🧮 algebra

1. **Evaluate the expression** $6^{-2} - 4^{-2} - (-8)^{-2} - \frac{1}{36}$ step-byn step. 2. Recall that $a^{-n} = \frac{1}{a^n}$.

1. The problem is to find the function that fits the user's query and to provide a detailed explanation with steps. 2. Here we assume the function is $y=a^x$ with $a>0$ and $a\ne 1

1. **Problem:** GOAL and FCTR are squares. Area of GOAL is given by $$9x^4 - 12x + 4$$ cm² and this area is larger than FCTR's area by $$5x^2 + 8x - 21$$ cm². Find the side length

1. Identifikasi daerah arsiran dan batas-batas sistem pertidaksamaan pada gambar pertama. - Titik-titik penting: (-2,0), (4,0), garis vertikal antara y=2 dan y=4.

1. The problem asks to find the third proportional to the expressions $(x+y)^2$ and $x^2 - xy - 2y^2$. 2. Recall that if $a$, $b$, and $c$ are in proportion, then $\frac{a}{b} = \f

1. The problem is to expand and simplify the expressions $(x+y)^2$ and $x^2-xy-2y^2$. 2. To expand $(x+y)^2$, use the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab +

1. The third proportional to two numbers $a$ and $b$ is a number $x$ such that $\frac{a}{b} = \frac{b}{x}$. 2. This means $x$ satisfies the equation $a \times x = b \times b$.

1. The problem gives two expressions: $(x+y)^2$ and $x^2 - xy - 2y^2$. 2. First, let's expand the square of the binomial $(x+y)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$.

1. We are given the trinomial $$10r^3s + 35rs^4 - 100rs$$ and asked to factor it, which represents the amount paid by Ms. Umali for bananas. 2. We will find the polynomial represen

1. **State the problem:** Solve the equation $$ (2r^2) \sin^3(2a) = \frac{r^2}{4} $$ for $\sin(2a)$. 2. **Isolate terms:** Divide both sides by $r^2$ (assuming $r \neq 0$) to get

1. The problem is to solve the exponential equations:\nc) Solve for $x$ in $4 \cdot 5^x = 210$.\nd) Solve for $x$ in $80 = 100 \cdot \left(\frac{1}{2}\right)^x$.\n\n2. For equation

1. The problem states that a barrel already contains 10 gallons of water and is being filled with oil at a constant rate of 7.5 gallons per minute. 2. We want to write an expressio

1. Let's start by recalling the point-slope form of a line: $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope. 2. The standard form of a line i

1. The problem asks us to find the standard form equation of the line passing through points $ (25,34) $ and $ (35,50) $.\n\n2. First, calculate the slope $ m $ of the line using t

1. Let's clarify your question: it seems you are asking about when to move numbers to the other side of an equation. 2. In algebra, to isolate a variable, we often move terms (incl

1. Given points are $(2, -5)$ and $(-1, 1)$ which lie on a line. We need to find the equation of this line in standard form. 2. First, calculate the slope $m$ using the formula $$m

1. Let's denote the three consecutive natural numbers as $n$, $n+1$, and $n+2$. 2. The problem states that their sum is 63, so we write the equation:

1. Consider the instruction to write math in full form, not in English. 2. Since no specific math problem is given, no equations or expressions to convert.

1. Stated problem: Simplify the expression $$2r\cdot\cos\left(\frac{a}{2}\right)\cdot \frac{\sin(a)}{\sin\left(\frac{a}{2}\right)\sin\left(\frac{3a}{2}\right)}.$$\n\n2. Use the dou

1. The problem is to simplify the expression $$\sqrt[4]{64m^{6}n^{12}}$$. 2. Start by expressing each part inside the fourth root separately: $$\sqrt[4]{64} \times \sqrt[4]{m^{6}}

1. **Stating the problem:** Solve the equation $x + 4 = 6$ for $x$. 2. **Isolating the variable:** To find $x$, subtract 4 from both sides of the equation.