🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{27.5 \times 10^{-3}}{28} \Big/ \left( \frac{27.5 \times 10^{-3}}{28} + \frac{180}{18} \right)$$. 2. **Rewrite the expressi

1. **State the problem:** We have a set of 7 consecutive odd numbers. 2. Let the smallest odd number be $x$. Then the numbers are: $x, x+2, x+4, x+6, x+8, x+10, x+12$.

1. The problem is to simplify the expression $$\frac{48 \times 18}{(18 \times 46) + (36 \times 92)}$$. 2. First, calculate the numerator: $$48 \times 18 = 864$$.

1. **State the problem:** Simplify the expression $$(2a^6 - 6a^3)^2$$. 2. **Recognize the form:** This is a square of a binomial, so we use the formula $$(x - y)^2 = x^2 - 2xy + y^

1. Stating the problem: Simplify the expression $$(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)$$. 2. Notice the expression is of the form $$(a+b)(a-b)(a+b)(a-b)(a+b)(a-b)$$ whi

1. Stating the problem: We want to simplify the expression $(4+3c^5)(4-3c^5)$.\n\n2. This expression is in the form of $(a+b)(a-b)$, which is a difference of squares formula: $$ (a

1. The problem is to expand the expression $$(4+7a^2)^2$$. 2. Use the formula for the square of a binomial: $$(x+y)^2 = x^2 + 2xy + y^2$$ where here $x=4$ and $y=7a^2$.

1. **Stating the problem:** Simplify the expression $$(7b^5 - 4b)(7b^5 + 4b)$$. 2. **Recognize the pattern:** This is in the form of $$(x - y)(x + y) = x^2 - y^2$$ where $$x = 7b^5

1. We are asked to add the fractions $\frac{3}{2}$ and $\frac{25}{16}$. 2. To add fractions, they must have a common denominator. The denominators here are 2 and 16.

1. **State the problem:** Given the expansion of $$(ax - 2)^4 \left(1 + \frac{b}{x}\right)^3$$ written in descending powers of $x$, the first three terms are $$81x^4 + 999x^3 + cx^

1. Stating the problem: We need to find a solution to the user's math question. However, no explicit problem statement was provided. 2. Since the user only asked for a "correct sol

1. Stating the problem: We need to simplify each expression under the square root, breaking it down into factors with perfect squares and variables with even powers so we can simpl

1. The problem is to simplify the expression $\frac{-5}{2} \times \frac{1}{2}$.\n\n2. Multiply the numerators together: $-5 \times 1 = -5$.\n\n3. Multiply the denominators together

1. We are given the system of equations: $$\begin{cases} x + 2y + z = 7 \\ x + \alpha z = 11 \\ 2x - 3y + \beta z = \gamma \end{cases}$$

1. The problem is to factor the quadratic expression $9x^2 + 5x - 80$. 2. We look for two numbers that multiply to $9 \times (-80) = -720$ and add to $5$.

1. The problem states: Find the range of the relation $R_2 = \{(1,0),(2,2),(3,2),(4,2)\}$.\n\n2. The range of a relation is the set of all possible output values (second elements)

1. نبدأ بكتابة الدالة المعطاة: $$k(x) = 8 - 3\sqrt{x} + 2$$

1. Let's start by understanding what domain and range mean. The domain of a relation is the set of all possible input values (x-values), and the range is the set of all possible ou

1. **Problem:** Sheila has 25000 to invest and wants to earn 12000 interest at 5.8% per year. Find the time (years). 2. **Formula for simple interest:** $$I = P \times r \times t$$

1. **State the problem:** We are given a straight line when plotting $e^y$ against $x^2$, with gradient $-3$ passing through $(4.30,5.85)$. We need to: (a) Find $y$ in terms of $x$

1. **State the problem:** We have a plot of $e^y$ versus $x^2$ that forms a straight line with gradient $-3$. The line passes through the point $(4.30, 5.85)$. We need to find (a)