🧮 algebra

1. **State the problem:** Solve the equation $$\frac{1}{3} + \frac{x + 2}{30} = \frac{x + 12}{10} - 2$$ for $x$ and express the answer as a decimal. 2. **Identify the goal:** We wa

1. The problem is to find the square root of 100. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. The problem is to find the values of $m$ and $k$ given four pairs: $(m=1, k=-5)$, $(m=1, k=5)$, $(m=-5, k=1)$, and $(m=5, k=1)$. 2. Since the pairs are given explicitly, the val

1. **Statement of the problem:** We have two exercises involving functions and polynomials.

1. **State the problem:** We are given points $A(2,5)$, $B(-6,-3)$, and $C(a,1)$. We need to find the possible values of $a$ such that the length of $AB$ is twice the length of $AC

1. **State the problem:** We are given vectors $A = \left[\frac{3}{2}, 2\right]$, $B = \left[\frac{1}{2}, 4\right]$, and $C = \left[a, b, c\right]$ with the equation $2A - 3B = 4C$

1. Let's clarify the problem you are referring to and why the answer might be "1". 2. Often, when a teacher marks "1" as the answer, it could be related to solving an equation, sim

1. **State the problem:** Evaluate the expression $6x + 2y - 4$ when $x = 4$ and $y = -5$. 2. **Write the expression:**

1. The problem is to evaluate the expression $2x^2 + 5x - 2$ when $x = -3$. 2. The formula given is a quadratic expression: $2x^2 + 5x - 2$.

1. **Stating the problem:** We are given the system of equations: $$x + y = 25$$

1. **State the problem:** Evaluate the expression $6x + 10$ when $x = 5$. 2. **Formula and explanation:** The expression is a linear algebraic expression where $x$ is a variable. T

1. **State the problem:** We are given the equation $x + y = 24$ and need to understand its properties or solve for one variable in terms of the other. 2. **Formula and rules:** Th

1. **State the problem:** Solve the quadratic equation $x^2 + 24x - 48 = 0$. 2. **Formula used:** The quadratic formula is given by

1. The first problem asks to expand the sigma notation $$\sum_{i=1}^5 \frac{2^2}{i}$$ into a series. 2. The formula for sigma notation expansion is to substitute each integer value

1. The problem asks to represent the series $4^2 + 5^2 + 6^2 + 7^2$ in sigma notation. 2. Sigma notation is a concise way to write sums using the Greek letter $\Sigma$. The general

1. The first problem asks to represent the series $(1+2) + (2+2) + (3+2) + (4+2) + (5+2)$ in sigma notation. 2. Notice each term is of the form $i + 2$ where $i$ runs from 1 to 5.

1. **Stating the problem:** We have a grid with letters and numbers, and we want to find what numbers the letters represent based on the patterns in the table. 2. **Observing the t

1. Problem: Solve the equation $\frac{x}{3} = \frac{5}{x} + 8$ to find $x$. Formula: Cross multiply to clear denominators: $x \cdot x = 3(5 + 8x)$.

1. The problem states the equation $y^3 + z^3 = k$. 2. This is a cubic equation involving two variables $y$ and $z$, and a constant $k$.

1. **Problem 19:** Find the equation of combined variation where $y$ varies directly as $x$ and inversely as $z$, given $y=6$ when $x=8$ and $z=4$. Then find $y$ when $x=12$ and $z

1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} x+2 & \text{if } x<0 \\ x^2 & \text{if } x \geq 0 \end{cases}$$