🧮 algebra

1. **State the problem:** We need to find how many degrees the minute hand of a clock moves from 11:10 to 11:45. 2. **Formula and rules:** The minute hand completes a full circle (

1. The problem is to solve the exponential equation $$7^x = 343$$ for the variable $x$. 2. Recall that $343$ can be expressed as a power of $7$ because $7^3 = 343$.

1. The problem is to solve the equation $$7^x = 343$$ for the variable $x$. 2. We recognize that 343 is a power of 7. Specifically, $$343 = 7^3$$.

1. **Problem stated:** Find the complex roots of $f(x)=-\frac{1}{x-2}-\ln(x-4)$ and its asymptotes. 2. **Formula and domain rules:** A root is found by solving $f(x)=0$.

1. **Problem statement:** Simplify each expression given in parts 8 and 9. ---

1. The problem asks to identify which equation corresponds to the given graph. 2. The graph is a straight line with positive slope, crossing the y-axis at (0, 6) and the x-axis at

1. **State the problem:** Put the equation of the line $$5x + y = -4$$ into slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2.

1. **Problem statement:** Write the given expressions as the square of a binomial. 2. **Formula used:** A perfect square trinomial can be written as $$(ax + b)^2 = a^2x^2 + 2abx +

1. **Problemstellung:** Untersuche, ob die Gleichung $(-a - b)^2 = (a + b)^2$ oder $(-a - b)^2 = -(a + b)^2$ gilt.

1. **State the problem:** We are given the formula $$F = 1 - \left(\frac{M}{K}\right)^2$$ and need to transpose it to make $M$ the subject. 2. **Isolate the squared term:** Start b

1. **State the problem:** We are given the equation $$Z = \sqrt[3]{\frac{x^2}{w}}$$ and need to make $w$ the subject.

1. **State the problem:** Solve the equation $20 + x : (-3) = 18 \frac{1}{2}$ for $x$. 2. **Rewrite the equation:** The colon $:$ means division, so the equation is

1. **State the problem:** Solve the equation $$3x + \frac{2}{4} - x + \frac{1}{3} = 2x - \frac{2}{6} - 1 - \frac{x}{2}$$ for $x$. 2. **Simplify fractions:** Note that $\frac{2}{4}

1. Il problema chiede di risolvere la proporzione $\frac{x}{3,6} = \frac{0,4}{1,8}$. 2. La formula per risolvere una proporzione $\frac{a}{b} = \frac{c}{d}$ è $a \times d = b \time

1. Il problema chiede di risolvere la proporzione cerchiata in colonna: $$\frac{12}{9} = \frac{x}{15}$$. 2. La formula per risolvere una proporzione $$\frac{a}{b} = \frac{c}{d}$$ è

1. **State the problem:** Noel is a farm worker paid 00 per kaing basket of mangoes harvested. He works 20 days a month and saves 30% of his monthly income (since he spends 70%). W

1. The problem asks to find the value of 70%. 2. Percent means per hundred, so 70% means 70 out of 100.

1. نبدأ بكتابة المعادلة المعطاة: $$l^3 = x^2 - 3x$$ حيث نريد إيجاد قيم $x$ التي تحقق هذه المعادلة. 2. نفترض أن $l^3$ هو ثابت معين، لكن بما أن السؤال لا يحدد قيمة $l$، سنعتبر المعاد

1. **Problem Statement:** Find the value of $x$ that satisfies the equation $$8x^2 - 6x^3 = \frac{7}{3} - l$$ where $l$ is a constant.

1. نبدأ بكتابة المعادلة المعطاة: $$8 - 3x^{-2} = \frac{1}{7}$$ 2. الهدف هو إيجاد قيمة $x$ التي تحقق هذه المعادلة.

1. **Problem Statement:** Find the slope of the secant line to the curve $n(x) = 3x^2 - 2$ passing through the points $(1, n(1))$ and $(2, n(2))$. 2. **Formula:** The slope $m$ of