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
7
votes
7 answers

$A+B+C=2149$, Find $A$

In the following form of odd numbers If the numbers taken from the form where $A+B+C=2149$ Find $A$ any help will be appreciate it, thanks.
Oiue
  • 1,055
7
votes
6 answers

Solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{100}$?

I encountered this problem yesterday and successfully solved it. I'm interested in seeing other people's approach to solving this problem. Problem: How many ordered pairs $(a, b)$ are solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{100}$ where…
EgoKilla
  • 2,538
7
votes
10 answers

Caden has 4/3 kg of sand which fills 2/3 ​​ of his bucket. How many buckets will 1kg sand fill?

I have already finished Calculus II but I go back and practice the basics on Khan Academy. This problem confuses me conceptually every time. I know what the answer is, but I am having a hard time rationalizing the steps. What are the mental steps…
Stryker Graham
  • 73
7
votes
1 answer

Solving $x$ for $y= 3^x-2^x$

Is there a way to solve for $x$ given the function: $$y= 3^x-2^x$$ in terms of $y$? I tried a lot of algebraic manipulations but I ended up nothing. Or, should we say it it impossible to do so?
Keneth Adrian
  • 1,118
7
votes
5 answers

Calculate width and height of rectangle containing given area and conforming to given ratio.

My algebra is so rusty, this should be an easy one! The area of a rectangle is $$A = W \times H$$ If you're given $A$ (say $150$) and a ratio of $W:H$ (say $3:2$) how can you calculate $W$ and $H$?
Ryan
  • 173
7
votes
3 answers

What is the minimum possible value of $(a+b+c)$?

$a, b$ and $c$ are real positive numbers satisfying $ \frac 13 \le ab+bc+ca \le 1 $ and $abc \ge \frac 1{27}$ then what is the minimum possible value of $(a+b+c)$? Applying AM $\ge$ GM gives $(a+b+c) \ge 1$ and if we apply AM $\ge$ HM gives $(a+b+c)…
Quixotic
  • 22,431
7
votes
2 answers

No. of different real values of $x$ which satisfy $17^x+9^{x^2} = 23^x+3^{x^2}.$

Number of different real values of $x$ which satisfy $17^x+9^{x^2} = 23^x+3^{x^2}.$ $\bf{My\; Try::}$Using Hit and trial $x=0$ and $x=1$ are solution of above exponential equation. Now we will calculate any other solution exists or not. If $x\geq…
juantheron
  • 53,015
7
votes
2 answers

Need help in figuring out what I am doing wrong when solving for n..

Here is the expression that I am trying to solve for n: $$ \frac{4}{16+n} = \frac{10}{16+n} \frac{10}{16+n}$$ I am doing the following: \begin{align} \frac{4}{16+n} & = \frac{100}{(16 + n)^2} \\[8pt] \frac{4}{16+n} & = \frac{100}{16^2 + 32n + n^2}…
UserMoon
  • 349
7
votes
1 answer

Fermat's Last Theorem: Contemplation.

So my friend and I are studying elliptic curves and Fermat's Last Theorem appeared several times in the subject matter. So the proof of Fermat's Last Theorem was settled by Andrew Wiles with the work of many prominent mathematicians which I won't…
Rene Cabrera
  • 342
  • 1
  • 9
6
votes
6 answers

Solving quadratic equation

$$\frac{1}{x^2} - 1 = \frac{1}{x} -1$$ Rearranging it I get: $1-x^2=x-x^2$, and so $x=1$. But the question Im doing says to find 2 solutions. How would I find the 2nd solution? Thanks.
Thomas
  • 451
6
votes
3 answers

Factoring with fractional exponents

I really hate to keep asking questions but I just can't figure this out, I don't know what is wrong with me but I can't figure it out. I stared at it for 5 minutes and not a thought came into my head on how to do it that actually accomplished…
user138246
6
votes
4 answers

Solving these two equations simultaneously

I'm having a hard time to solve these two equations simultaneously. I'm arriving to a very long equation.. $$x_0^2+y_0^2=(7\sqrt{2})^2=98$$ $$\sqrt{25+(x_0+2)^2}+\sqrt{4+(y_0-5)^2}=7\sqrt{2}$$
dgzz
  • 195
  • 1
  • 6
6
votes
9 answers

Why does $(a+b)^2= a^2+b^2 + 2ab$? Why is the $2ab$ there?

When I was doing research on finding the derivative I came across something strange. If $f(x) = x^2$ you find the derivative by going $$\frac{f(x+h)^2-f(x)^2}{h} =\frac{x^2+2xh+h^2-x^2}{h}.$$ Why is there the $2xh$? Can someone explain the logic…
Ray Kay
  • 1,353
6
votes
4 answers

Example of a real-life graph with a "hole"?

Anyone ever come across a real non-textbook example of a graph with a hole in it? In Precalc, you get into graphing rational expressions, some of which reduce to a non-rational. The cancelled factors in the denominator still identify…
JackOfAll
  • 4,701
6
votes
1 answer

If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f) (x)$.

If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f)(x)$. My answer is $\frac{x-1}{x+1}$. However, the answer key in the book states $\frac{2x}{x+1}$. How is that? Is the book wrong?
Cetshwayo
  • 3,092
1 2 3
…
99 100