🧮 algebra

1. **State the problem:** We are given an arithmetic sequence: -16, -11, -6, -1, ... We need to find an explicit formula for the $n^{th}$ term $a_n$.

1. The problem asks us to find the explicit formula for the $n^{th}$ term $a_n$ of the arithmetic sequence: 12, 19, 26, 33, ... 2. An arithmetic sequence has a constant difference

1. **Stating the problem:** We are given the center of a circle at coordinates $(2a, a - 7)$ and a point on the circle $(11, -9)$. The diameter of the circle is $10\sqrt{2}$ units.

1. The problem is to graph the linear inequality $y > 2x - 4$. 2. The inequality represents all points $(x,y)$ where the $y$-value is strictly greater than the line $y = 2x - 4$.

1. Énoncé du problème : Comparer $a$ et $\frac{1}{a}$ pour $a > 0$. 2. Justification de l'identité : Montrons que

1. **Stating the problem:** Simplify the products of powers with the same base: $5^3 \cdot 5^2$, $(-6)^2 \cdot (-6)^7$, and $7^3 \cdot 3^7$.

1. **State the problem:** There are 400 students in Maureen's high school, and 90% of them are taking Spanish. We need to find how many students are taking Spanish. 2. **Formula us

1. **State the problem:** Shelby's Cafe sold 80 espressos in total, and 20% of them were single-shot. We need to find how many single-shot espressos were sold. 2. **Formula used:**

1. **State the problem:** Kendrick received 90 pins in total, and 70% of them were orange. We need to find how many orange pins he received. 2. **Formula used:** To find a percenta

1. **State the problem:** Milton read 28% of his book on Friday and 46% on Saturday. The book has 350 pages. We need to find how many pages Milton will read on Sunday to finish the

1. **State the problem:** Mr. Jamison wants to buy art supplies: 8 dozen sketch pencils, 6 dozen colored pencils, and 3 dozen art gum erasers. We need to find the total cost includ

1. Statement of the problem: Find the equation of the line in slope-intercept form that passes through the points $(-1, 7)$ and $(4, -8)$. 2. Formula: Use the slope formula $m = \f

1. Stating the problem. Solve for $x$ in the linear equation $3x + 5 = 20$.

1. **State the problem:** Find the equation of the line passing through the points $(-2, -3)$ and $(2, 1)$ in slope-intercept form. 2. **Formula for slope:** The slope $m$ of a lin

1. **State the problem:** Calculate the value of the expression $$19 \div (3.75 - | - \frac{4}{8} |) \cdot 3^3$$. 2. **Recall the rules:**

1. **State the problem:** Evaluate the expression $$31 + (7.8 - | - 1 \frac{3}{5} |) \cdot (-3)^2 - 7 \frac{3}{5}$$. 2. **Convert mixed numbers to decimals:**

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$ and draw its graph. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two n

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **Problem:** For the pair of functions $f(x) = \frac{1}{x}$ and $g(x) = x$, identify one characteristic they share and one that distinguishes them. 2. **Common characteristic:**

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the slope, y-intercept, and equation of the line. 2. **Recall the formulas:**

1. **State the problem:** We are given a line graph with points (1, 6) and (4, 30). We need to find the slope, y-intercept, and equation of the line. 2. **Formula for slope:** The