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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Calculating Trump's Approval Rating for Non-Republicans

My father asked me this question yesterday, and as a math major I was a little embarrassed that I was not immediately sure that the answer I obtained was correct. He asked: If President Trump's overall approval rating is 38% among 125 million total…
FofX
  • 1,041
6
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Algebraic identities

Given that $$a+b+c=2$$ and $$ab+bc+ca=1$$ Then the value of $$(a+b)^2+(b+c)^2+(c+a)^2$$ is how much? Attempt: Tried expanding the expression. Thought the expanded version would contain a term from the expression of $a^3+b^3+c^3-3abc$, but its not…
Soumee
  • 1,087
6
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3 answers

Given that $x+\frac{1}{x}=\sqrt{3}$, find $x^{18}+x^{24}$

Given that $x+\frac{1}{x}=\sqrt{3}$, find $x^{18}+x^{24}$ Hints are appreciated. Thanks in advance.
Mathxx
  • 7,570
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4 answers

The product of digits equal to the sum of digits

How to find the number(or numbers ) that has $4$ digits, the product of these digits equal to the sum of these digits ?
htm
  • 63
6
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3 answers

What are the steps to solve this simple algebraic equation?

This is the equation that I use to calculate a percentage margin between cost and sales prices, where $x$ = sales price and $y$ = cost price: \begin{equation} z=\frac{x-y}{x}*100 \end{equation} This can be solved for $x$ to give the following…
Adam J. Forster
  • 163
6
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5 answers

If $2^{2017} + 2^{2014} + 2^n$ is a perfect square, find $n$.

If $2^{2017} + 2^{2014} + 2^n$ is a perfect square, find $n$. My first shot would be to assume the perfect square is $2^{2018}$, but how would I prove that? Even if it is, what is $n$? All help is appreciated.
Regina Dea
  • 389
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2 answers

How to lower/upper bound $n!$ using $1+x\leq e^x$?

I need to prove for all positive integer $n$ $$ e\left(\frac{n}{e}\right)^n\leq n!\leq en\left(\frac{n}{e}\right)^n, $$ using the hint $1+x\leq e^x$ for all $x\in \mathbb{R}$. I did this: The hint says for $x=0$, $1\leq 1$; for $x=1$, $2\leq…
Zir
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  • 12
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proving $t^6-t^5+t^4-t^3+t^2-t+0.4>0$ for all real $t$

proving $t^6-t^5+t^4-t^3+t^2-t+0.4>0$ for all real $t$ for $t\leq 1,$ left side expression is $>0$ for $t\geq 1,$ left side expression $t^5(t-1)+t^3(t-1)+t(t-1)+0.4$ is $>0$ i wan,t be able to prove for $0
DXT
  • 11,241
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Evaluate $\frac{1}{zx+y-1}+\frac{1}{zy+x-1}+\frac{1}{xy+z-1}$ if $x+y+z=2,x^2+y^2+z^2=3,xyz=4$

Evaluate $\frac{1}{zx+y-1}+\frac{1}{zy+x-1}+\frac{1}{xy+z-1}$ if $x+y+z=2,x^2+y^2+z^2=3, xyz=4$ The first thing that I notice is that it is symetric to $a,b,c$ but it can't help me .The other idea is finding the numbers but giving it to wolfram…
Taha Akbari
  • 3,559
6
votes
4 answers

prove that all lines $ax+y=b$ such that coefficients $a, 1, b$ constitute arithmetic sequence have one common point

Prove that all lines $ax+y=b$ such that coefficients $a,$$1,$$b$ constitute arithmetic sequence have one common point. We know that $1-a=b-1$ and solving for b we get $b=$$2-a$ replacing b in the equation $y = 2-a-ax$ but I am not sure where to go…
Michelle Stasso
  • 193
6
votes
2 answers

finding the sum of the absolute values for the roots

How to find the sum of the absolute values for the roots of this equation: $$x^4-4x^3-4x^2+16x-8=0$$
dfr
  • 63
6
votes
5 answers

Why is $\frac{p(1-p)}{1−(1−p)^2}=\frac{1-p}{2-p}$?

I found this solution in an old exam: $$\frac{p(1-p)}{1−(1−p)^2}=\frac{1-p}{2-p}$$ Without any further explanation. Could someone explain to me how to do this transition?
Bastian Hofmann
  • 161
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1 answer

Number of $3$s in the units place

I'm stuck on this problem: (1) In the sequence $7,7^2,7^3,7^4,\ldots,7^{2014}$ how many terms have $3$ as the units digit? After some random stuff, I have found that the unit digits of $7$ go in the order $7,9,3,1$ And then back to $7$. But I don't…
user332252
6
votes
4 answers

Cube root of a binomial

The cube of a certain binomial is $8y^3-36y^2+54y-27$. Find the binomial. I know that $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ and that$(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$ but don't know how to go further...
thunderbolt
  • 767
6
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3 answers

Expansion of $\bigl(\sum x_i\bigr)^4$

Show that $$(\sum_{i=1}^n X_i)^4=\sum_{i=1}^n X_i^4+4\sum_{i\neq j}^n X_i^3X_j+3\sum_{i\neq j}^n X_i^2X_j^2+6\sum_{i\neq j\neq k}^n X_i^2X_jX_k+\sum_{i\neq j\neq k\neq l}^n X_iX_jX_kX_l$$ Please show it step by step.Thanks in advance.
Argha
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