🧮 algebra

1. **State the problem:** We have a mixture of juices with ingredients Apple, Orange, and Cranberry in the ratio 4:3:1, and the total amount of juice is 48 cups. 2. **Formula and r

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Four friends bought 4 large iced coffees for 18. We need to find the cost of each coffee, how many coffees can be bought with 35, and the cost of 9 coffee

1. **State the problem:** Elena swam 14 laps in 10 minutes, and Ava swam 28 laps in 35 minutes. We need to find Elena's swimming rate in laps per minute and Ava's time per lap in m

1. **Problem Statement:** We have the export function $$E(P) = P - 10000$$ where $$P \geq 10000$$ and $$P$$ represents production in thousands of avocados.

1. **Problem 1: Sunny and Rainy Days** Last month, there were 4 sunny days for every rainy day, and the month had 30 days total. We want to find how many days were rainy.

1. **Problem 1: Red and Yellow Paint Ratio** We have a tape diagram showing 3 cups of red paint repeated 3 times and 3 cups of yellow paint repeated 2 times.

1. **State the problem:** We are given the proportion $$\frac{a}{b} = \frac{c}{d}$$ and need to find the missing values for two cases. 2. **Recall the formula:** In a proportion $$

1. The problem gives two functions: $f(x) = 3 - x^2$ and $g(x) = x + 1$. 2. We can analyze these functions individually or perform operations like addition, subtraction, multiplica

1. **State the problem:** Solve the equation $5^{\sqrt{x+5}} = 25^{x+5}$ for $x$. 2. **Rewrite the equation with the same base:** Note that $25 = 5^2$, so rewrite the right side as

1. **State the problem:** Solve for the missing variable in the ratio equation $$\frac{a}{b} = \frac{c}{d}$$ given values for three variables and rounding to the nearest hundredth.

1. The quadratic formula is used to solve quadratic equations of the form $ax^2 + bx + c = 0$. 2. The formula is given by:

1. **State the problem:** Solve the equation $5^{\sqrt{x+5}} = 25^{x+5}$ for $x$. 2. **Rewrite the bases:** Note that $25 = 5^2$, so rewrite the right side as $25^{x+5} = (5^2)^{x+

1. **State the problem:** We need to analyze the inequality $$y \geq x^2 + 6x + 4$$ which describes the region where the value of $y$ is greater than or equal to the quadratic expr

1. The problem involves analyzing and understanding a system of inequalities: 3) $y < |x-1|^{-4}$

1. The problem is to solve the inequality $y \geq x^2 + 6x + 9$. 2. This inequality means we want to find all points $(x,y)$ where the value of $y$ is greater than or equal to the

1. **Stating the problem:** Solve the equation $$2x^2 - 5x + 3 = 0$$ for $x$. 2. **Formula used:** For quadratic equations of the form $$ax^2 + bx + c = 0$$, the solutions are give

1. The user clarified that the variable is $y$, not $j$. 2. This means any equations or expressions should use $y$ as the variable.

1. **State the problem:** Solve the equation $2\log(3x+2) = \log(121)$.\n\n2. **Recall the logarithm properties:** The equation involves logarithms with the same base (assumed base

1. **State the problem:** Mitchell has scored 51 points so far this season. He plans to score 27 points in each of the next 7 games. If he does, he will break the record by 1 point

1. **Stating the problem:** We have several equations and expressions involving multiplication, division, and addition with unknowns represented by blanks. We need to find the valu