🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{3b^4 c^9 a - 15b^{10} c^2 a + 3b^4 c^5 a^2 + 24b^4 c^3}{3b^4 c^2}$$. 2. **Recall the division rule for exponents:** When d

1. The problem is to simplify the expression $25 - (16 \times \frac{8}{9})$. 2. According to the order of operations, we first calculate the multiplication inside the parentheses.

1. Stating the problem: Calculate the value of the expression $25 - (-16 \times 8 \div 9)$.\n\n2. Recall the order of operations: multiplication and division are performed before a

1. **State the problem:** Calculate $2^5 - (3^2 - 2^3)$.\n\n2. **Recall the order of operations:** Evaluate exponents first, then parentheses, then subtraction.\n\n3. **Calculate e

1. **State the problem:** Factorize the quadratic equation $6t^2 - 16t + 10 = 0$. 2. **Recall the factoring formula:** For a quadratic $at^2 + bt + c = 0$, we look for two numbers

1. **State the problem:** Simplify the expression $64-(9-16)$. 2. **Recall the order of operations:** Parentheses first, then subtraction.

1. Stating the problem: Calculate $$\left( \frac{3}{4^{-1}} + \frac{5}{3^{-2}} \right) \cdot 19^{-1}$$ and determine which option (A, B, C, or D) matches the result. 2. Recall the

1. Problem: Identify the transformation from the parent function $f(x) = x^2$ to $g(x) = (x + 7.5)^2$. 2. Formula: The parent function is $f(x) = x^2$. A transformation of the form

1. **State the problem:** A population increases by 5% each year. We need to find the total percentage increase after two years. 2. **Formula used:** When a quantity increases by a

1. **Stating the problem:** Calculate the value of the expression $$\frac{1 - 2^{-1} - 3^{-1}}{1 + 2^{-1} + 3^{-1}} \cdot 11$$. 2. **Recall the rules:**

1. The problem is to solve the equation shown in the image: $$\frac{2x+3}{x-1} = 4$$. 2. The formula used here is to solve rational equations by eliminating the denominator: multip

1. **State the problem:** Given $a=5+2\sqrt{6}$ and $b=\frac{1}{a}$, find $a^2 + b^2$. 2. **Recall the formula:** We want to find $a^2 + b^2$ where $b=\frac{1}{a}$.

1. The problem is to evaluate $-2$ raised to the power of 2, which is written as $-2^2$. 2. According to the order of operations, exponents are evaluated before applying the negati

1. The problem is to evaluate $(-2)^2$. 2. The formula for exponentiation is $a^n = a \times a \times \cdots \times a$ ($n$ times).

1. **State the problem:** Given $a=5+2\sqrt{6}$ and $b=\frac{1}{a}$, find $a^2+b^2$. 2. **Recall the formula:** We want to find $a^2 + b^2$. Since $b=\frac{1}{a}$, we can write $a^

1. **Problem:** Graph the function $f(x) = e^x$ and find its domain and range. 2. **Formula and rules:** The function is an exponential function of the form $f(x) = e^x$, where $e$

1. The problem is to evaluate $-100^0$. 2. According to the rules of exponents, any nonzero number raised to the power of 0 is 1.

1. **State the problem:** Jonny, Nathan, and Ali share candy canes in the ratio 4 : 2 : 3. Ali has 12 candy canes. We need to find how many candy canes Jonny has. 2. **Understand t

1. **Problem statement:** Priya and Khan share ping pong balls in the ratio 3 : 5. Khan has 45 ping pong balls. We need to find the number of ping pong balls Priya has and match th

1. **State the problem:** Priya and Khan share ping pong balls in the ratio 3 : 5. Khan has 45 ping pong balls. We need to find the values corresponding to the numbers 1, 2, 3, and

1. **State the problem:** Kerry and Stuart share Pokemon cards in the ratio 5:3. Stuart has 30 cards. We need to find how many cards Kerry has. 2. **Understand the ratio:** The rat