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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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How to prove that $\frac{x}{a} + \frac{y}{b} = 1$ where $a$ is $x$-intercept and $b$ is $y$-intercept

How to prove that $\dfrac{x}{a} + \dfrac{y}{b} = 1\;$ where $\,a\,$ is the $\,x$-intercept and $\,b\,$ is the $\,y$-intercept for all $\,a,b \neq 0$ This was a question on my son's math analysis test today, and neither of us is sure how to…
user62071
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7 answers

Maximum value of $x$ when equality is given

$$ x + y = \sqrt{x} + \sqrt{y} $$ Find maximum value of $x$. $x$ and $y$ are reals.
maveric
  • 2,168
4
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8 answers

Real numbers in math

What are real numbers for a person who doesnt know ANYTHING about math, and had to explain them what real numbers are. Are real numbers only rational and irrational? if so then do we have to say what are rational and irrational and please it cant…
MathGeek
  • 886
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1 answer

How to find more numbers like this?

We have the number 153, which has the following special property: $$153 = 1^3 + 5^3 + 3^3$$ How can we find more numbers like this mathematically (so without making guesses (or even educated guesses) but purely by mathematics)?
TimBurton
  • 43
4
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5 answers

Product of numbers

Pair of numbers whose product is $+7$ and whose sum is $-8$. Factorise $x^{2} - 8x + 7$. I can factorise but it's just I can't find any products of $+7$ and that is a sum of $-8$. Any idea? Thanks guys! Thanks.
user61406
4
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3 answers

Elementary Level Algebra Question

I'm trying to solve the following homework problem: If $a\neq b$, $a^3-b^3 = 19x^3$ and $a-b=x$, which of the following conclusions is correct? \begin{align} \text{(1) }& a = 3x \\ \text{(2) }& a = 3x \text{ or } a = -2x \\ \text{(3) }& a = -3x…
CandidFlakes
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How to express $\max(x+y,0)$ in terms of $\max(\pm x, 0)$ and $\max(\pm y, 0)$

Suppose we define $X^+, X^-$ as $\max(X, 0)$ and $\max(-X, 0)$ respectively. Then, given $Z = X + Y$, I've been trying to figure out how to express $Z^+$ and $Z^-$ in terms of $X^\pm$ and $Y^\pm$, which is supposedly possible. I know that $\max(x,…
user3002473
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3 answers

Apply a 1% discount 100 times - elegant way to solve?

A recent story about Kohl's treating "60% off, followed by 25% off" as being equivalent to "85% off" made me think about the extreme case of this: A "100% discount" by applying a 1% discount 100 times. (On a separate note, I have not convinced…
Philip
  • 153
4
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1 answer

Given $f(a-x)=f(a+x)$ and $f(b-x)=f(b+x)$, where $a,b$ are positive constants $(a>b)$, prove that $f(x)$ is a periodic function

Given $f(a-x)=f(a+x)$ and $f(b-x)=f(b+x)$, where $a,b$ are positive constants $(a>b)$, prove that $f(x)$ is a periodic function I have done the following: $f(a-x)=f(a+x)$....(1) or, $f(-(x-a))=f(x+a). $ Putting $x=x+a$, we get $f(-x)=f(x+2a)…
Anubhab Giri
  • 81
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3 answers

Find all positive integral values of $x$ if $\prod_{m=0}^{1008} (x-{2m+1 \over 2})^{2m+1} \lt 0$

Lately, I have been taking multiple classes on such math problems. So while I was solving some math problems, I came over this question. The question originally says: How many positive integer solutions has the following inequality:…
user587054
  • 1,245
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2 answers

Algebra: Can you think of each side of the equation as a term?

For example with the equation $$5x-4 = 2x +5$$ Is the accepted theory that you think of this equation in terms of: $(5x-4) = (2x+5)$ when you are doing an operation to both sides. Lets say I wanted to multiply by $3$, I would do: $$3(5x-4) =…
Marlon Henderson
  • 131
4
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1 answer

Why the equation $3\cdot0=0$ needs to be proven

In Algebra by Gelfand Page 21 ( for anyone owning the book). He tries to prove that: $3\cdot(-5) + 15 = 0$. Here's his proof: $3\cdot(-5) + 15 = 3\cdot(-5) + 3\cdot5 = 3\cdot(-5+5) = 3\cdot0 = 0$. After that he said: The careful reader will asky…
Xiryts
  • 43
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3 answers

Function transformation: shrink horizontally

Write the formula for $f(x)$, if the graph of $f$ can be obtained from the graph of $y = g(x)$ by shrink horizontally by a factor of $5$ then shift left $3$ units The equation should be $f(x) = g(5(x+3))$ or $g\left(\frac{1}{5}(x+3)\right)$? I…
Trư Bát Giới
  • 41
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3 answers

Minimum of $\left(\frac{1+\sin^2x}{\sin^2x}\right)^n+\left(\frac{1+\cos^2x}{\cos^2x}\right)^n$

I would like to find the minimum of $$f(x)=\left(\frac{1+\sin^2x}{\sin^2x}\right)^n+\left(\frac{1+\cos^2x}{\cos^2x}\right)^n,$$ where $n$ is a natural number. I know there is possible by derivate, but $$f'(x)=n \left(\left(\cos ^2(x)+1\right) \sec…
user596235
4
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4 answers

Solve for $x$: $(x+0.6)^2 = 1.4x^2$

I am very terrible at some aspects of algebra and I would like to ask how to solve this problem (It's actually only a small part of a larger physics problem). I've looked up the laws of exponents and from what I can tell I cannot easily seperate the…
PedroPovedaQ
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