🧮 algebra

1. The problem asks to estimate the number of months when the population of guppies and tetras will be the same. 2. From the data, the tetras population at months $n=0,1,2,3,4$ is

1. **State the problem:** Solve for $f$ in the equation $$\frac{f}{3} + 12 = 17.$$\n\n2. **Isolate the term $\frac{f}{3}$:** To isolate $\frac{f}{3}$, subtract 12 from both sides:\

1. The problem is to solve the equation $12 = x$ for $x$. 2. This is a simple algebraic equation where the variable $x$ is already isolated.

1. **State the problem:** We need to find the total gallons of water used per day if 16.8% of the total is 67.2 gallons. 2. **Formula used:** To find the total when a percentage an

1. **State the problem:** Solve each equation for the variable. 2. **Equation 1:** $x - 3 = 11$

1. **State the problem:** Priya has 5 pencils, each of length $x$ inches. When lined up end to end, their total length is 34.5 inches. 2. **Formulate the equation:** Since there ar

1. **State the problems:** Solve the quadratic equations from 29 to 36. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solutions are given

1. The problem is to simplify the expression $X \times 30 \times X \times 15$. 2. We start by recognizing that multiplication is associative and commutative, so we can rearrange th

1. The problem is to understand what 42% means and how to express it as a decimal and a fraction. 2. The percent symbol (%) means "per hundred," so 42% means 42 out of 100.

1. **Problem statement:** We are given a function $f(x)$ with vertical asymptotes at $x = -1$ and $x = 1$, and a horizontal asymptote at $y = 0$. We need to solve the inequality $f

1. **State the problem:** We are given a function $f$ with vertical asymptotes at $x=-2$ and $x=2$, and a horizontal asymptote at $y=0$. We need to solve the inequality $f(x)<0$ us

1. **State the problem:** Solve the linear equation $7x - 8 = 57$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add or subtract

1. El problema consiste en identificar el error en las multiplicaciones dadas en los dos apartados. 2. Para multiplicar polinomios, se debe aplicar la propiedad distributiva: cada

1. **State the problem:** Solve the equation $2x + 4 = 16$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **State the problem:** We are given the function $c(x) = \sqrt{4x + 1}$ and a graph with points including $(0,1)$ that matches this function. We want to confirm or rewrite the e

1. The problem asks to find the improper fraction equivalent to the mixed number $4 \frac{3}{5}$. 2. A mixed number consists of a whole number and a fraction. To convert it to an i

1. **State the problem:** Aron planted vegetables where \(\frac{5}{12}\) were carrots, \(\frac{3}{12}\) were cucumbers, and the rest were tomatoes. We need to find the fraction of

1. The problem asks to find another way to write the fraction $\frac{5}{6}$. 2. The fraction $\frac{5}{6}$ means 5 divided by 6, which can be written as $5 \div 6$.

1. The problem asks which pair of fractions are equivalent. 2. Two fractions are equivalent if their cross products are equal, i.e., for fractions $\frac{a}{b}$ and $\frac{c}{d}$,

1. **State the problem:** Determine the domain on which the function is increasing. 2. **Identify the function:** From the description, the function is a downward-opening parabola

1. The problem asks to determine the domain on which the quadratic function is increasing. 2. The graph is a parabola opening upwards with vertex at approximately $(2, -4)$.