x - 1)(x - 3)$ of degree 3. - Sum of coefficients: Expand and calculate the values.

1. The problem is to simplify and analyze the expression $$\frac{3^2}{3x-1}$$. 2. First, calculate the numerator: $$3^2 = 9$$.

1. Stating the problem: Calculate the factorial of 6, denoted as $6!$. 2. Factorial definition: The factorial of a positive integer $n$ is the product of all positive integers from

1. The problem asks to find the product of $\frac{3}{4}$ and 5, then multiply the result by $\frac{1}{6}$. 2. First, multiply $\frac{3}{4}$ by 5:

1. We are asked to evaluate the sum \( \sum_{i=2}^{3} 2^i \). 2. This means we need to calculate the values of \(2^2\) and \(2^3\) and then add them together.

1. The problem Q-1 a) asks: If given some values or expressions (not fully provided), find a certain value or expression. Since the full question is not visible, we can illustrate

1. **Stating the problem:** We have the quadratic equation $2x^2 + mx - 2m + 1 = 0$. Its roots are $x'$ and $x''$. We need to find expressions in terms of $m$ for the following:

1. The problem asks to find the cube root of 64. 2. Recall that the cube root of a number $a$ is a number $b$ such that $b^3 = a$.

1. The sigma symbol $\Sigma$ is commonly used in mathematics to denote "summation". 2. It represents the sum of a sequence of terms, typically expressed as:

1. Let's first interpret the expression: $\frac{3}{4} \times 5 \times \frac{1}{6}$. 2. Multiply the fractions and the whole number. To do this, write 5 as a fraction: $\frac{5}{1}$

1. The problem is to find the value of the expression $e^3$. 2. Here, $e$ is the mathematical constant approximately equal to 2.71828.

1. Given matrices $$A = \begin{bmatrix}3 & 2 \\ -1 & 5\end{bmatrix}, B = \begin{bmatrix}2 & -4 \\ 3 & 1\end{bmatrix}$$

1. Stating the problem: Solve the equation $$2=\frac{x}{3x-15}$$ for $x$. 2. Multiply both sides by the denominator $3x-15$ to eliminate the fraction:

1. Problem statement: Solve the quadratic equation $2x^2 - 4x - 6 = 0$. 2. Begin by identifying coefficients: $a = 2$, $b = -4$, $c = -6$.

1. **State the problem:** A missionary mixes 3 kg of premium rice at 60 per kg with 2 kg of regular rice at 40 per kg. We want to find the cost per kilogram of the mixture. 2. **De