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
5
votes
1 answer

Popularity formula (using votes and age)

I need to create a simple formula for determining the popularity of an item based on votes and age. Here is my current formula, which needs some work: 30 / (days between post date and now) * (vote count) = weighted vote Whenever a vost is cast for…
makeee
  • 153
5
votes
1 answer

Simplifying log

I have been told that $10^{\log_{10}(x)}$ is simply x I have also been told that $10^{\log_{10}}$ are the inverse of each other and cancel each other out but am having trouble understanding this. Can somebody kindly explain how the above is simply x…
Y.M.80
  • 441
  • 1
  • 4
  • 10
5
votes
1 answer

Inverse normalization function

As far as I know the the normalization function is capable of normalize values between 0 and 1: $$\frac{X - \min}{\max - \min}.$$ With this the highest value will be mapped as $1$ and the lowest as $0$. My question is the following: is there a way…
user840718
  • 181
5
votes
3 answers

How do we prove that $f(x)$ has no integer roots, if $f(x)$ is a polynomial with integer coefficients and $f( 2)= 3$ and $f(7) = -5$?

I've been thinking and trying to solve this problem for quite sometime ( like a month or so ), but haven't achieved any success so far, so I finally decided to post it here. Here is my problem: If $f(x)$ is a polynomial with integer coefficients…
Shreya
  • 3,035
5
votes
1 answer

Given that $x^3+x^2=1$, express the infinite product $(1+x)(1+x^2)(1+x^4)(1+x^8)\ldots$ in the form $A+Bx+Cx^2$.

Given that $x^3+x^2=1$ and $x\in\mathbb{R}$, express the infinite product $$(1+x)(1+x^2)(1+x^4)(1+x^8)\ldots$$ in the form $A+Bx+Cx^2$. In the earlier parts of the question, I have already shown…
A. Goodier
  • 10,964
5
votes
3 answers

How to find the absolute value of the difference of two variables?

The problem is as follows: Let $x$ and $y$ integers which satisfy the following equations: $$x+y-\sqrt{xy}=7$$ $$x^2+y^2+xy=133$$ Find the value of $\;|x-y|.$ I'm stuck on this problem due the fact that there appears a square root of $xy$…
Chris Steinbeck Bell
  • 4,175
5
votes
5 answers

Is the division property of equality just a special case of the multiplication property?

My textbook clearly states after the lesson on Transforming Equations: Addition and Subtraction "Notice that the subtraction property of equality is just a special case of the addition property, since subtracting the number c is the same as adding…
user 85795
  • 1,659
5
votes
3 answers

Intersection of two x powers

Many months ago in class I came up with the problem: $$x^{(x+1)} = (x+1)^x$$ Using the solve function on my calculator I have found that the answer is around 2.29... This is backed up by the graph. However I was determined to find the inverse…
Tom Hickson
  • 213
5
votes
2 answers

Simplify: $\frac{\sqrt{\sqrt[4]{27}+\sqrt{\sqrt{3}-1}}-\sqrt{\sqrt[4]{27}-\sqrt{\sqrt{3}-1}}}{\sqrt{\sqrt[4]{27}-\sqrt{2\sqrt{3}+1}}}$

I am doing a pretty hard problem: $$\frac{\sqrt{\sqrt[4]{27}+\sqrt{\sqrt{3}-1}}-\sqrt{\sqrt[4]{27}-\sqrt{\sqrt{3}-1}}}{\sqrt{\sqrt[4]{27}-\sqrt{2\sqrt{3}+1}}}$$ So it is a pretty long and complicated problem. I got stuck though. My idea was to turn…
RiktasMath
  • 689
5
votes
2 answers

Rationalize denominator: $\frac{1}{\sqrt[3]{5}+\sqrt[3]{1}+\sqrt[3]{6}}$

$$\frac{1}{\sqrt[3]{5}+\sqrt[3]{1}+\sqrt[3]{6}}$$ So this is what I thought: the square root of 1 is obviously one, so I have $1^3 +(\sqrt[3]{5} + \sqrt[3]{6})$. In my head I see that this is the first part for the sum of cubes formula. I multiplied…
RiktasMath
  • 689
5
votes
3 answers

Difficult word problem

I have a problem I haven't been able to solve for a class. A man took a trip in a car. He drove $70$ miles at a slower speed. Then, he went the next $300$ miles at a speed that was $40$ mph faster than earlier. The time he spent driving at the…
shiv
  • 53
5
votes
2 answers

Let $h(4x-1)=2x+7$. For what value of $x$ is $h(x)=x$?

Let $h(4x-1)=2x+7$. For what value of $x$ is $h(x)=x$? If $h(a)=a$, then $4x-1=2x+7$ which implies $x=4$. So $a=15$ when I substitute $x=4$ into both linear equations. Is the value of $x$ $15$?
ddswsd
  • 1,337
5
votes
1 answer

solution set of the inequality $\frac{x^2-1}{(x+2)(x+3)}>2$

Question: Find the solution set of the inequality $$\frac{x^2-1}{(x+2)(x+3)}>2$$ From the answer given in the previous problem I got this: First $x\neq -2,-3$. solving the equation I get $-(2\sqrt{3}+5)
user467365
  • 1,093
5
votes
1 answer

The sum of the roots

The function $f(x)$ has exactly six different roots, and is such that $f(11+x)=f(11-x)$. How do you find the sum of the roots ?
crb
  • 53
5
votes
4 answers

System of equations with 4 unknowns.

I'm trying to solve this system of equations but I'm reaching a dead end. $$\begin{array}{lcl} xyz & = & x+y+z \ \ \ \ \ \ \ (1)\\ xyt & = & x+y+t \ \ \ \ \ \ \ (2)\\ xzt & = & x+z+t \ \ \ \ \ \ \ (3)\\ yzt & = & y+z+t \ \ \ \ \ \ \…
Parseval
  • 6,413
1 2 3
…
99 100