🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt[20]{x^{12}}$$ and match it to one of the given options. 2. **Recall the rule for radicals and exponents:** $$\sqrt[n]{x^m}

1. Masalah yang diberikan adalah menyelesaikan persamaan $$\frac{1}{4} (\phi + i0) = \frac{2}{3} \phi - 5$$. 2. Kita akan menyelesaikan persamaan ini untuk mencari nilai $\phi$.

1. The problem is to convert the decimal number 16/3 into a fraction. 2. Note that 16/3 is already a fraction, where 16 is the numerator and 3 is the denominator.

1. **State the problem:** Solve the quadratic expression $m^2 - 10m - 11$ for its roots. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the so

1. **State the problem:** Solve the equation $8r - 12 = -28$ using the bar method. 2. **Understand the equation:** The equation means that when you take $8$ times a number $r$ and

1. Énoncé du problème : Calculer puis simplifier l'expression $A = -\frac{8}{5} + \frac{11}{3}$. 2. Formule et règles importantes : Pour additionner des fractions, il faut un dénom

1. **State the problem:** Solve the linear equation $$2 = 5(5w - 21) - 9(3w - 2)$$. 2. **Apply the distributive property:** Multiply inside the parentheses:

1. **State the problem:** Find the maximum or minimum value of the function $y = x^2 - 8x$ and the corresponding value of $x$. 2. **Formula and rules:** For a quadratic function $y

1. **State the problem:** Sophia wants to buy 2 meals. We need to find the difference between the total prices she would pay at Restaurant A and Restaurant B. 2. **Restaurant A pri

1. **State the problem:** We want to evaluate the infinite nested radical expression $$\sqrt{16 \sqrt[5]{2 \sqrt[16]{\sqrt{2 \ldots}}}}}$$. 2. **Understand the structure:** The exp

1. The problem asks to find the ratio of the change in $x$ to the change in $y$ between two points on a line. 2. From the graph, the two points are approximately $(2,1)$ and $(4,6)

1. Let's start by understanding what a matrix and determinant are. 2. A matrix is a rectangular array of numbers arranged in rows and columns.

1. **Problem:** Simplify $-5(2x + 1) + 2(3x - 2y)$. 2. **Formula and rules:** Use the distributive property $a(b + c) = ab + ac$ to remove parentheses.

1. **Stating the problem:** We are given a sequence of numbers and need to find the pattern or rule governing the sequence. 2. **Analyzing the first sequence:** 4, 21, 12, 36, 108,

1. نبدأ بكتابة الدالة المعطاة: $$f(x) = \frac{x^2 + 2}{x + 5}$$ 2. هذه دالة كسرية حيث البسط هو كثير حدود من الدرجة الثانية والمقام كثير حدود من الدرجة الأولى.

1. مسئله: حل سه سوال داده شده است. 2. سوال اول: \(\sqrt{5 + \sqrt{7}}^3\)

1. The problem asks to solve the equation $$\frac{3x+1}{x-2} = 2$$ for $x$. 2. The formula used here is to solve rational equations by eliminating the denominator: multiply both si

1. Let's solve the equation step-by-step. 2. Suppose the equation is $3x - 5 = 16$.

1. **State the problem:** We need to expand and simplify the expression $$(7-5y)^2$$. 2. **Formula used:** The square of a binomial $(a-b)^2$ is given by the formula:

1. **State the problem:** Evaluate $$\log_2\left(\log_2 82 - \log_{\sqrt{3}} 27 + \log_{\sqrt{10}} 10\right)$$. 2. **Recall logarithm change of base formula:**

1. **Problem statement:** Given the equation $$Ay^2 = (3A - 4)x$$ where $A \in \mathbb{R}$, find the value of $A$ such that the curve passes through the point $(3, -\frac{1}{4})$.