🧮 algebra

1. **State the problem:** Simplify the expression $2\sqrt{48} - \frac{6}{\sqrt{3}}$. 2. **Recall the rules:**

1. **State the problem:** We need to find the number of adults at a funfair given relationships between adults, boys, and girls.

1. **Stating the problem:** We are given the quadratic function $$y = -\frac{1}{2}x^2 - x + 1$$ and need to analyze its properties.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we need to undo the operations applied to it. Here, $x$

1. **State the problem:** We are given the quadratic function $$y = -\frac{1}{2}x^{2} - x + 1$$ and need to analyze its properties. 2. **Formula and rules:** A quadratic function i

1. The problem is to simplify the expression $$\sqrt[4]{256} \cdot 81$$. 2. Recall that the fourth root of a number $a$ is a number $b$ such that $b^4 = a$.

1. **State the problem:** Simplify the cube root of the fraction $\frac{27}{8}$, written as $\sqrt[3]{\frac{27}{8}}$. 2. **Recall the property of cube roots:** The cube root of a f

1. **State the problem:** We have a sequence defined by the recurrence relation $$u_{n+3} = u_n + 2$$ with initial values $$u_1 = 0$$, $$u_2 = 1$$, and $$u_3 = 5$$. We need to find

1. **State the problem:** Simplify the radical expression $$\sqrt[3]{\frac{81x^{2}y^{8}}{3x^{8}y^{2}}}$$ and find which option is equivalent. 2. **Write the expression inside the c

1. **State the problem:** We are given the quadratic function $y = -4x^2 + 32x - 57$ and need to analyze it. 2. **Formula and rules:** A quadratic function is generally written as

1. **State the problem:** We are given the quadratic function $y = -4x^2 + 32x - 57$ and need to analyze it. 2. **Formula and rules:** A quadratic function is generally written as

1. The problem asks to simplify the expression $2\sqrt{3\sqrt{x^5}}$ using rational exponents. 2. Recall that radicals can be expressed as rational exponents: $\sqrt[n]{a} = a^{\fr

1. Masalah: Tentukan letak dan jenis titik ekstrim parabola untuk fungsi: (a) $y = 3x^2 - 30x + 77$

1. **State the problem:** Simplify the expression $$\frac{\sqrt[4]{x^9}}{\sqrt[4]{x^2}}$$ using rational exponents. 2. **Rewrite radicals as rational exponents:** Recall that $$\sq

1. **State the problem:** We are given the quadratic function $y = -4x^2 + 32x - 57$ and need to analyze it. 2. **Formula and rules:** The general form of a quadratic function is $

1. **State the problem:** Simplify the expression $$(7c + 2)(6c + 3) - (5c - 2).$$ 2. **Use the distributive property (FOIL) to expand the first product:**

1. **State the problem:** Simplify the expression $(-7k + 6) + (4k + 5)(-5k + 5)$. 2. **Use the distributive property:** Expand the product $(4k + 5)(-5k + 5)$.

1. **State the problem:** We are given terms of an arithmetic progression (A.P.): $T_7 = 23$, $T_n = 43$, and $T_{2n} = 91$. We need to find the first term $a$, the common differen

1. **State the problem:** We are given terms of an arithmetic progression (A.P.): $T_7 = 23$, $T_n = 43$, and $T_{2n} = 91$. We need to find the first term $a$, the common differen

1. The problem is to solve the equation without any constraints. 2. Since no specific equation is given, I cannot solve it directly.

1. **State the problem:** Solve the equation $27x = \frac{1}{9}$ for $x$. 2. **Recall the formula and rules:** To isolate $x$, divide both sides of the equation by 27.