🧮 algebra

1. **State the problem:** Simplify the expression $$(2a^2bc^3)^4$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power:

1. **State the problem:** Simplify the expression $ (2a^2bc^3)^4 $. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power: $

1. **State the problem:** Translate the sentence "The sum of 3 and y is less than or equal to -20" into an inequality. 2. **Identify the sum:** The sum of 3 and y is written as $3

1. **State the problem:** Translate the sentence "Two more than the product of a number and 6 is equal to 7" into an equation using the variable $b$ for the unknown number. 2. **Id

1. **State the problem:** We are given the midpoint M(65.5, 58.5) of segment ST and one endpoint S(66, 19). We need to find the coordinates of the other endpoint T(x, y). 2. **Form

1. **State the problem:** We are given the midpoint $M$ of segment $CD$ with coordinates $(1.5, -12.5)$ and one endpoint $C$ with coordinates $(5, -18)$. We need to find the coordi

1. **State the problem:** We are given the midpoint $M(11.5, 4)$ of segment $VW$ and one endpoint $V(9, 3)$. We need to find the coordinates of the other endpoint $W$. 2. **Formula

1. **State the problem:** We are given the zeros, axis of symmetry, max or min value, and vertex of a quadratic function. We need to verify these characteristics for the first quad

1. **State the problem:** Simplify the expression $$\frac{p}{2} - (q + p - (2 + q))$$ and then substitute $p=2$ and $q=10$. 2. **Write the expression:**

1. The problem is to match parabolas of the form $y = ax^2 + bx + c$ with their $a$-values based on the shape and direction of their graphs. 2. Recall that the coefficient $a$ dete

1. The problem is to match parabolas with their corresponding $a$-values in the quadratic function $y = ax^2 + bx + c$. 2. The value of $a$ determines the direction and steepness o

1. **Problem Statement:** Graph and compare the functions $y = x^2 + 3$, $y = (x + 3)^2$, and $y = x^2$. Identify similarities and differences.

1. **State the problem:** Solve the equation $$\frac{8}{14} = \frac{5}{x}$$ for $x$. 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{a}{

1. **State the problem:** Solve for $x$ in the proportion $\frac{x}{1} = \frac{4}{7}$. 2. **Formula used:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross products are equa

1. **State the problem:** Solve for $a$ in the equation $$\frac{a - 2}{4a + 2} = \frac{1}{2}.$$\n\n2. **Use the cross-multiplication rule:** When two fractions are equal, their cro

1. Problem: Simplify $4\sqrt{6} \cdot \sqrt{15}$. 2. Use the property of radicals: $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$.

1. **State the problem:** The grocer buys 620 kg of onions, correct to the nearest 20 kg, and packs them into bags each containing 5 kg of onions, correct to the nearest 1 kg. We n

1. **State the problem:** Find $\frac{2}{3}$ of $\frac{1}{5}$. This means multiply $\frac{2}{3}$ by $\frac{1}{5}$. 2. **Formula used:** To find a fraction of another fraction, mult

1. **State the problem:** Find half of one-fourth, i.e., calculate $\frac{1}{2}$ of $\frac{1}{4}$. 2. **Formula used:** To find a fraction of another fraction, multiply the two fra

1. **State the problem:** Multiply the fractions $\frac{1}{4}$ and $\frac{4}{5}$.\n\n2. **Formula:** To multiply fractions, multiply the numerators together and the denominators to

1. The problem asks us to multiply the fractions $\frac{1}{3}$ and $\frac{1}{2}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times