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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Mathematics language, how to say that a specific value of $x$ is included in the functions domain?

For instance, we have the function $y=-2(x+1)^2-10$. $x=0$ is included in this functions domain. How can I say this mathematically, instead of typing out a sentence and saying that $x=0$ exists in the functions domain?
Jason
  • 3,563
3
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2 answers

Exponents with Logs

Could someone show work for why $e^{2\ln(x)}$ = $x^2$ ? I ran across this while solving an ODE but have completely forgotten the rules used here. I hate to ask it, but i'd rather ask it this once than go on in ignorance.
123
  • 1,708
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Help with finding a vertex

I am having trouble with this math problem. The coordinate of the vertex of $f(x) = ax^2 + bx +c, a \ne 0$, is______. Now I know that to find the $x$ coordinate I would use this formula. $x = \frac{-b}{2a}$ However I am not sure how to find the y…
user163505
  • 147
3
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If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is

If $ab+bc+ca=0$ then the value of $1/(a^2-bc)+1/(b^2-ac)+1/(c^2-ab)$ is...
jyothika
  • 115
3
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1 answer

Exponential Form Conversion

Does $(\sqrt[3]{3k})^4 = (3k)^{4/3}$ or $((3k)^{1/3})^4$? I thought the first one is correct, but when I looked at it again I saw that $(3k)^{4/3} = \sqrt[3]{(3k)^4} $
user169562
3
votes
3 answers

How to solve? $3A^2 - 2A^3 = 1.60$

How do I solve this? I'm not good enough to solve this. Sorry! $$ 3A^2 - 2A^3 = 1.60 $$
Sammy R
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3
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2 answers

Find distance between two stations given travel times of trains

Problem Two trains A and B start from two points P1 and P2 respectively at the same time and travel towards each other. The difference between their speed is 10 kmph and train A takes one hour more to cover the distance between P1 and P2 as compared…
Abhinav.K
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$e^x$ defined $a^x$

I have read the chapter up and down but I do not see how, I would like to not take anything from the book but start on e fresh example as I think that would help me to realise what is going on. Im struggling to see how $e^x$ is defined for all real…
ALEXANDER
  • 2,099
3
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2 answers

If $ \sum_{r=1}^{13}\frac{1}{r} = \frac{x}{13!}\;,$ Then the Remainder when $x$ is Divided by $11$

If $\displaystyle \sum_{r=1}^{13}\frac{1}{r} = \frac{x}{13!}\;,$ Then the Remainder when $x$ is Divided by $11$. $\bf{My\; Try::}$ Given $\displaystyle \sum_{r=1}^{13}\frac{1}{r} = \frac{x}{13!}\Rightarrow…
juantheron
  • 53,015
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Cannot find any excluded values in this fraction

I am learning about excluded values. I am faced with this problem: $$\frac{x}{ x^2 + 9}$$ I started by trying to solve $x$ for $0$ in the denominator: $$x^2 + 9 = 0$$ $$x^2 + 3^2 = 0$$ I then tried to break it up into a formula like $(x + a) (x - a)…
user163505
  • 147
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4 answers

If $x^n=y^n$ and $n$ is odd then $x=y$

Here, we suppose that $x,y\in\mathbb{R}$ and that $x^n=y^n$, where $n$ is odd. I want to prove that $x=y$. Maybe we can use that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1})$ So, it suffices to show that if $x^n=y^n$ then…
Solyx91
  • 381
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Im trying to find what I got wrong in simplifying

The question states " Simplify: $$\frac{6\left ( 27^{2n+3} \right )}{9^{3n+6}}$$ What I did was factoring $9$ and and $27$ to make it $3$. In the end I got a $\frac{6}{27}$ answer, simplified: $\frac{2}{9}$. but my problem is that in the book, the…
bie
  • 33
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1 answer

Easy leg and heads problem

Some chickens and rabbits have a total of 100 feet. If each chicken is exchanged for a rabbit and each rabbit is exchanged for a chicken there would be a total of 86 feet. How many chickens are there? How many rabbits? I know that for a problem…
suomynonA
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Solving the equation $-2x^3 +10x^2 -17x +8=(2x^2)(5x -x^3)^{1/3}$

I wanna know how to solve this equation: $-2x^3 +10x^2 -17x +8=(2x^2)(5x -x^3)^{1/3}$ I have some trouble to do that and I'd glad with any help I may get.
tom
  • 119
3
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1 answer

Which of the following relations are functions of q?

Firstly, what is a function of q? Am I correct to assume it means $f(q)$? $w=q+1$ For this one, it is a linear function, so it has to be a function of q. But I'm not sure how to express it? $wq=-27$ Again, $w=\frac{-27}{q}$ This is a linear…
Jason
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