🧮 algebra

1. Problem: Find the equation of the line passing through point A(2,4) and parallel to the line $y=5x-3$. 2. Formula: Lines parallel to $y=mx+b$ have the same slope $m$. Here, slop

1. **State the problem:** Find the product of $$\left(\frac{3}{5}x - \frac{y}{2}\right) \left(\frac{5}{3}x + 6y\right)$$ and verify the result for $$x = -1$$ and $$y = 2$$. 2. **Us

1. **State the problem:** Solve for $n$ in the equation $$\frac{5}{3} = \frac{5}{n+2} - \frac{n}{6n}.$$\n\n2. **Rewrite the equation:** Note that $\frac{n}{6n} = \frac{1}{6}$ for $

1. **State the problem:** We need to find the equation of a line with slope $-\frac{3}{5}$ that passes through the point $(-3,3)$. The equation should be in slope-intercept form $y

1. **State the problem:** We need to find the equation of a line with slope $m=3$ that passes through the point $(-2,-15)$ in slope-intercept form $y=mx+b$. 2. **Recall the slope-i

1. The problem asks us to find the equation of a line in slope-intercept form given the slope and a point on the line. 2. The slope-intercept form of a line is given by the formula

1. **State the problem:** We need to find the equation of a line with slope $\frac{3}{5}$ that passes through the point $(11,6)$ in slope-intercept form $y=mx+b$. 2. **Recall the s

1. The problem asks for the equation of a line with slope 0 passing through the point $(5,-16)$. 2. Recall the slope-intercept form of a line is given by $$y = mx + b$$ where $m$ i

1. **Problem Statement:** Prove by mathematical induction that for all integers $n \geq 2$,

1. **Problem statement:** Prove by induction that $$\sum_{r=1}^n r = \frac{n(n+1)}{2}$$ for all natural numbers $n$. 2. **Base case:** For $n=1$, the left side is $1$ and the right

1. **State the problem:** We need to find the equation of a line with slope $-4$ passing through the point $(2,-15)$ in slope-intercept form $y=mx+b$. 2. **Recall the slope-interce

1. Bài toán yêu cầu giải phương trình $$x^2 - 3x + (x - 3) = 0$$. 2. Ta bắt đầu bằng cách rút gọn biểu thức trong dấu ngoặc:

1. Write as a single power **a.** $3^2 \times 3 = 3^{2+1} = 3^3$

1. **State the problem:** Write $a\ 3^2 \times 3$, $b\ 7 \times 7^3$, $c\ 12 \times 12^5$, and $d\ 15^4 \times 15$ as a single power. 2. **Recall the rule for multiplying powers wi

1. Diberikan fungsi $f(x) = x^3 + 2$ dan $g(x) = \sqrt{3} x$. Kita diminta menentukan komposisi fungsi $(f \circ g)(x)$ dan domainnya. 2. Komposisi fungsi $(f \circ g)(x)$ berarti

1. The problem is to analyze the function $f(x) = 1 - \cos\left(x^{\frac{1}{2}}\right)$ on the interval $(a,b)$.\n\n2. The function involves the cosine of the square root of $x$. W

1. **Énoncé du problème :** Déterminer le noyau de $A_\alpha - 2I_3$ où

1. **State the problem:** We have two families buying tickets for children and adults at Rollercoaster World. The Brown family paid 170 for 3 children and 2 adults, and the Peckham

1. **Stating the problem:** We start with a point $S = (a,b)$ in the plane where $0 < b < a$. We generate a sequence of points $(x_n, y_n)$ defined by:

1. **State the problem:** Solve the compound inequality $$4 - 3x > x + 12 < \frac{3x + 29}{2}$$ and find the integral values of $x$ that satisfy it. 2. **Rewrite the compound inequ

1. **State the problem:** We have a parametric curve defined by the equations: $$x = 9 + 2t^2$$