# Tagged Questions

Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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### Solve Equation for x and state any restrictions on the variable difficulties

I am a high school student in Algebra II and while I normally have no trouble with problems dealing with algebraic equations, I simply cannot muster the answer to this question. Solve for x. State ...
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### How to explain combinatorial identities?

The setup of binomial expansion formula can be traced by two paths, one of which is "pure" proof by induction (using properties of combinatorial numbers), the other is "practical" comprehension by ...
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### On the proof that $\left|\frac{z_1-z_2}{1-z_1\bar{z_2}}\right|\lt 1$

Question: Prove that $\left|\dfrac{z_1-z_2}{1-z_1\bar{z_2}}\right|\lt 1$ if $|z_1|\lt1$, $|z_2|\lt 1$ My solution: I had no idea how to go about this one so instead I started simplifying the ...
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### Eliminate $x_1,x_2,y_1,y_2,c$ from the following equations

I need to eliminate $x_1,x_2,y_1,y_2,c$ from the following equations.What would be the correct ( and quick ) technique to do so? $x_1y_1=1$ $y_1=4x_1+c$ $x_2y_2=1$ $y_2=4x_2+c$ ...
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### Solving the Inequality $\frac{14x}{x+1}<\frac{9x-30}{x-4}$

The question says to find all the integral values of x for which the inequality holds. the question is $$\frac{14x}{x+1}<\frac{9x-30}{x-4}$$ My Solution \begin{align} & \frac{14x}{x+1} < ...
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### theorem 2 of perfect powers with all equal digits but one

Can someone help me understand what happened to this equation from the paper entitled Perfect Powers With All Equal digits but one...I don't understand the part when it lets $a$ and $c$ not equal to ...
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### A and B are doing a job together. How long will take B alone to do the job? [closed]

A and B working together can do a job in 6 days.A become ill after 3 days of working with B, and B finished the job, continuing to work alone, in 9 more days. How long will take B alone to do the job?
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### Showing a system of equations having two solutions in $\mathbb{R}^2$

Consider the system of equations in $\mathbb{R}^2$ \begin{align*} \xi^2 + \eta^2 &= 4\\ e^{\xi} + \eta &= 1 \end{align*} Show that the system has two solutions in $\mathbb{R}^2$ has two ...
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### Why should $b$ groups of $a$ apples be the same as $a$ groups of $b$ apples?

Why should $b$ groups of $a$ apples be the same as $a$ groups of $b$ apples? We where taught this so it seems rather trivial but the more I think about it the more I feel that it is not. I'm trying ...
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### Why don't parentheses matter in this case of multipication

Very basic question but can't seem to wrap my head around why this happens. Normally parentheses indicate that the operation inside must be carried out first. In this case: (a * a * a)*(a * a * a * ...
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### Evaluate the limit of the form $\lim_{h\to 0} \frac{f(x_o+h)-f(x_0)}{h}$

Limits of the form $$\lim_{h\to 0} \frac{f(x_o+h)-f(x_0)}{h}$$ occur frequently in calculus. Evaluate this limit for the given $x_0$ and function $f$: $f(x)=3x-4, \ \ \ \ \ \ x_0=2$ Okay so I know ...
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### The roots of $ax^2+bx+c$ are 6 and $P$. The roots of $cx^2+bx+a$ are $Q$ and $R$ what is the value of $P\times Q\times R$

Problem The roots of $ax^2+bx+c$ are 6 and $P$. The roots of $cx^2+bx+a$ are $Q$ and $R$ And we are asked to find $P\times Q\times R$ by using the identities: $P(x)=Q(x)\times D(x)+R(x)$ where $P(x)$ ...