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Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

47234 questions
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After $t$ hours, the hour hand was where the minute hand had been, and vice versa

On Saturday, Jimmy started painting his toy helicopter between 9:00 a.m. and 10:00 a.m. When he finished between 10:00 a.m. and 11:00 a.m. on the same morning, the hour hand was exactly where the minute hand had been when he started, and the…
asdf
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How does $3^n-1+2 \cdot 3^n$ evaluate to $3^{n+1}-1$?

Can anybody here help me with this simple problem? I've been thinking about this for half an hour and I am not able to come to a solution. How does $3^n-1+2 \cdot 3^n$ evaluate to $3^{n+1}-1$?
3n3n3
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Solution of a system with 3 variables

$$\begin{array}{rcrcrcr} x & - & 2y & + & 3z & = & 7 \\\ 2x & + & y & + & z & = & 4 \\\ -3 x & + & 2y &- &2z & = & -10 \end{array}$$ I have no idea how to do this and my math book is just telling me to do it, and explains nothing. I have a problem…
Adam
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How to get the days worked?

I have this statement: It was calculated that $750$ meters of a ditch could be excavated in $10$ days. If $7$ workers made $350$ meters and later with $5$ assistants they finished the work in the fixed term, how many days did the assistants …
ESCM
  • 3,161
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Find $xyz$ if $x-\frac{1}{x}=y$, and $y-\frac{1}{y}=z$, and $z-\frac{1}{z}=x$

If $$x-\frac{1}{x}=y, \qquad y-\frac{1}{y}=z, \qquad z-\frac{1}{z}=x$$ find the value of $xyz$. This is how far I proceeded: $x+y+z=z-1/z+x-1/x+y-1/y=>1/x+1/y+1/z=0 =>xy+yz+zx=0$ Also from question, $x^2-1=xy,y^2-1=yz,z^2-1=zx$. Adding…
Shubham Kumar Verma
  • 81
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How do I make $r$ the subject of formula?

Comment: How to go about this question has been a Herculean task for me. I would be glad if an explanation is provided alongside with the calculation as regards making $ r $ the subject of formula in the equation: $$ pv = \frac{1}{r} - \frac{1}{r(r…
Nzewi Ernest Kenechukwu
  • 178
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What is the formula for add/removing compound and non-compound tax from a value?

I had posted this question on stack overflow because I am trying to implement a method that will loop through a set of percentages and add or remove them to a value based on some properties that are set. Here is a link to the question. I believe I…
Xaisoft
  • 363
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Solving a Fractional Equation Involving a Logarithm

I may be being stupid right now, so I've come to Stack to see if this elementary algebra holds up. Suppose I have the equation $$\frac{\ln x}{(1+ \ln x)^2} = \frac{1}{4}$$ My chosen way to solve this would be to cross multiply and expand brackets,…
PhysicsMathsLove
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unknown polynomial divided by $x^2(x-1)$, find the remainder.

I took an exam today and there's a problem stuck in my head; I still can't figure out yet. Here's the question (just the concept as I can't remember precisely). An unknown polynomial divided by $(x-1)^2$ leaves the remainder of $x + 3$ (not sure…
TAP TAP TAP
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Simplifying repeating square roots.

How can I solve the equation: $$\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x...}}}} = \frac{1+\sqrt{53}}{2}$$
ChrisHeneghan
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Question about the proof of simple algebra rule $\frac{1}{\frac{1}{a}} = a$

I have a question about a proof I saw in a book about basic algeba rules. The rule to prove is: \begin{eqnarray*} \frac{1}{\frac{1}{a}} = a, \quad a \in \mathbb{R}_{\ne 0} \end{eqnarray*} And the proof: \begin{eqnarray*} 1 = a \frac{1}{a}…
2c31
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Next Term Of Strange Sequence

I tutored a 10th grader and I was asked this puzzle and I had spent nearly an hour with it and got “no where”. Any one can crack it? Please let me know. Thank you. Question: Find the $14$ th term of the sequence: $$ \frac{1}{2}, \frac{3}{7},…
DeepSea
  • 77,651
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How to know when you can focus only on a specific part of an expression with an even power?

I stumbled upon this problem as I was going through the Algebra 2 course of https://brilliant.org. It goes as follows: Starting from $x = \sqrt{\sqrt{3 \sqrt{\sqrt{3 \sqrt{\sqrt{3 \dots}}}}}}$, I manage on my own to reach the following…
glendc
  • 95
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Solving in terms of $t$?

If $m=t^3$ for any positive integer $t$, and if $w=m^2 +m,\;$ what is $w$ in terms of $t$ ? From what I tried so far I set $m=t^3.$ Thus I get $t^3=t^3\cdot t^2 \cdot t.$ Is this close to the answer?
Jon
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What are the possible solutions of $x+y+ {1\over x}+{1\over y}+4=2 (\sqrt {2x+1}+\sqrt {2y+1})$?

I encountered a question in an exam in which we had: Find all possible solutions of the equation $$x+y+ {1\over x}+{1\over y}+4=2 (\sqrt {2x+1}+\sqrt {2y+1}) $$ where $x $ and $y$ are real numbers. I tried squaring both sides to eliminate the…
shsh23
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