🧮 algebra

1. **State the problem:** We need to find which pair of inequalities matches the graph described. 2. **Analyze the graph:** The graph shows two dashed lines:

1. El problema es completar la tabla para la función $$y = x^2 + 1$$ con los valores dados de $$x$$. 2. La fórmula para esta función es $$y = x^2 + 1$$, donde elevamos $$x$$ al cua

1. **State the problem:** We are given the quadratic form equation $$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$ with $$A=1$$, $$B=-2$$, $$C=1$$, and the discriminant condition $$B^2 - 4

1. **State the problem:** We are given a parabola with specific points and asked to identify its x-intercepts, y-intercept, vertex, and axis of symmetry.

1. **State the problem:** We are given a parabola with certain points and need to find its x-intercepts, y-intercept, vertex, and axis of symmetry.

1. **Problem statement:** Write the equation of a line in slope-intercept form that passes through the points $(-1, 3)$ and $(4, 13)$. 2. **Formula used:** The slope $m$ of a line

1. **State the problem:** We need to find the sum of $\frac{2}{5}$ and 6. 2. **Write the expression:**

1. **State the problem:** A printer prints $\frac{2}{3}$ of a page in $\frac{1}{8}$ of a minute. We want to find how many pages it prints in 1 full minute. 2. **Formula used:** To

1. **State the problem:** Solve the linear equation $3x - y = 7$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by mov

1. **Problem Statement:** Identify the slope and y-intercept of each line. 2. **Part (a):** The line passes through points (-2,-1), (0,1), and (1,2).

1. **State the problem:** Solve the equation $$\frac{x - 4}{2} = \frac{x + 3}{1}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the

1. **State the problem:** We are given two equations to solve for the number $x$. Equation 1: $3x = 45$

1. The problem is to find the value of $N(3)$ given the formula $N(3) = 1000e^{k(3)}$. 2. This formula represents an exponential function where $N(t) = N_0 e^{kt}$, with $N_0$ as t

1. **State the problem:** We need to find three consecutive odd integers whose sum is 51. 2. **Define variables:** Let the first odd integer be $x$. Then the next two consecutive o

1. **State the problem:** We need to find the number of solutions to the system of linear equations: $$6x + 5y = 7$$

1. The problem is to determine how many solutions the system of linear equations has: $$4x + 9y = -2$$

1. **State the problem:** We need to find the number of weeks $x$ when Plant A and Plant B have the same height $y$. 2. **Write the equations:**

1. **State the problem:** Solve the system of linear equations: $$2x + 3y = 16.9$$

1. **State the problem:** Solve the system of linear equations: $$3y = \frac{3}{2}x + 6$$

1. **State the problem:** Solve for $n$ in the equation $$2 - \frac{1}{2}n = 3n + 16$$. 2. **Write down the equation:** $$2 - \frac{1}{2}n = 3n + 16$$.

1. Problem: Simplify $\frac{x^{-4} \cdot x^{3}}{x}$. 2. Use the laws of exponents: $a^{m} \cdot a^{n} = a^{m+n}$ and $\frac{a^{m}}{a^{n}} = a^{m-n}$.