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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How to find $10 + 15 + 20 + 25 + \dots + 1500$

During a test I was given the following question: What is $$10+15+20+25+...+1490+1495+1500=?$$ After process of elimination and guessing, $ came up with an answer. Can anyone tell me a simple way to calculate this problem without having to try to…
Ronnie
  • 127
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What is the equation for finding a number that is X% less than another number?

I know this seems like a juvenile question, but for some reason I can't recall how to do this. Lets say I want to find 87 reduced by 99.75%. What is the equation to do that? Thanks!
Dream Lane
  • 143
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Help needed with whole numbers

I need help on this. I tried simplifying it, putting some numbers on it but there has to be a simple way to figure this one out. Thanks in advance. a, b and c are whole numbers. $$a > b > c$$ $$ (a + 2b)/c = b $$ what is the lowest number that a…
alik
  • 187
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The logic behind the rule of three on this calculation

First, to understand my question, checkout this one: Calculating percentages for taxes Second, consider that I'm a layman in math. So, after trying to understand the logic used to get the final result. I was wondering: Why multiply $20,000 by 100…
Keyne Viana
  • 213
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If $2x^3+4x^2+6x+8=2468$ and $x$ is a positive number, what is the value of $x^3+9x^2+8x+8$

If $2x^3+4x^2+6x+8=2468$ and $x$ is a positive number, what is the value of $x^3+9x^2+8x+8$ I'm trying to find $x$: this is what i did so far: $2x^3+4x^2+6x+8=2468$ Divide by $2$ $x^3+2x^2+3x+4=1234$ Minus $4$, $x^3+2x^2+3x=1230$ factor out an…
Caddy Heron
  • 1,249
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3 answers

After how much time, in total is the tank full again given the following conditions?

A tank is full of water.A drain pipe,which can empty the full tank in 60 minutes,is opened.18 minutes later another pipe which can fill the empty tank in 30 minutes is opened.After how much time, in total is the tank full again? options: a) 18…
justin takro
  • 1,288
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Calculating percentages for taxes

Let's say that I have a tax of 17% over my services and I want to receive $20,000.00 regardless (after paying) the tax. So I want something like: $$X - 17\% = \$20,000.00$$ Where $X$ is the final value that I need to charge to receive…
Keyne Viana
  • 213
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How would I solve this higher degree equation?

$$(x^{ 2 }-2x+3)(x^{ 2 }-2x+3)=121$$ Steps I took: $$x^4-2x^3+3x^2-2x^3+4x^2-6x+3x^2-6x+9=121$$ $$x^{ 4 }-4x^{ 3 }+10x^{ 2 }-12x+9=121$$ $$x^{ 4 }-4x^{ 3 }+10x^{ 2 }-12x-112=0$$ At this point I don't see how I can possibly find the solution using…
Cherry_Developer
  • 4,239
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If $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ then $\frac{1}{a^5}+\frac{1}{b^5}+\frac{1}{c^5}=\frac{1}{a^5+b^5+c^5}.$

Suppose that $\displaystyle\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ . Then , prove that $\displaystyle\frac{1}{a^5}+\frac{1}{b^5}+\frac{1}{c^5}=\frac{1}{a^5+b^5+c^5}.$ Attempt : From the given relation , $\displaystyle…
Empty
  • 13,012
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Find the real root of $x^5+5x^3+5x-1$

Find the real root of $$x^5+5x^3+5x-1$$ I have tried with squaring but the numbers that I got is not correct, any help ?
Bacew
  • 59
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Solve the equation in the following question

Solve the equation $$\sqrt{x+1}+\sqrt{2-x}+2=x^2+2x$$ I tried with squaring both sides, but I got confused, any help will be thankful.
Rnas
  • 41
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2 answers

I need to solve for $x$ in the following equation...

$$3(x+1) - 7(x+1) = -4x +9$$ How do I solve for $x$? I get $0x = 13$, which is mathematically impossible...
Andy
  • 41
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Prove that $x^4 + x^3 + x^2 + x + 1$ has no roots

Prove that $x^4 + x^3 + x^2 + x + 1$ has no roots. I can see two ways of proving it. The first one is to notice, that $x^5 - 1 = (x - 1)(x^4 + x^3 + x^2 + x + 1)$. It has the only root 1. And it is not the root of $x^4 + x^3 + x^2 + x + 1$. So, $x^4…
Photon
  • 147
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3 answers

Find the value below

Let $a,b,c$ be the roots of the equation $$8x^{3}-4x^{2}-4x+1=0$$ Find $$\frac{1}{a^{3}}+\frac{1}{b^{3}}+\frac{1}{c^{3}}$$ It's just for sharing a new ideas, thanks:)
Oiue
  • 1,055
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Find the value of $(x^{2}+y^{2})$

If $x^{3}-3xy^{2}=10$, $y^{3}-3x^{2}y=30$ Find $$(x^{2}+y^{2})$$ I tried but I got nothing, any help please?
Bsdbsrc
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