🧮 algebra

1. Асуудлыг ойлгох: Марлаа 364 эрдэнийн чулуутай бөгөөд түүний тэн хагасыг 14 найздаа тэнцүү хувааж өгсөн. 2. Тэн хагасыг олох: $$\frac{364}{2} = 182$$ чулууг 14 найздаа хувааж өгс

1. **State the problem:** We analyze the parabola's graph to determine its direction, vertex coordinates, intercepts, and axis of symmetry. 2. **Direction of the parabola:** The pa

1. **State the problem:** We are given the quadratic function $$g(x) = 2x^2 + 16x + 25$$ and need to rewrite it in vertex form $$g(x) = a(x - h)^2 + k$$ and find the vertex \((h, k

1. The problem asks for the five points you are supposed to plot on a graph. 2. Typically, these points depend on the function or data you are working with.

1. **State the problem:** We are given the quadratic function $$g(x) = 2x^2 + 16x + 25$$ and need to write it in vertex form $$g(x) = a(x - h)^2 + k$$ and find the vertex \((h, k)\

1. **Problem statement:** (a) Calculate the volume of water from 1 cm of rain on a roof measuring 20 m by 8 m.

1. Let's start by stating the problem: We want to find the domain of a function, which means determining all possible input values $x$ for which the function is defined. 2. The dom

1. **Problem statement:** A tank contains 12 litres of oil. The oil is emptied into containers holding 300 ml each. We need to find how many containers are filled. 2. **Important c

1. **Problem:** Find which value of $x$ satisfies the equation $2x^2 + 5x = 7$. **Step:** Substitute each option into the equation and check.

1. **State the problem:** Solve the equation $2\sqrt{x}x + 2 = 3\sqrt{x}2$ for $x$. 2. **Rewrite the equation:** The equation is $2\sqrt{x}x + 2 = 3\sqrt{x} \cdot 2$.

1. **Find all the zeros of** $f(x) = x^2 - 2x$. - The zeros of a polynomial are the values of $x$ for which $f(x) = 0$.

1. The problem asks to find the interval where the function $f(x) = x^2 - 4$ is decreasing. 2. The function $f(x) = x^2 - 4$ is a parabola opening upwards with vertex at $(0, -4)$.

1. The problem is to solve the equation or expression given previously, but using a different method. 2. Since the original problem is not specified here, let's consider a common a

1. **State the problem:** Calculate the value of $\sqrt{2}^5$. 2. **Recall the properties of exponents:** For any positive number $a$ and rational exponents $m$ and $n$, we have $\

1. **State the problem:** Calculate $\sqrt{2}^3$. 2. **Recall the properties of exponents:** For any positive number $a$ and rational exponent $m/n$, $a^{m/n} = (\sqrt[n]{a})^m$.

1. **State the problem:** We are given $\log_{10} P = 2.7712$ and need to find the value of $P$. 2. **Recall the definition of logarithm:** If $\log_b a = c$, then $a = b^c$.

1. **State the problem:** We are given the equation $$y = 3^x$$ and ordered pairs where one coordinate is missing. We need to find the missing coordinate so that the pair satisfies

1. The problem is to find the y-coordinate for the point where $x=2$ on the graph of the function $y=3^x$. 2. The formula given is $y=3^x$, which means for any value of $x$, $y$ is

1. **State the problem:** Calculate the value of $\sqrt{8} + \sqrt{2}$.\n\n2. **Recall the properties of square roots:** The square root of a product can be expressed as the produc

1. **Problem statement:** Find the y-intercept of the graph of the function $y=2^x$. 2. **Formula and explanation:** The y-intercept of a graph is the point where the graph crosses

1. **Problem Statement:** Identify the slope and y-intercept of the given line. 2. **Given Information:** The line crosses the y-axis at $7$, so the y-intercept $b = 7$.