Mathematics Stack Exchange
Mathematics Stack Exchange

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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Find the minimum of this radical expression

For $x\in[0,6]$, find the minimum of $m=x+\dfrac{96-16x}{3\sqrt{x^2+16}}$. I used derivatives and found that the $x$ which minimizes $m$ is the positive root of \[9x^6+432x^4-2304x^2-49152x-28672=0.\] The approximate value is $x\approx4.71183$,…
user1034536
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I came across this fun pattern, can anyone give me a proof for this?

The Pattern $\begin{align*}1(8)&=(3^2)-1\\ 2(8)&= (3+1)^2 \\ 3(8)&= (3+2)^2-1\\ 4(8)&= (3+3)^2 - 4\\ 5(8)&= (3+4)^2- 9\\ 6(8)&= (3+5)^2-16\end{align*}$ Conjecture I think the pattern is that the numbers appear in the following form: $$8(n+1) =…
Satvik Shubh
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Finding all solutions to an inequality equation

I have the following inequality that I need to find all solutions of: $2x^3-8x > 5x^2-20$ My guess is that you would have to turn this into a polynomial equation and let the right hand side equal to $0$ (i.e. $2x^3-5x^2-8x+20=0$). By using the…
Ryan
  • 305
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Simplify $(xy^{-1})/(y^2/x^3)^{-1}$

Need to simplify this equation: $$(xy^{-1})/(y^2/x^3)^{-1}$$ So far I have $= \frac{x/y}{1/(y^2/x^3)}$ But don't know what to do next. Any help much appreciated
user88720
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How to find the second solution of this $\log_{x}(2x^{x-2} - 1) + 4 = 2x$ logarithmic equation?

I have to find the points where: $$ \log_{x}(2x^{x-2} - 1) + 4 = 2x $$ It's easy to see that $x=2$ is a solution but, when graphing the function I see that there is another solution around 1. How can I find the value exact value of $x$? If I try…
latticed-smile
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Given $8\sqrt{p} = q\sqrt{80}$, where $p$ is prime, is the solution unique?

I had this maths question: Given that $$8\sqrt{p} = q\sqrt{80}$$ where $p$ is prime, find the value of $p$ and the value of $q$ I did this by simplifying the RHS to $4q\sqrt{5}$ and comparing clearly gives $p=5$ and $q=2$ However, I also thought…
PhysicsMathsLove
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Solve for $x$ without using logs: $3^{2x-1} = 9^{-x}$

Solve for $x$ without using logs: $3^{2x-1} = 9^{-x}$ Any clues on how to start this problem would be welcomed.
Gez Bishop
  • 771
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Find equation that represents $m$ as the subject

$$P_b=m(x\bar{x})+ m\left(\frac{my ̅\bar{y}(m+1)}2\right)- m\left(\frac x{f_x} + \frac y{f_y} \right)S - M$$ I am a novice at maths, but me and a friend came up with a formula for a hobby of ours, and as I couldn't find any tags that I really…
Nick
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Simple algebra question

$$\dfrac{\qquad\dfrac{5p+10}{p^2-4}\qquad}{\dfrac{3p-6}{(p-2)^2}}$$ Im all confused about this question. Can someone go through it step by step. Can you please list when I can cancel numbers. Thanks.
John
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How does $\frac{\sqrt{3}}{2} = \sqrt{\frac{3}{4}}$?

I'm studying trigonometry and one of the key triangles (60 30 90) has a side of $\frac{\sqrt{3}}{2}$. I understand that it is derived from an equilateral triangle of sides 1, however I can't see how $\frac{\sqrt{3}}{2} = \sqrt{\frac{3}{4}}$ and why …
Sam
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How do I combine multiple sets of ratios in order to meet an overall "target" ratio? (word problem supplied to illustrate)

(I had no idea how to tag this, any help would be great) :) I am a programmer with little math experience beyond high school - this will be demonstrated by my explanation. I am developing an application that needs a formula. The formula involves…
Matt Miller
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Interesting percentage calculation shortcut formulae

I came across the following shortcut formulae while going through a text book: For questions of the type: If the price of a commodity increases by R%, find the % decrease in the consumption given that the expenditure remains same One can directly…
peakit
  • 481
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show that there exists a function $g(x)=\frac{\alpha x+\beta}{\gamma x+\delta}$ such that $f(g(x))=x$

question: Let $a,b,c,d$ be given constants with the property that $ad-bc\neq0$. If $f(x)=\frac{ax+b}{cx+d}$, show that there exists a function $g(x)=\frac{\alpha x+\beta}{\gamma x+\delta}$ such that $f(g(x))=x$. Also show that for these two…
Broken Dreams
  • 291
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Is $0$ the root of the equation $\frac{x^2}{ x}= 0$?

I want to understand if I understand the concept of equation correctly. For this I want to know if $0$ is the root of the equation $\frac{x^2}{x} = 0$. If we simplify the equation then we can get equation $x = 0$ and then we have solution $0$. But…
user341
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Is it okay to say that $|{x}|=\sqrt{x^2}$ in a function?

While analyzing a certain function I was asked to integrate $$\int \left|f'\left(x\right)\right|f\left(x\right)dx$$ Since I don't know how to integrate an absolute value function, I noticed that it could be re-written as $$\int…
libanobovich
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