🧮 algebra

1. Let's state the problem: We want to know if the slope of a line perpendicular to another line is always the negative inverse of the original line's slope. 2. The formula for the

1. **State the problem:** We have line C with equation $y=4x-1$ and line D is perpendicular to line C. They intersect at point $(1,3)$. We need to find the equation of line D. 2. *

1. The problem is to simplify the summation \(\sum_{k=1}^n (5k + 2)\) correctly. 2. The formula for the sum of the first \(n\) natural numbers is \(\sum_{k=1}^n k = \frac{n(n+1)}{2

1. **Stating the problem:** We are given that the sum of two numbers is 40 and one number is twice the other. 2. **Forming the equations:** Let the two numbers be $x$ and $y$.

1. **State the problem:** Two numbers have a sum of 18, and one number is 6 more than the other. 2. **Write the simultaneous equations:** Let the two numbers be $x$ and $y$.

1. **State the problem:** We are given the ratio of the height to the horizontal distance of Baldwin Street as 1:1.34, and the height it rises is 47 m. We need to find the horizont

1. **State the problem:** Solve for $x$ in terms of $a$ and $b$ from the equation $$\frac{a^{2}b}{x^{2}} + \left(1 + \frac{b}{x}\right) a = 2b + \frac{a^{2}}{x}.$$\n\n2. **Rewrite

1. **State the problem:** We have a collection of stamps where initially the number of local stamps is $\frac{2}{3}$ of the total number of stamps. After adding 156 local stamps, t

1. **Problem 1: Earnings and Savings** Celine earns 525 more than Abbas each month.

1. **State the problem:** Given $x = -2$ and $y = 5$, evaluate the expression $$3x^2 - 2y.$$ 2. **Recall the formula and rules:** The expression involves squaring $x$ and multiplyi

1. **State the problem:** Simplify the expression $X = 2 \sqrt{2x - 4}$. 2. **Recall the formula and rules:** The square root of a product can be written as the product of square r

1. **State the problem:** Solve algebraically the equation $$\sqrt[2]{19a + 6} - 2a = 3$$. 2. **Rewrite the problem:** Since the index is 2, the radical is a square root. So the eq

1. **Problem Statement:** We need to find Chris's earnings based on a tiered commission structure for different sales amounts (Q3).

1. **Problem 1: Find James' age given the ratio of Macy's age to James' age is 3:8 and Macy is 15 years younger than James.** 2. Let Macy's age be $3x$ and James' age be $8x$ since

1. **Stating the problem:** We have two functions: $$y=2x - m^2 - 2$$ and $$y=-2x - m^2 - 2$$. We need to analyze their range, domain, vertex, and maximum value. 2. **Domain:** Bot

1. The problem asks to calculate $f(-1)$, $f(0)$, and $f(2)$ for the piecewise function: $$f(x) = \begin{cases} 8x - 4 & x < 0 \\ 8x - 8 & x \geq 0 \end{cases}$$

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ that passes through the point $(-3,5)$ and has slope $m=-2$. 2. **Recall the slope

1. **State the problem:** We need to find the slope of a line parallel to the line given by the equation $$y = -\frac{5}{8}x + 5$$ and the slope of a line perpendicular to this lin

1. **State the problem:** Find the slope of a line parallel and perpendicular to the line given by the equation $$3y + 8x = 9$$. 2. **Rewrite the equation in slope-intercept form:*

1. **State the problem:** Find the slope of the line given by the equation $$y = -\frac{5}{4}x - \frac{7}{8}$$. 2. **Recall the slope-intercept form:** The equation of a line in sl

1. **State the problem:** Find the slope $m$ of the line given by the equation $$9x - 6y = -9.$$\n\n2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is