🧮 algebra

1. The problem is to simplify the expression $5 \div \frac{2}{3}$. 2. Division by a fraction is the same as multiplication by its reciprocal. The reciprocal of $\frac{2}{3}$ is $\f

1. **State the problem:** Solve the equation $$4^{x-2} = \frac{1}{8}$$ for $x$. 2. **Recall the bases:** Note that $4$ and $8$ can be expressed as powers of $2$:

1. **State the problem:** Solve the equation $$3^x = \frac{1}{27}$$ for $x$. 2. **Recall the properties of exponents:** We know that $27 = 3^3$, so $$\frac{1}{27} = 3^{-3}$$ becaus

1. **Problem Statement:** We know that when a polynomial $f(x)$ is divided by $x - 1$, the remainder is $R$. We want to find the remainder when $f(x + 1)$ is divided by one of the

1. **State the problem:** We have a polynomial $$f(x) = ax^4 + 8x^3 + 8b + 7$$ where $$a$$ and $$b$$ are constants.

1. **Problem:** In an examination, 42% of students failed in Mathematics and 52% failed in English. If 17% students failed in both subjects, find the percentage of those students w

1. The problem is to evaluate the expression $$-\sqrt{(3 - 9.69)^2}$$ given the numbers 0.144 and 9.69. 2. Recall the formula for the square root of a square: $$\sqrt{x^2} = |x|$$,

1. The problem is to evaluate the expression $3-(4,6)^2$. 2. First, clarify the notation: $(4,6)$ typically represents a point or vector, but here it seems to be a typo or misuse.

1. **Problem statement:** Given sets $A = \{3, 7, a^2\}$ and $B = \{2, 4, a+1, a+b\}$ with all elements integers, and $A \cap B = \{4, 7^2\}$, find: a) values of $a$ and $b$

1. **State the problem:** Solve the equation $x - 3 - 3x(x - 3) = 0$ for $x$. 2. **Rewrite the equation:** The equation is $x - 3 - 3x(x - 3) = 0$.

1. **Stating the problem:** Solve the equation $$x^3 - x^3 - x^3 = 0$$. 2. **Simplify the expression:** Combine like terms:

1. प्रश्न समजून घेऊया: 90 ते 180 अंकांची सरासरी आणि 80 ते 160 अंकांची सरासरी यामध्ये फरक किती आहे हे शोधायचे आहे. 2. सरासरी काढण्याचा सूत्र: $$\text{सरासरी} = \frac{\text{एकूण बेरी

1. **Problem Statement:** Solve the quadratic equation $x^2 - 5x + 6 = 0$ and sketch its graph. 2. **Formula Used:** The quadratic equation $ax^2 + bx + c = 0$ can be solved using

1. The problem is to find which number line model represents the expression $3 \frac{1}{2} + (-6)$. 2. First, convert the mixed number to an improper fraction or decimal: $3 \frac{

1. **State the problem:** Solve the equation $$4x + (5x - (6x - (7x - (8x - 9)))) = 10$$ for $x$. 2. **Understand the problem:** This is a nested expression with multiple parenthes

1. **Problem Statement:** Find the domain and range of the function $f(x) = \sqrt{4 - x^2}$.\n\n2. **Understanding the function:** The function involves a square root, so the expre

1. **State the problem:** We want to verify the determinant of the 3x3 matrix:

1. **State the problem:** Simplify the expression $$\frac{x - x - y + y}{2x^2 + 3xy + y^2} \cdot \frac{y^2 - 4x^2}{2x^2 + xy - y^2}$$. 2. **Simplify the numerator of the first frac

1. The problem is to simplify the expression $\frac{3}{\sqrt{3}}$. 2. The formula used here is to rationalize the denominator, which means to eliminate the square root from the den

1. **Stating the problem:** Andi has an aquarium of size 60 cm x 45 cm x 45 cm.

1. **Stating the problem:** Kita diminta mencari harga dari 5 ikan mas koki, 2 ikan komet, dan 3 ikan molly berdasarkan informasi harga yang diberikan.