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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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Transformations on rational functions where x is in the numerator and denomiator.

The problem was to plot $ f(x) = \frac{x-2}{x-1} $ using transformations. There are samples and videos online on transforming simpler rational functions like: $$ y = \frac{1}{x} $$ and that easy to understand. But nothing this complex. In this case,…
Marty B.
  • 1,054
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Is there a more direct way to solve in $\Bbb R$ the following equation? $\displaystyle \sqrt{x+4-4\sqrt {x}}+\sqrt{x+9-6\sqrt {x}}=1$.

Solve in $\Bbb R$ the following equation: $\displaystyle\sqrt{x+4-4\sqrt {x}}+\sqrt{x+9-6\sqrt {x}}=1$.$\qquad\text{(1)}$ My try: The set of Perfect squares is: $\left\{\color{blue}{0,1,4,9,16,25,36,49\ldots}\right\}$ Some guesswork:…
user93957
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1 answer

Which is wrong in the proof?

Consider the following steps: \begin{align} a &= x \\ a+a &= a+x && \text{[add }a\text{ to both sides]}\\ 2a &= a+x && \text{[}a+a = 2a\text{]}\\ 2a-2x &= a+x-2x && \text{[subtract }2x\text{ from both sides]}\\ 2(a-x) &= a+x-2x &&…
Vishnu
  • 63
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3 answers

Unable to understand this profit loss problem

I got this question from here. A man sold $250$ chairs and had a gain equal to selling price of $50$ chairs. His profit percent is? The answer says it will be $25\%$ of profit. But, how? It should be $20\%$. My solution is $\dfrac{50}{250}\times…
Rasmi Ranjan Nayak
  • 193
3
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3 answers

Factoring over a set of complex numbers

Ahem. I can only now laugh at how blind I am to not see such a simple answer, LMAO. Thanks to Isaac ♦, Paul VanKoughnett, and Bill Dubuque! Case closed! How would you factor $6x^2 + 18x - 60$ over a set of complex numbers? When I did it myself, I…
Danielle
3
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2 answers

Find max. and min. value of 'r'

Find $\max$ and $\min$ values of $r$ if $$r^2 - 4x + 3 = 0$$ where $r= \sqrt{x^2+y^2}$ Tried differentiating but didn't get any result for max. value of $ \sqrt{x^2+y^2}$
MathGod
  • 5,458
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1 answer

Prove that $(a^2+b^2)(b^2+c^2)(c^2+a^2) \geq 8a^2b^2c^2$

This is my proof. I'm not sure if it is true but perhaps someone would tell me yes or (no and why). Since $(a^2+b^2), (b^2+c^2), (c^2+a^2)$ are greater than or equal to zero, then $(a^2+b^2)(b^2+c^2)(c^2+a^2) \geq 0$. I'll spare you the…
JetRex
  • 337
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3 answers

Simple algebra calculation

$$-5x = 5$$ to get $x$ on its own, does the minus sign cancel when it goes underneath the line? like $x = 5/5$ or is it $x = -5/5$ Sorry I really can't remember this stuff...
user2387699
  • 45
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2 answers

work rate problem. GMAT -related

I'm looking for a good formula/system to use for these problems. Too often I'm just relying on raw intuition and it takes me too much time to solve these questions. Is there a good starting place to solve these problems? What's like a good step 1…
Jwan622
  • 5,704
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5 answers

Which is bigger, $1+3\sqrt{2}$ or $3\sqrt{3}$?

Which is bigger, $a = 1+3\sqrt2$ or $b = 3\sqrt3$? To find out result, I am doing: $(3\sqrt3)^2-(1+3\sqrt2)^2=8-2\sqrt{18}$. But how can I find if the value of $8-2\sqrt{18}$ is positive or negative? Thank you.
nolocimatt
  • 33
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6 answers

How to calculate $(a+b)(c+d)$

How would you calculate something like this:? $(a+b)(c+d)$ I have been out of maths for a while and I can remember we got tought to do: $$ac + ad + bc + bd$$ but how does that work? Are there other methods?
Mazzy
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Finding the point of intersection between a linear and quadratic function.

$$x-2y=2$$ $$y^2-x^2=2x+4$$ Find the points of intersection between these two functions. I haven't done these problems before but I tried to use substitution (treating it like two linear functions, which I have done before). $$x=2+2y\text{ , }…
Kot
  • 3,273
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what is the square root of 144

I am preparing for GRE and can anybody explain this to me What is $\sqrt{144}$. Why is the answer not $12 , -12. $ The calculator gives 12. does it mean -12 is incorrect?
jay
  • 33
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1 answer

Standard form of the equation of a circle involving two points.

For parts (a), (b), and (c), consider the points $\mathrm A=(-1,3)$ and $\mathrm B=(5,3)$ in the $xy$-plane. Distance is measured in meters. c) Find the standard form of the equation of a circle that has the line segment $\overline{\mathrm{AB}}$ as…
user123940
  • 183
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3 answers

Writing a linear function?? Precalculus

I am suppose write a linear function for $h(x)$ and I am given $h(6) = -3$ and $h(2) = 7$ Iam not asking u to do the problem for me just a link or a little help thanks
PreCal Noob
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