🧮 algebra

1. **State the problem:** We are given a line graph with points (1, 6) and (4, 30). We need to find the slope, y-intercept, and equation of the line. 2. **Formula for slope:** The

1. **State the problem:** We have Sam's savings represented by the equation $y = 35x + 10$, where $y$ is the balance and $x$ is the number of weeks. Sam's sister's savings are show

1. **State the problem:** We have a tank with water draining over time. The table shows minutes and gallons remaining: (0,60), (4,50), (8,40), (12,30). 2. **Identify the relationsh

1. **State the problem:** Royce jogs 30 meters in 10 seconds. We want to find how many meters he can jog in 25 seconds. 2. **Formula used:** Since jogging distance is proportional

1. The problem asks us to find the price for 1 pound of grapes given a table of prices for different weights. 2. We observe the table:

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 5$ and draw its graph. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two n

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. The problem involves identifying a 4-letter code from a 3x3 grid of algebraic expressions and numbers. 2. Each box in the grid contains an expression or number:

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+