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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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Why can we use inspection for solving equation with multiple unknowns?

In our algebra class, our teacher often does the following: $a + b\sqrt{2} = 5 + 3\sqrt{2} \implies \;\text{(by inspection)}\; a=5, b = 3 $ I asked her why we can make this statement. She was unable to provide a satisfactory answer. So I tried…
Gerard
  • 4,264
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3 answers

Rounding number nearest 0.05

I have question about rounding and please help me, suppose that question is round given number nearest 0.01 or 0.1 or 0.05 or maybe nearest 0.5, then what could i do? For example we are given some rational value 0.16 or 0.167, how could I round it…
giorgi
  • 357
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Range scaling problem

I have a few ranges which I want to scale but I'm missing the formula (and common sense). For example I have a scale range from 40 to 100, but I want my data to range from 0 - 100. What formula do I have to apply to my numbers? Another range I have…
Kta
  • 101
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If $a,b$ are roots for $x^2+3x+1=0$.Calculating $(\frac{a}{b+1})^2 +(\frac{b}{a+1})^2$

If $a,b$ are roots for the equation $x^2+3x+1=0$.How to calculate $$\left(\frac{a}{b+1}\right)^2 +\left(\frac{b}{a+1}\right)^2$$
user84258
  • 103
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Substituting an equation into itself, why such erratic behavior?

Until now, I thought that substituting an equation into itself would $always$ yield $0=0$. What I mean by this is for example if I have $3x+4y=5$, If I substitute $y=\dfrac {5-3x}{4}$, I will eventually end up with $0=0$. However, consider the…
Ovi
  • 23,737
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Rationalizing expressions

In my precalc book, I have the following problem: Calculate $a+b+c$ if $a,b,c\in\mathbb{Q}$ and $$\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}$$ I think that the RHS can stay untouched, while operating the LHS, but I can't find a way…
chubakueno
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Solving $2x + 1 = 11$: Why, when subtracting $1$, do I only do it to a single term on the left but, if dividing by $2$, I must divide both terms?

Solving $2x + 1 = 11$ (for example) Why, when subtracting $1$, do I only do it to a single term on the left but, if dividing by $2$, I must divide both terms ?
D. MacDonald
  • 149
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Convert any number to positive. How?

How to convert any number (negative or positive) into a positive number.. For example, my input can be 4545 or -4545, I need the out come to be positive value 4545.
Muneer
  • 219
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6 answers

For $(x+\sqrt{x^2+3})(y+\sqrt{y^2+3})=3$, compute $x+y$ .

I am trying to find $x+y$ given that $$(x+\sqrt{x^2+3})(y+\sqrt{y^2+3})=3.$$ It is the radicals in $\sqrt{x^2 +3}, \sqrt{y^2+3}$ that is bugging me. I tried to expand the left hand side $$ xy + y\sqrt{x^2+3} + x\sqrt{y^2 +3} +…
Hung nguyen
  • 699
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Where does the equation of asymptotes of a hyperbola come from?

It's known that the asymptotes of a hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is given by $y=\pm\frac{b}{a}x$ if $a>b$. I tried to find a proof of the fact that why the equations of these asymptotes are like that,however the only…
user794034
10
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3 answers

If $x=\sqrt{{\sqrt{5}+1\over \sqrt{5}-1}}$ What is the value of $5x^2-5x-1?$

If $$x=\sqrt{{\sqrt{5}+1\over \sqrt{5}-1}}$$ What is the value of $5x^2-5x-1?$ Efforts: After rationalization, I got $x={\sqrt{5}+1\over 2}$ and $x^2={\sqrt{5}+1\over \sqrt{5}-1}$. Going by this method is very tedious and boring. Is there a more…
Shweta Aggrawal
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Minimum value of $\sqrt{x^2+25}+\sqrt{y^2+16}$ if $x+y=12$

If $x,y\in\mathbb R^+$, $x+y=12$, what is the minimum value of $\sqrt{x^2+25}+\sqrt{y^2+16}$? I got the question from a mathematical olympiad competition (of China) for secondary 2 student, so I don't expect an "analysis" answer. The answer should…
Tony Ma
  • 2,358
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2 answers

Sum of fifth roots of roots of cubic.

$a,b,c$ are the (real) roots of $x^3-16x^2-57x+1=0$. Prove that $\sqrt[5]{a} + \sqrt[5]{b} +\sqrt[5]{c} = 1 $ ................................................................................ edit : my answer to this question on another forum Let…
URCHIN
  • 119
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Domain of a Polynomial function

A polynomial function is given as, $P(x)= a_nx^n+a_{n-1}x^{n-1}+.....+a_1x+a_0$ Notice the last but one term $a_1x$. This term is a simplified form of $a_{n-(n-1)}x^{n-(n-1)}$. Now let us take the last term of the Polynomial. The term $a_0$ is a…
R004
  • 983
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Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.

Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational. I've tried to attempt algebra on this problem. I noticed that there is some kind of nesting effect when trying to solve this. Please help me to understand how to attempt to denest this…
Garrett
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