🧮 algebra

1. **State the problem:** Solve for $y$ in the equation $$\sqrt{25} - 3y = y + 1$$ where $y$ is a real number. 2. **Recall the value of the square root:** $$\sqrt{25} = 5$$ because

1. **State the problem:** We need to solve for the real number $u$ such that $$\sqrt[3]{2u - 8} = \sqrt[3]{7u + 2}.$$ 2. **Use the property of cube roots:** Since cube root is a on

1. **State the problem:** Solve for $v$ in the equation $$\sqrt[4]{3v + 1} + 3 = 5$$ where $v$ is a real number. 2. **Isolate the fourth root:** Subtract 3 from both sides:

1. **State the problem:** We are given three points $(-4,10)$, $(-2,7)$, and $(6,-5)$ on a linear function and need to find which of the given equations matches this relationship.

1. **State the problem:** We have $x$ dimes and $y$ pennies in a jar. 2. **Given:** Total amount of money is $9.16$ dollars and total number of coins is $81$.

1. **State the problem:** Simplify the fraction $\frac{9999}{9999999999999}$.\n\n2. **Recall the formula:** Simplifying a fraction means dividing numerator and denominator by their

1. The problem asks us to determine the nature of the number $\sqrt{9}$. 2. Recall that the square root of a number $x$ is a value that, when multiplied by itself, gives $x$.

1. **State the problem:** Solve the logarithmic equation $$\log_6 x + \log_6 10 = 1$$ for $$x$$. 2. **Recall the logarithm property:** The sum of logarithms with the same base can

1. **State the problem:** Solve the logarithmic equation $$2 \log x = \log (8x - 160) + 1$$ for $$x$$. 2. **Recall logarithm properties:**

1. **State the problem:** Grace wants to compare two cell phone plans based on their monthly cost depending on the number of minutes $x$ used.

1. **State the problem:** Harita has to memorize a total of $90$ measures. She memorizes $18$ measures every $3$ days. We want to find an equation for $m$, the number of measures l

1. **State the problem:** Sarah has a total of $27$ coins consisting of nickels and quarters, and their total value is $4.75$. We need to find how many nickels and quarters she has

1. **State the problem:** We need to find the value of $x$ from the given context. 2. **Analyze the information:** The user mentions font sizes increasing by 2 at intervals 0, 5, 1

1. **State the problem:** Solve the compound inequality:

1. **State the problem:** Solve the system of inequalities:

1. **State the problem:** Solve the compound inequality $0 < -6 - 2x < 2$. 2. **Use the rule for compound inequalities:**

1. **State the problem:** We have the function $$f(x) = x^2 - x - 1$$ and need to find: (a) $f(a+h)$

1. **State the problem:** We need to find the average rate of change of sales with respect to the number of catalogs distributed over the intervals 15 to 25, 25 to 35, and 35 to 45

1. **State the problem:** We need to find the average rate of change of the function $$f(x) = \frac{1}{x - 4}$$ between $$x = -3$$ and $$x = 3$$. 2. **Recall the formula for averag

1. **State the problem:** We need to find the average rate of change of the function $$f(x) = \sqrt{4x + 1}$$ between $$x = 0$$ and $$x = 2$$. 2. **Recall the formula:** The averag

1. **State the problem:** We need to find the average rate of change of the function $$f(x) = x^2 + 9x$$ between $$x=0$$ and $$x=9$$. 2. **Formula for average rate of change:**