🧮 algebra

1. **State the problem:** Solve the equation $$-2y + 1 = -9$$ for the variable $y$. 2. **Isolate the term with $y$:** Subtract 1 from both sides to move the constant term.

1. **State the problem:** Solve the equation $$-8 = 3d + 4$$ for the variable $$d$$. 2. **Isolate the term with $$d$$:** Subtract 4 from both sides to move the constant term.

1. **State the problem:** Simplify the expression $5p^0 + (7p)^0$. 2. **Recall the rule:** Any nonzero number raised to the power of 0 is 1, i.e., $a^0 = 1$ for $a \neq 0$.

1. **State the problem:** Simplify the expression $$\frac{4(x^2 y)^3 \times 2xy^2}{2x^2 y}$$. 2. **Recall the exponent and multiplication rules:**

1. **State the problem:** Simplify the expression $$\sqrt{x} \cdot \sqrt{4x} + \sqrt{100x^2} - \sqrt{9} \sqrt{x}$$. 2. **Recall the properties of square roots:**

1. **State the problem:** We have a population model for coyotes given by $$P = 1024(1.078)^n$$ where $n$ is the number of years since 2005. 2. **Find the initial population in 200

1. **State the problem:** You want to find out how long it takes to read a 540-page book if you read 30 pages per hour. 2. **Formula used:** Time = \frac{Total Pages}{Pages per Hou

1. Let's verify each fraction operation step-by-step. 2. For the first line: $\frac{3}{4} \times \frac{5}{6} = \frac{15}{24} = \frac{5}{8}$ (simplified).

1. **State the problem:** Solve the equation $-4 = h - 20$ for $h$. 2. **Formula and rules:** To isolate $h$, add 20 to both sides of the equation to cancel out the $-20$ on the ri

1. **State the problem:** We need to graph the quadratic function $$y = -x^2 - 10x - 21$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The quadra

1. **State the problem:** Solve the equation $$3.4d = 17.34$$ for the variable $$d$$. 2. **Formula and rules:** To isolate $$d$$, divide both sides of the equation by $$3.4$$.

1. **State the problem:** We need to graph the quadratic function $$y = x^2 + 8x + 7$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The quadratic

1. المشكلة: تبسيط الكسر \( \frac{8}{10} \). 2. القاعدة: لتبسيط كسر، نقسم البسط والمقام على القاسم المشترك الأكبر (GCD).

1. The problem is to find the domain and range of a combined function, which typically means a function formed by operations like addition, subtraction, multiplication, division, o

1. The problem asks to create a function $t(n)$ to model the growth of Lin's tetra population, where $n$ is the number of months since she bought the tetras. 2. From the table, the

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