🧮 algebra

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.

1. **State the problem:** Solve for $x$ in the equation $3x = 243$. 2. **Understand the equation:** The equation means $3$ multiplied by $x$ equals $243$.

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

1. **State the problem:** Solve the inequality $\frac{4}{x} \geq x$. 2. **Rewrite the inequality:** Multiply both sides by $x$, but remember to consider the sign of $x$ because it

1. **Problem Statement:** Given an arithmetic progression (A.P.) with terms $T_7 = 23$, $T_n = 43$, and $T_{2n} = 91$, find the first term $a$, the common difference $d$, and the t

1. **Problem:** Calculate the value of $20P_3$. 2. **Formula:** The permutation formula is given by

1. **State the problem:** There are 364 first-grade students in total at Park Elementary School. There are 26 more girls than boys. We need to find out how many girls there are. 2.

1. Diberikan fungsi parabola $y = 3x^2 - 30x + 77$. Kita diminta menentukan letak dan jenis titik ekstrimnya. 2. Titik ekstrim parabola terjadi pada titik stasioner, yaitu saat tur

1. **State the problem:** Calculate the value of $-24 + 33$. 2. **Formula and rules:** Addition of integers involves combining their values. When adding a negative and a positive n

1. **State the problem:** We need to find the length and width of a tennis court given that the perimeter is 228 feet and the length is 6 feet longer than twice the width. 2. **Set

1. **State the problem:** We want to analyze the function $$y = \sqrt[3]{x^5}$$. 2. **Rewrite the function using exponents:** The cube root can be expressed as a fractional exponen