🧮 algebra

1. **State the problem:** Solve for $f$ in the equation $$6 = 5 + \sqrt{64} + f$$. 2. **Recall the formula and rules:** The square root of a number $x$ is a value that, when multip

1. **State the problem:** Solve for $d$ in the equation $$-55 + 48\sqrt{d} = 89.$$\n\n2. **Isolate the square root term:** Add 55 to both sides to get $$48\sqrt{d} = 89 + 55.$$\n\n

1. **State the problem:** Solve the system of linear equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the equation $$4(-\frac{1}{4}x + 3) = 6.5$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses:

1. **Evaluate the expression** $8 + 8 \div 8 + 8$. - According to order of operations (PEMDAS), division comes before addition.

1. Evaluate $18 - 3^2 \cdot 2$. First, calculate the exponent: $3^2 = 9$.

1. The problem asks to evaluate four expressions and find the corresponding letter for each answer. 2. Evaluate expression 1: $8 + 4^2 \div 2$

1. **State the problem:** We need to evaluate each of the four expressions and find their values. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplicat

1. **Evaluate** $3 \cdot (7 - 2) - 5$. Start by solving inside the parentheses:

1. **State the problem:** Simplify the expression $$\frac{1B^3}{-3a^3c^3} \cdot \frac{a^2B}{-4B^2}$$. 2. **Write the expression as a single fraction:**

1. **State the problem:** Simplify the expression $$\frac{3x^7 \cdot x^2}{x^9}$$ with no negative exponents. 2. **Use the laws of exponents:** When multiplying powers with the same

1. **State the problem:** We have a 9 by 16 tile plot of land, and each sprinkler waters 24 adjacent tiles. We need to find how many sprinklers are required to water all the tiles.

1. **State the problem:** Solve the quadratic equation $x^2 + 1 = 2x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $$\frac{x-2}{5} = \frac{x}{3}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products

1. Masalah yang diberikan adalah menyelesaikan persamaan linear $$-3x + 2y = 12$$ untuk variabel tertentu atau menulis ulang persamaan tersebut. 2. Kita bisa menyelesaikan persamaa

1. **State the problem:** Simplify the expression $3x - 4x^2 - 9x + 12$. 2. **Group like terms:** Combine the terms with $x^2$, $x$, and constants separately.

1. نبدأ بتحليل العبارة إلى جداء عاملين من الدرجة الأولى. 2. لنفترض أن العبارة هي \( ax^2 + bx + c \).

1. **State the problem:** Simplify the expression $$\frac{\ln(2t) - \ln(8)}{\ln(3) - \ln(2t) + \ln(4)}$$. 2. **Recall logarithm rules:**

1. Let's solve the equation step-by-step as if we were solving a real equation with equal signs and showing all work. 2. Suppose the problem is to solve for $x$ in the equation $2x

1. **State the problem:** Find the quotient and remainder when dividing the polynomial $x^4 - 16x^3 + 4x^2 + 10x - 11$ by a divisor (not specified here, so we focus on understandin

1. The problem is to find the square root of 157. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.