🧮 algebra

1. **State the problem:** We need to find the correct transformation rule for a graph that undergoes the following changes: - Shifted 8 units to the right

1. The problem states that the function $h$ is defined by $h(x) = \frac{1}{x}$ for $x \neq 0$. We are asked to find $h^2(x)$, $h^3(x)$, $h^4(x)$ in simplest form, and then find $h^

1. **State the problem:** Solve the equation $2x - 1 = 67$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operat

1. **State the problem:** Solve the inequality $$1 > -3 \left( \frac{2}{3} x - 4 \right) - 1$$. 2. **Rewrite the inequality:**

1. **State the problem:** Solve the inequality $$1 > -3\left(\frac{2}{3}x - 4\right) - 1$$. 2. **Distribute the -3:**

1. **State the problem:** We want to express the set $$S = \{x \mid 0 \leq x < 3\}$$ in interval notation. 2. **Recall interval notation rules:**

1. সমস্যাটি হলো: একটি দ্রব্যের ক্রয়মূল্য ১০০ টাকা ধরে, বিক্রয়মূল্য ২০% লাভে এবং বিক্রয় কমিশন ১০%। আমাদের জানতে হবে ক্রয়মূল্যের উপর কত শতাংশ বেশি মূল্য তালিকাভুক্ত করা হয়েছে। 2

1. **State the problem:** We are given the function $$F(b) = \frac{b - b^2}{1 + b^2}$$ and need to find the values of $F(0)$, $F(1)$, $F(\frac{1}{2})$, and $F(\tan x)$. 2. **Recall

1. **State the problem:** We need to evaluate the sum $$\sum_{j=2}^{6} (j^3 - 1)$$ which means adding the values of $j^3 - 1$ for $j=2,3,4,5,6$. 2. **Formula and rules:** The summa

1. **Problem statement** Create a $35$–$40$ second vertical $9:16$ TikTok mathematics challenge video for **Math With Olamide**.

1. **State the problem:** Solve the equation $$4 + \frac{1}{2} x + 3 = 10$$ for $$x$$. 2. **Combine like terms:** Add the constants $$4$$ and $$3$$ on the left side.

1. **Problem Statement:** If 20% of a number is 36, find the number.

1. **State the problem:** Solve the equation $$7x - 10x + 18 + 2x = -5$$ for $$x$$. 2. **Combine like terms:** Group the $$x$$ terms together.

1. **State the problem:** We know the selling price after a 25% discount is $1200. We want to find the original price before the discount.

1. The problem asks to simplify the expressions or answers labeled $6$ and $7$. 2. To simplify any algebraic expression, we combine like terms, factor where possible, and reduce fr

1. **State the problem:** Solve the system of equations: $$x + y = 2$$

1. **State the problem:** We are given the graph of $y = f(x)$ and need to find the graph of $y = -f(x - 4) + 1$ by repositioning points. 2. **Understand the transformation:** The

1. **State the problem:** We are given the graph of $y = f(x)$ and need to transform it to the graph of $y = -f(x + 3) + 2$. 2. **Understand the transformations:** The function $y

1. **Problem:** Find the inverse of $f(x) = \sqrt{2x + 1}$ and verify they are inverses. 2. **Step 1: Write the function as an equation:**

1. **State the problem:** Find the equation of the line passing through the points $(1,0)$ and $(2,3)$ in general form. 2. **Recall the formula for slope:** The slope $m$ of a line

1. **State the problem:** We need to determine if the graph of the equation $$y=-7x^3+9x$$ is symmetric with respect to the $x$-axis, $y$-axis, and the origin. 2. **Recall symmetry