🧮 algebra

1. The problem asks us to compare the rates of change (slopes) of two linear functions, M and P. 2. Function P is given by the equation $$y = 7x + 9$$, so its rate of change (slope

1. Рассмотрим первый пример: $z = xy(x + y - 1)$. 2. Здесь нам нужно раскрыть скобки и упростить выражение.

1. **State the problem:** We need to write 4 expressions equal to $$\frac{8a^{16}}{ab^{10}}$$ each using a different power law from the given four:

1. **State the problem:** We need to find Penny's current age given that in six years, she will be three times as old as she was four years ago. 2. **Define variables:** Let Penny'

1. The problem asks to find the slope of the line given by the equation $y = 5x + 4$. 2. Recall that the equation of a line in slope-intercept form is $y = mx + b$, where $m$ is th

1. **Stating the problem:** Simplify the expression $$\frac{1}{a} \sqrt{\frac{ab^{2}}{4} + 3b} \left[ \frac{1}{\sqrt{4a}} - a \sqrt{ab^{2}} \right].$$ 2. **Recall important formula

1. **State the problem:** Simplify the expression $\left(\frac{1}{5}c - 8\right) + \left(-\frac{2}{3}c + 4\right)$. 2. **Write the expression:**

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$.

1. **State the problem:** We are given that $y = -6$ when $x = 2$, and we need to find $y$ when $x = 5$. 2. **Assumption:** Since no explicit relationship is given, we assume a lin

1. **State the problem:** Given the equation where $y=14$ when $x=5$, find $x$ when $y=28$. 2. **Identify the relationship:** Since $y$ changes with $x$, assume a direct proportion

1. Problem: Given sets A = {2,3,4}, B = {1,3,5,7}, and C = {3,4,5}, find: a) $B \cup C$

1. Problem 10: Find the range of the given functions with specified domains. 2. For each function, the range is the set of all possible output values $f(x)$ when $x$ varies over th

1. **Problem:** Determine the rule, in general form, of a quadratic function with vertex $V(1, -8)$ and one zero at $x=3$. 2. **Recall the vertex form of a quadratic function:**

1. **State the problem:** Solve the system of equations: $$-4x - 4y = 7$$

1. **State the problem:** We need to determine which fraction is larger: $\frac{7}{8}$ or $\frac{8}{9}$.\n\n2. **Find a common denominator:** To compare fractions, we convert them

1. The problem is to determine which fraction is larger: $\frac{2}{3}$ or $\frac{7}{10}$. 2. To compare fractions, we find a common denominator. The denominators are 3 and 10. The

1. Problem 2: In an arithmetic sequence, given $u_6 = -5$ and $u_9 = -20$, find $S_{20}$ (sum of first 20 terms). 2. Formula for $n$th term of arithmetic sequence: $$u_n = a + (n-1

1. Let's start by stating the problem clearly: You want to know how to solve the question, but since the exact question is not provided, I will explain a general approach to solvin

1. The problem asks if the point (5, 4) lies on the line given by the equation $y = x$. 2. The equation $y = x$ means that for any point on the line, the $y$-coordinate must be equ

1. **State the problem:** Factorize the cubic polynomial $$x^3 - 3x^2 - 4x + 12$$. 2. **Recall the factoring approach:** To factor a cubic polynomial, try to find rational roots us

1. The problem: What number is 25% of 64? 2. Set up the proportion: \( \frac{n}{64} = \frac{25}{100} \)