🧮 algebra

1. **State the problem:** Solve the system of equations: $$100 \times 10^{-6} = \frac{x}{180 \times 10^{6}} - \frac{0.28}{180 \times 10^{6}} y$$

1. **Тэгш хэмжээт бодлогыг ойлгох:** Таны өгсөн тэгшитгэл нь дараах хэлбэртэй байна:

1. **Problem:** Find the remainder when $y = x^4 + x^3 - 7x^2 + x + 3$ is divided by $x - 1$. 2. **Formula:** The Remainder Theorem states that the remainder of a polynomial $f(x)$

1. **Nêu bài toán:** Giải hệ phương trình bậc nhất hai ẩn: $$\begin{cases} 3x + 2y = 1 \\ 2x - y = 3 \end{cases}$$

1. The problem is to find the sum of the first 100 natural numbers: $1 + 2 + 3 + \cdots + 100$. 2. We use the formula for the sum of an arithmetic series: $$S_n = \frac{n}{2}(a_1 +

1. **State the problem:** Simplify the expression $$\frac{x^m}{x^n}$$ and express it as a power of $x$. 2. **Recall the exponent rule:** When dividing powers with the same base, su

1. **Problem Statement:** Find the percentage of total number of males in U.P., Manipur, and Goa together to the total population of all the given states. 2. **Given Data:**

1. Diberikan fungsi linear $f(x)$ yang melalui titik $A(2,5)$ dan $B(x,11)$. 2. Nilai $x$ memenuhi persamaan $3x - 5 = 10$.

1. The problem is to find $\log 25$. 2. Recall the logarithm property: $\log a^b = b \log a$.

1. **State the problem:** We are given data relating orbital speed $x$ (km/s) and distance from the sun $y$ (millions of km). We need to find a power regression equation of the for

1. সমস্যা: একটি বীজগণিতের সমীকরণ সমাধান করতে হবে। 2. সূত্র: সাধারণত, বীজগণিতের সমীকরণ সমাধানে আমরা ব্যবহার করি সমীকরণের মূল নিয়ম, যেমন যোগ, বিয়োগ, গুণ, ভাগ এবং সমীকরণের দুই পাশে

1. **Stating the problem:** Simplify the expression $$(3 - 7)(3^2 - 7^2)$$. 2. **Recall the formulas and rules:**

1. **Stating the problem:** Solve the equation $\frac{x}{2} = 16$ for $x$. 2. **Formula and rules:** To isolate $x$, multiply both sides of the equation by 2 to cancel the denomina

1. **Problem Statement:** We have a square cardboard of side length 40 inches. Four squares of side length $x$ and two rectangular regions are cut out and discarded. The remaining

1. **Problem:** Find a set of three rational numbers between 1 and 2. 2. **Understanding Rational Numbers:** Rational numbers are numbers that can be expressed as a fraction \(\fra

1. Let's start by understanding what a function is. A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output

1. **State the problem:** Simplify the expression $$4^3 \div 2^2$$. 2. **Recall the rules:**

1. The problem asks to express $\frac{7^{10}}{7}$ as a single power. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$ where $a$ is the base

1. El problema consiste en resolver una ecuación cuadrática cualquiera para encontrar sus raíces. 2. La fórmula general para resolver ecuaciones cuadráticas es $$x = \frac{-b \pm \

1. **State the problem:** Factor the quadratic expression $60v^2 + 54v + 162$. 2. **Identify the greatest common factor (GCF):** The coefficients 60, 54, and 162 share a GCF of 6.

1. **State the problem:** Solve the inequality $1 + 2(x - 3) > 0$. 2. **Apply the distributive property:**