🧮 algebra

1. Let's state the problem: We need to solve or analyze the given mathematical expression or equation (please provide the specific problem for detailed steps). 2. The formula or me

1. **State the problem:** Solve the simultaneous equations by elimination method. 2. **General idea:** The elimination method involves adding or subtracting the equations to elimin

1. **State the problem:** We are given two equations: $$x = 5y + 9$$ and $$z = 7x + 12$$. We need to substitute the expression for $x$ from the first equation into the second equat

1. Soal 1a: Carilah himpunan penyelesaian dari pertidaksamaan bertingkat $$2x + 6 \leq 5x - 3 \leq 2x - 9$$. 2. Langkah pertama, pisahkan menjadi dua pertidaksamaan:

1. সমস্যাটি হলো একটি ৩x৩ ম্যাট্রিক্সের শেষ ঘরে কোন সংখ্যা বসবে তা নির্ণয় করা। 2. ম্যাট্রিক্সটি হলো:

1.1 Solve for x in each equation: 1.1.1 Solve $x^2 + x = 12(3)$

1. **State the problem:** Solve the quadratic inequality $$x^2 - x - 12 < 0$$. 2. **Formula and rules:** To solve quadratic inequalities, first find the roots of the corresponding

1. The problem asks to find the center, asymptotes, and vertices of given hyperbolas numbered 1 to 3. 2. For a hyperbola in standard form $$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2

1. **State the problem:** We need to simplify and analyze the function $$w = \left(\frac{1 + 3z}{3z}\right)(3 - z)$$. 2. **Write the formula and rules:** This is a product of a rat

1. **State the problem:** We are given the function $f(x) = 2x^2 + 7$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $f(x) = ax^2 + bx +

1. **State the problem:** Solve the equation $$(y - 3)(x^2 - 8)(5x + 2) = 0$$ for $x$ when $y = 3$. 2. **Substitute the given value:** Replace $y$ with 3 in the equation:

1. **Problem:** Sketch the graph of the hyperbola and find its asymptotes for the equation $x^2 - 5y^2 + 8x + 30y - 54 = 0$. 2. **Rewrite the equation in standard form:** Complete

1. **Problem:** Sketch and analyze the hyperbola given by $$x^2 - 5y^2 + 8x + 30y - 54 = 0$$. 2. **Step 1: Rewrite in standard form.** Group $x$ and $y$ terms:

1. The problem is to solve for the variable $x$ in an equation or expression. 2. To solve for $x$, we need the specific equation or context where $x$ appears.

1. **Stating the problem:** We need to determine which table of values represents a function. 2. **Definition of a function:** A function is a relation where each input $x$ has exa

1. Problem 1: Find two numbers where the sum of their squares decreased by 75 is 50, and their quotient is 2. 2. Let the two numbers be $x$ and $y$. The conditions are:

1. **State the problem:** Multiply the binomials $$(2x + 4)(x - 4)$$ and find the correct expanded form from the options. 2. **Recall the distributive property (FOIL method):** To

1. **State the problem:** Solve the inequality $$10 \leq - \frac{2}{3} (9 + 12b)$$ for $b$. 2. **Write the inequality:** $$10 \leq - \frac{2}{3} (9 + 12b)$$

1. **Problem Statement:** We need to verify the correctness of several mathematical statements and provide reasons.

1. Problem 7: ₦2000 is shared in the ratio 7 : 3 between Faka and Osarentin. 2. To find how much each receives, use the formula for sharing in ratio: If total amount is $T$ and rat

1. Problem: Find the solution set of the equation \( \frac{x}{p(x)} - \frac{x}{r(x)} - 1 = 0 \) where \( p(x) = x - 4 \), \( r(x) = x^2 - 2x - 8 \). 2. Step 1: Write the equation e