🧮 algebra

1. **State the problem:** We need to find the maximum or minimum value of the quadratic function $$y = -10x^2 + 20x - 5$$. 2. **Recall the formula:** For a quadratic function $$y =

1. **Problem Statement:** Determine how many roots each quadratic equation has. 2. **Recall the quadratic formula and discriminant:** For a quadratic equation $ax^2 + bx + c = 0$,

1. The problem asks to express the number $2.6 \times 10^{-4}$ in ordinary decimal form. 2. The scientific notation $a \times 10^{n}$ means move the decimal point in $a$ by $n$ pla

1. **State the problem:** Solve the quadratic equation $$6x^2 - 7x - 5 = 0$$ using the quadratic formula and round the solutions to 2 decimal places. 2. **Recall the quadratic form

1. সমস্যাটি হলো: একটি সরলরেখার সমীকরণ নির্ণয় করা যা বিন্দু $A(2,3)$ দিয়ে যায় এবং যার ঢাল $m=4$। 2. সরলরেখার সমীকরণ সাধারণত হয়: $$y - y_1 = m(x - x_1)$$ যেখানে $(x_1, y_1)$ হলো

1. প্রশ্ন: ২৬ সংখ্যাটিকে কোন ভিত্তি মৌলিক সংখ্যার সমষ্টি ভাবে কত ভাবে প্রকাশ করা যায়? 2. সূত্র: মৌলিক সংখ্যার সমষ্টি হিসেবে একটি সংখ্যা প্রকাশের জন্য আমরা বিভিন্ন মৌলিক সংখ্যার যো

1. **Problem:** How many ways can the number 27 be expressed as the sum of two prime numbers? 2. **Formula and Rules:** This is related to the Goldbach conjecture for odd numbers,

1. The problem is to identify which trinomials are NOT perfect squares. 2. A perfect square trinomial has the form $$a^2 - 2ab + b^2 = (a - b)^2$$ or $$a^2 + 2ab + b^2 = (a + b)^2$

1. Задача: Обчислити визначник матриці 4x4: $$\begin{vmatrix} 1 & 4 & 8 & 2 \\ 3 & 2 & 1 & 1 \\ 1 & 4 & 2 & -3 \\ 5 & 2 & -1 & 0 \end{vmatrix}$$

1. **State the problem:** Expand and simplify the expression $$(A-2y)(7+2y)$$ and express it in the form $$49 + By^2$$.

1. **State the problem:** Solve the system of equations using row operations to reach echelon or reduced echelon form: $$\begin{cases} x + 2y + z = 1 \\ 2x + 2y + 0 = 2 \\ 3x + 5y

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, we cannot solve it directly. 2. To solve an alge

1. **State the problem:** Solve the system of equations using row operations to reach echelon or reduced echelon form. The system given is: $$x + 2y = 0$$

1. **Identify the numerical coefficient, variable, and constant term in each expression:** - a) $3x + 2$

1. Masalah: Diberikan fungsi kuadrat asli $y = f(x) = x^2$ yang ditranslasi oleh vektor translasi $T = \begin{pmatrix}0 \\ -b\end{pmatrix}$ sehingga diperoleh fungsi bayangan $f'(x

1. **Stating the problem:** We have two linear expressions: $y=5x-1$ and $y=2x+7$. The question asks to "bracket this in one bracket," which means to express the difference or comb

1. **Stating the problem:** We want to analyze the inequalities $2^n > n$ for $n \geq 1$ and $n \geq 2^n$ for all integers $n \geq 4$. 2. **Understanding the inequalities:**

1. **Stating the problem:** Your mother is 12 years more than twice your age. After 8 years, your mother's age will be 3 times your age. We need to find your present age.

1. **Problem Statement:** Given the height function of a bungee jumper $$h(t) = -0.5t^2 + v_0t + h_0$$ with $$v_0=0$$ and $$h_0=210$$ meters, analyze the domain, range, vertex, max

1. **State the problem:** We need to solve the algebraic expression or equation given by the user. Since no specific problem was provided, please provide the problem statement for

1. **Problem Statement:** Simplify the expression $$\frac{2}{3x - 2y} - \frac{3y}{x(3x + 2y)} - \frac{8y}{9x^2 - 4y^2}$$ by performing the subtractions and reducing to the lowest t