🧮 algebra

1. **State the problem:** A rower travels upstream at 6 km/h and back downstream at 10 km/h. The total journey takes 48 minutes. We need to find the distance upstream. 2. **Define

1. **State the problem:** Find the equation of the line passing through the point $(-6, 3)$ and perpendicular to the line given by $6x - 5y = 5$. 2. **Rewrite the given line in slo

1. **State the problem:** Simplify the expression $$6 \cdot \left(\frac{1}{6} + \frac{3}{7}\right) + \frac{2}{7}$$. 2. **Use the distributive property:** Multiply 6 by each term in

1. **State the problem:** Determine if $x=43$ is a solution to the equation $$16 = x - 27$$ 2. **Write the equation and substitute the value:** Substitute $x=43$ into the equation:

1. Problem: Determine if $k=32$ is a solution to $k + 19 = 51$. 2. Substitute $k=32$ into the equation:

1. **State the problem:** Solve the linear equation $2x + 5 = 9$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtra

1. **State the problem:** We need to analyze the function $$y=\frac{(x+2)^3}{(x+1)^2}$$. 2. **Recall the formula and rules:** This is a rational function where the numerator is $(x

1. **State the problem:** We need to add the two fractions $$\frac{5}{n+5} + \frac{4n}{2n+6}$$.

1. **State the problem:** Simplify the expression $$6 - \frac{x + 5}{(7x - 5)(x + 4)}$$. 2. **Identify the formula and rules:** To simplify, we need to combine terms by finding a c

1. **State the problem:** Solve the expression $$\left(\frac{2}{7} + \frac{1}{3}\right) + \frac{2}{3}$$ using properties and mental math. 2. **Recall the formula and rules:** To ad

1. The problem is to make the letter in the brackets, which is $a$, the subject of the formula from the equation $k = 4a - b$. 2. Start with the original equation:

1. The problem is to express a function in the form $f(x)$. 2. A function $f(x)$ represents a rule that assigns each input $x$ to exactly one output.

1. **State the problem:** We need to find a polynomial function that matches the given graph with roots approximately at $x = -2$, $x = 0$, and $x = 4$. The graph passes through th

1. **State the problem:** Solve the inequality $ (x-2)^2 \leq 0 $. 2. **Recall the property of squares:** For any real number $a$, $a^2 \geq 0$ and $a^2 = 0$ if and only if $a=0$.

1. **State the problem:** We need to find how many milligrams of vitamin C are in 1 serving of orange juice and cranberry juice. 2. **Formula:** To find the amount of vitamin C per

1. **State the problem:** Simplify the expression $$\left(-\frac{3}{7} + \frac{1}{3}\right) - \left[ 2 - \left(3 - \frac{1}{7}\right) + \left(1 - \frac{7}{3}\right) \right].$$ 2. *

1. **State the problem:** Darin mows 90 lawns in 45 hours. We want to find how many hours it will take to mow 12 lawns at the same rate. 2. **Identify the formula:** Since the lawn

1. **State the problem:** Howard has golf lessons for Driver every 5 days, Putter every 6 days, and Sand Bunker every 8 days. He had all three lessons on the same day. We need to f

1. **State the problem:** Solve the equation $2x + 5 = 9$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 5 fr

1. **State the problem:** Calculate the percentage of the pizza that is cheese. 2. **Formula:** Percentage of a part = $\frac{\text{part}}{\text{whole}} \times 100$%

1. The problem asks which of the three curves (green, red, blue) is NOT a function. 2. Recall the definition of a function: For each input $x$, there must be exactly one output $y$