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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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Finding the "triangular root" of a number.

A triangular number is a number that is the sum of the natural numbers up to some $n$. The closed form is $x = \frac{n(n+1)}{2}$. How do I get $n$ on one side? I've been looking at it from every angle, and I can't find out how. Any help?
undo_all
  • 255
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I don't get the same graph, before and after solving for Y?

Now, if I draw the following: $3x+y=3$ $2x^2-y^2=-1$ With Wolfram I get the following graph. But if I draw the following functions that I have solved for Y $y=\sqrt{1+2x^2}$ $y=3-3x$ I seem to be loosing some information Is all this simply a…
Algific
  • 1,899
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How do I get from $\frac{-x+1}{-x+2}$ to $1 + \frac{1}{x-2}$

wolframalpha tells me it's the same but I can not follow how to get from one to another. $$\frac{-x+1}{-x+2} = \frac{1-x}{2-x} = \>? \dots$$ I don't get any further, always end up where I started.
user132393
  • 43
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How did I lose some solutions?

Solve the following equation for x. $$\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}=y$$ My solution ($u=e^x$): $$\frac{e^{x}+\frac{1}{e^{x}}}{e^{x}-\frac{1}{e^{x}}}=y\\ \frac{u+\frac{1}{u}}{u-\frac{1}{u}}.\frac{u}{u}=y\\ \frac{u^2+1}{u^2-1} =…
kptlronyttcn
  • 391
4
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4 answers

If $p$ is a prime and both roots of $x^{2} +px−444p=0$ are integers what is $p$

If p is a prime and both roots of $x^{2}+px−444p=0$ are integers, what is $p$ I got that for the roots to be integers the discriminant must be a perfect square. Thus, $p(p + 1776)$ must be a perfect square. However, at this point I am stuck and…
1110101001
  • 4,188
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Correct standard form for the equation of a line?

So I was tutoring an Algebra 1 student yesterday and we were reviewing the three forms in which one can write the equation for a line: point-slope form, slope-intercept form and standard form. I told him to write an equation in standard form and he…
user3175426
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How to know difference between sum of numbers?

If all the $6$ are replaced by $9$, then the algebraic sum of all the numbers from $$1 to $100$ (both inclusive) varies by? Question - What is the difference between algebraic sum of numbers(with $6$ and when $6$ is replaced by $9$)? Answer - Answer…
Android developer
  • 235
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4 answers

Simplify the surd expression.

Simplify the surd. $(2\sqrt 3 + 3\sqrt 2)^2$ I know I should us this formula: $(a^2+2ab+b^2)$ But this gets complicated later. Please explain. :(
Kiara
  • 900
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Proving that for reals $a,b,c$, $(a + b + c)^2 \leq 3(a^2+b^2+c^2)$

Proving that for reals $a,b,c$, $(a+b+c)^2\leq 3(a^2+b^2+c^2)$. This is a homework question and I have no clue where to even start on this. I don't know if I am just tired or what but I can't get anywhere. I've expanding both sides and seeing if…
Logan Serman
  • 679
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Parabola $\sqrt {x}+\sqrt {y}=1 $

How do I prove that the equation $\sqrt {x}+\sqrt {y}=1 $ is part of parabola. My attempt:rotation in 45 degrees brings the equation to $ -2a^2=1-2\sqrt {2}b $ when $ x= \frac {a-b} {\sqrt {2} } $ and $ y= \frac {a+b} {\sqrt {2} } $. It is a…
mathlover
  • 333
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1 answer

Solve for a Specificed Variable

I have the following literal equation that needs to be solved for h: $$S= \pi r \sqrt{r^2+h^2} $$ I isolated the square root and got this: $$\frac{S}{ \pi r} = \sqrt{r^2+h^2}$$ Then I squared both sides to eliminate the square root on the…
ProfessorStealth
  • 395
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Prove that there is a real number $r>0$ such that...

Prove that there is a real number $r>0$ such that: There is no point in $\mathbb{R}^3$ with 3 rational coordinates, whose distance from $(0,0,0)$ equals $r$. In other words, if we build a sphere with radius $r$ and center in $(0,0,0)$, it will…
Dunno
  • 1,327
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Simplifying Exponents in Fractions

From my Algebra 2 class. Not homework. $$4x^3/2x^5y^2$$ Divide the bases and subtract the exponents: $$2x^{-2}y^2$$ Get rid of negative exponent by division: $$2y^2/x^2$$ Then the answer should be: $$2x^2y^2$$ Is this correct?
david
  • 41
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2 answers

If both integers $x$ and $y$ can be represented as $a^2 + b^2 + 4ab$, prove that $xy$ can also be represented like this ...

There is a set $Q$ which contains all integral values that can be represented by $$a^2 + b^2 + 4ab$$, where $a$ and $b$ are also integers. If some integers $x$ and $y$ exist in this set, prove that $xy$ does too. I really have no idea how I can go…
skatter
  • 47
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How to solve this equation: $\frac{\sqrt[5]{x^3 \sqrt{x\sqrt[3]{x^{-2}}}}}{\sqrt[4]{x\sqrt[3]{x}}}=3$

Please, help me to solve this equation: $$\frac{\sqrt[5]{x^3\sqrt{x\sqrt[3]{x^{-2}}}}}{\sqrt[4]{x\sqrt[3]{x}}}=3$$ I tried to shorten fraction, but I get very weird numbers like $$\frac{\sqrt[30]{x^{19}}}{\sqrt[3]{x}}=3,$$ and I'm stuck there :(
toni.a
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