🧮 algebra

1. **Problem:** Find the distance between the pair of parallel lines given by the equations: $$y = 7$$ and $$y = -1$$

1. **State the problem:** We are given two expressions:

1. **State the problem:** Evaluate the division of fractions $$\frac{2}{7} \div \frac{8}{3}$$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by i

1. **State the problem:** Evaluate the division of fractions $\frac{4}{3} \div \frac{7}{8}$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its

1. **State the problem:** Evaluate the division of fractions $$\frac{3}{5} \div \frac{1}{9}$$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by i

1. **State the problem:** We need to evaluate the division of two fractions: $$\frac{5}{4} \div \frac{3}{5}$$. 2. **Recall the rule for dividing fractions:** To divide by a fractio

1. The problem asks which expression is equal to $\frac{6}{7}$.\n\n2. Let's analyze each option:\n\n- A: $6 - 7 = -1$, which is not equal to $\frac{6}{7}$.\n- B: $6 \times 7 = 42$,

1. **State the problem:** Add the fractions $\frac{4}{6}$ and $\frac{4}{8}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. The problem is to multiply the mixed number $2 \frac{3}{4}$ by the fraction $\frac{4}{5}$. 2. First, convert the mixed number to an improper fraction.

1. **State the problem:** Yoko's Coffee Shop makes a blend of two types of coffee: Type A costs 4.05 per pound, Type B costs 5.80 per pound. The total blend is 158 pounds and costs

1. **State the problem:** We are given a proportional relationship between the size of Tammy's garden $x$ (in square feet) and the number of carrots $y$ she can grow, modeled by th

1. **State the problem:** We are given a proportional relationship between the size of Tammy's garden $x$ (in square feet) and the number of carrots $y$ she can grow.

1. **State the problem:** Simplify the expression $8y + 6x - 4y$. 2. **Identify like terms:** Terms with the same variable can be combined. Here, $8y$ and $-4y$ are like terms, whi

1. **State the problem:** We need to find the total cost of 3 pens and 2 boxes. 2. **Given information:**

1. **State the problem:** Find the rate of interest per annum when the simple interest (SI) on 800 for 3 years is 54. 2. **Formula for simple interest rate:**

1. **Nêu bài toán:** Cho đa thức $M = 3x^{2}y - 2xy + 3$ và $N = x^{2}y + xy - 3$. Tính đa thức $P = M + N$ và giá trị của $P$ khi $x = -4$ và $y = 2$. 2. **Công thức và quy tắc:**

1. **State the problem:** Solve the inequality \(\left|\frac{1}{2}w - \frac{3}{4}\right| < 2\). 2. **Recall the rule for absolute value inequalities:**

1. **Problem Statement:** Michelle bought 20 jars for 3500 with a 15% discount and sold 10 jars for 1800 and the remaining 10 jars at 185 each. Find the profit percent. 2. **Formul

1. **Problemstellung:** Wir sollen den Schnittpunkt der Graphen von $f(x) = x^2$ und $g(x) = 4x - 4$ berechnen. 2. **Formel und Vorgehen:** Der Schnittpunkt zweier Funktionen liegt

1. **Problemstellung:** Berechne die Schnittpunkte der Graphen von $$f(x) = x^2 - 3x + 7$$ und $$g(x) = x + 2$$. 2. **Gleichung aufstellen:** Die Schnittpunkte liegen dort, wo $$f(

1. **State the problem:** Solve for $a$ in the equation $$4a + 5 = 2 + 3.25a$$. 2. **Write down the formula and rules:** To solve for $a$, we need to isolate $a$ on one side of the