🧮 algebra

1. **State the problem:** We have an arithmetic sequence with the first three terms: 7, 5, and $1 - 3x$. We need to find the value of $x$ and the next term in the sequence. 2. **Re

1. **Problem Statement:** We have two ellipses on a Cartesian plane: one gray ellipse representing a function $f(x)$ and one black ellipse representing a function $g(x)$. The black

1. **Stating the problem:** We need to find the sum of the fractions $\frac{3}{25} + \frac{1}{2} + \frac{7}{10} + \frac{3}{5} + \frac{11}{50}$.\n\n2. **Find a common denominator:**

1. **State the problem:** We need to find the slope of the highlighted line segment on the graph, which represents the helicopter descending at a constant rate. 2. **Recall the slo

1. **State the problem:** We are given the equation $8d + 1 = -8$ and asked to analyze the related equation $10c - 3 = 8$. 2. **Solve for $d$ in the first equation:**

1. The problem is to find the domain of a function, which means determining all possible input values ($x$) for which the function is defined. 2. The domain depends on the type of

1. **State the problem:** Simplify the function $f(x) = \frac{x^{3} + 2x^{2}}{x^{2} - 1}$. 2. **Recall the formula and rules:** To simplify a rational function, factor numerator an

1. The problem is to simplify the expression or equation given by the user. 2. Since the user did not provide a specific expression, I cannot simplify anything without the original

1. Find the 16th term of the sequence 9, 16, 23, 30. The sequence is arithmetic with first term $a_1=9$ and common difference $d=16-9=7$.

1. **State the problem:** We need to find the 20th term of an arithmetic sequence where the 3rd term is 19.6 and the 7th term is 48.8. 2. **Recall the formula for the nth term of a

1. The problem is to simplify the fraction $\frac{2}{4}$. 2. The formula for simplifying fractions is to divide the numerator and denominator by their greatest common divisor (GCD)

1. **State the problem:** Simplify the expressions and determine which can be simplified to $a^6$. 2. **Recall the laws of exponents:**

1. The problem is to find the nth term formula for each linear sequence given. 2. The formula for the nth term of a linear sequence is generally $$a_n = dn + c$$ where $d$ is the c

1. **State the problem:** Simplify the expression $$0.5(-6y + 10) + 0.7y$$. 2. **Apply the distributive property:** Multiply 0.5 by each term inside the parentheses:

1. **State the problem:** Simplify the expression $-0.3(2v - 7) + 0.3v$. 2. **Apply the distributive property:** Multiply $-0.3$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $-5d - 5(-0.8d - 0.7)$. 2. **Apply the distributive property:** Multiply $-5$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $3u - 10(10u - 10)$. 2. **Apply the distributive property:** Multiply $-10$ by each term inside the parentheses:

1. **State the problem:** Solve the equation $$\sqrt{7 + x} + 2 = \sqrt{3 - x}$$ for $x$. 2. **Isolate one square root:** Subtract 2 from both sides:

1. **State the problem:** Simplify the expression $9(-7t + 4t - 10) - 9t$. 2. **Apply the distributive property:** Multiply 9 by each term inside the parentheses.

1. **State the problem:** Solve the equation $$16x + 16 = x^2 + 2x + 1$$. 2. **Rewrite the equation:** Notice that $$x^2 + 2x + 1 = (x + 1)^2$$, so the equation becomes:

1. **State the problem:** Simplify the expression $8(-6f - 9) + 2(9f + 2)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.