🧮 algebra

1. **Problem statement:** Given the function $q = f(t) = 54 - 2.5t$ representing the volume of water in quarts in a sink $t$ seconds after removing the stopper, find the inverse fu

1. The problem is to determine the domain and range of a graph consisting of two pieces: a vertical curve segment from approximately $(-1, -5)$ to $(-1, 2)$ and a short line segmen

1. **State the problem:** Simplify the expression $1 \frac{1}{2} \div \left( \frac{1}{3} + \frac{5}{6} \right) + 2$. 2. **Convert mixed number to improper fraction:**

1. **Problem 1:** Calculate $2 \frac{3}{4} \div \left(\frac{6}{8} - \frac{1}{4}\right) + 1 - 2$. 2. Convert mixed number to improper fraction: $2 \frac{3}{4} = \frac{11}{4}$.

1. The problem is to solve the expression $-8 + 13$. 2. This is a simple addition problem involving integers.

1. **State the problem:** Simplify the expression $\frac{1}{5} + \left(\frac{2}{3} \times \frac{2}{3}\right) \div \frac{5}{8}$.\n\n2. **Recall the order of operations:** Multiplica

1. **State the problem:** Simplify the expression $$2 \left(\frac{1}{2}\right) \div \left(\frac{5}{6} - \frac{1}{3}\right) + 1$$. 2. **Rewrite the expression:** $$2 \times \frac{1}

1. **State the problem:** Write the product $8 \cdot 2 \cdot 2 \cdot 4 \cdot 4 \cdot 4$ using exponential notation. 2. **Understand exponential notation:** Exponential notation exp

1. **Stating the problem:** (a) Find the number $x$ such that 75% of $x$ is 36.

1. **State the problem:** Ahmad's chocolate bar is 74% cocoa, and the total weight is 69 grams. We need to find how many grams of cocoa it contains, rounded to the nearest tenth. 2

1. The problem is to simplify the expression $Ex$. 2. Since $E$ is a constant and $x$ is a variable, the expression $Ex$ is already in its simplest form.

1. The problem states: Forty-five less a number is equal to the product of 3 and the sum of the number and 7. 2. Let the number be $x$.

1. **Énoncé du problème :** Simplifier l'expression rationnelle $$\frac{7}{5a^{2}b} + \frac{3}{2a^{3}} - \frac{1}{b^{2}}$$ et indiquer les restrictions.

1. **State the problem:** Rearrange the equation $$a = b \left( \frac{1}{c} - \frac{1}{d} \right)$$ to isolate $c$. 2. **Start by dividing both sides by $b$ to isolate the parenthe

1. The problem states: "The product of 5 and the sum of -6 and a number is -20." We need to write this as an equation using $x$ to represent "a number."\n\n2. The phrase "the sum o

1. The problem states: "A number added to -6 is -7." We need to write this as an equation using $x$ to represent "a number."\n\n2. The phrase "a number added to -6" means $x + (-6)

1. **State the problem:** Rearrange the equation $$\left(a + \frac{b}{c}\right)(d - e) = f$$ to isolate the variable $a$. 2. **Formula and rules:** To isolate $a$, we need to undo

1. The problem is to simplify and solve the expression $\left(a + \frac{b}{c}\right)(d - e) = f$ for $a$. 2. Start by expanding the left side using the distributive property: $$\le

1. **State the problem:** We need to find the fraction of juice purchased that is orange juice given that out of every 192 containers, 82 are orange juice. 2. **Formula:** The frac

1. **Problem Statement:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and Rules:** To solve rational equations, multiply both sides by the denominator to elim

1. **State the problem:** We are given that 25 states have four-star hotels out of a total of 50 states. We need to find: (a) The fraction of states with at least one four-star hot