🧮 algebra

1. **State the problem:** Given the input-output pairs of a function: input $3,6,8,n$ and output $6,12,16,\square$, find the output when the input is $n$. 2. **Analyze the pattern:

1. The problem involves understanding the vertical line along the y-axis from -5 to -10. 2. A vertical line along the y-axis means the x-coordinate is constant, specifically $x=0$.

1. The problem asks to determine the coordinates of the vertex of a parabola from its graph. 2. The vertex of a parabola given by the equation $y = ax^2 + bx + c$ is the point wher

1. **State the problem:** We know a satellite travels 70 kilometers in 8 seconds. We want to find the time $t$ it takes to travel 630 kilometers at the same rate.

1. **State the problem:** Graph the inequality $y > x^2 - 8x + 17$. 2. **Rewrite the quadratic in vertex form:** To find the vertex, complete the square for $x^2 - 8x + 17$.

1. **State the problem:** Simplify the expression $5n + 4 - 8n + 7n - 5$. 2. **Combine like terms:** Group the terms with $n$ and the constant terms separately.

1. **State the problem:** Simplify the algebraic expression $5n + 4 - 8n + 7n - 5$. 2. **Combine like terms:** Group the terms with $n$ and the constant terms separately.

1. The problem is to create a picture using at least ten graphed relations, including at least two odd polynomial functions and two even polynomial functions, with proper domain an

1. The problem asks to express the number 25 300 000 in scientific notation. 2. Scientific notation expresses a number as $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an intege

1. **State the problem:** Calculate the value of $2.6 + 0.5 \times \left(1 \frac{3}{4}\right) - \frac{3}{2}$.\n\n2. **Convert mixed number to improper fraction:**\n\n$1 \frac{3}{4}

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

1. **Stating the problem:** Solve the system of linear equations: First system:

1. **Problem statement:** Solve the equation $2(3x + 2) = 2x + 28$. 2. **Distribute:** Apply the distributive property to the left side:

1. **Problem statement:** We are given that on day 1, 2% of the moon's surface is illuminated, and on day 2, 6% is illuminated. We need to predict the day when the illumination rea

1. **Problem Statement:** Identify which function among the options has a different range than the original function $f(x) = x^2$. 2. **Recall the range of $f(x) = x^2$:** The func

1. **State the problem:** We have an exponentially decreasing quantity $Q(t)$ represented by a semilog graph of $\ln Q(t)$ versus $t$. We want to find: (a) The half-life of $Q(t)$,

1. **Stating the problem:** Simplify the expression $$\frac{3^{2} \cdot 7^{3} \cdot x}{7^{8} \cdot 1}$$. 2. **Formula and rules:** When dividing powers with the same base, subtract

1. **State the problem:** We are given the linear equation $$y = \frac{2}{3}x + 1$$ and need to find the y-intercept and the slope. 2. **Recall the slope-intercept form:** The equa

1. **State the problem:** Find the equation of the line passing through the points $(-6, -7)$ and $(6, 7)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1, y_

1. The problem is to solve the equation $$-8 + 5x = 8x + 4$$ for $x$. 2. To isolate $x$, we first want to get all $x$ terms on one side and constants on the other.

1. **State the problem:** Solve the equation $$-8 + 5x = 8x + 4$$ for $x$. 2. **Rewrite the equation:** We want to isolate $x$ on one side. Start by moving all $x$ terms to one sid