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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 solve for $x \times x = y$ when I know $y$?

I'm trying to figure out a problem for a program I'm writing. I am calculating color values, and they get premultiplied by the alpha. I want to figure out what the alpha was before hand and divide the color by that. I have the new premultiplied…
M2tM
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Problem manipulating algebra in covariance formulas

I've seen $\text{cov}(x,y)$ expressed as $$\dfrac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{n} \tag{1}$$ and also as $E[xy] - E[x]E[y]$. The latter expands to $$\frac{\sum_{i=1}^nx_iy_i}{n} -…
PeteUK
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When can you add full equations together?

In a problem my teacher did the following: \begin{align*} 5a - 2b &= 3m \\ 5b - 2c &= 3n \\ 5a - 2c + 3b &= 3m + 3n \end{align*} I tried solving for $b$ in the first equation and then plugging it in to the second but could not get the…
Bradley Barrows
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From a ratio $q_1 = x_1/x_2$, how do I compute $q_2 = x_2 / (x_1 + x_2)$?

The question is mostly in the title. If I have a numerical value for a ratio $q_1 = x_1/x_2$, how do I compute $q_2 = x_2 / (x_1 + x_2)$? For example, if $x_1 = 1$ and $x_2 = 8$, we would be given $q_1 = 0.125$ (without explicitly being given $x_1$…
Jeff
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Question about factoring polynomial fraction

I ran into this problem in the review section of my math text but I'm not sure how to go about solving it. $$\frac{2x(x^2-9) - x^2(2x)}{(x^2-9)^2} = 0$$ I can't find a way to cancel the numerator with $(x^2 - 9)$. I guess I could multiply both sides…
Irresponsible Newb
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Write this surd in its simplest form.

Express $\dfrac{1}{2+ \sqrt3}$ in its simplest form. NB: The textbook has the answer as $2 - \sqrt3$ but I can't see how that was achieved. I tried $\dfrac{1}{2} + \dfrac{1}{\sqrt3}$ and multiplying the top and bottom by $\sqrt3 $ to get…
Andros
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An interesting equation involving many iterations.

Let $$f(x) = 1 -|1- 2x |.$$ Find the number of solutions of the equation $$f ( f ( f ( f ( f ( f ( f ( f ( f ( f (x))))))))))=x,$$ i.e., $f^{(10)}(x)=x$. And what about if there is an arbitrary number of iterations?
pmal
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real solution of eqn. in $\sin x+2\sin 2x-\sin 3x = 3,$ where $x\in (0,\pi)$.

The no. of real solution of the equation $\sin x+2\sin 2x-\sin 3x = 3,$ where $x\in (0,\pi)$. $\bf{My\; Try::}$ Given $\left(\sin x-\sin 3x\right)+2\sin 2x = 3$ $\Rightarrow -2\cos 2x\cdot \sin x+2\sin 2x = 3\Rightarrow -2\cos 2x\cdot \sin x+4\sin…
juantheron
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Estimating powers with rational exponents

The task is to predict the order of the following six expressions from lowest to highest, without the aid of a…
yroc
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simplify $\sqrt[3]{11+\sqrt{57}}$

I read in a book (A Synopsis of Elementary Results in Pure and Applied Mathematics) that the condition to simplify the expression $\sqrt[3]{a+\sqrt{b}}$ is that $a^2-b$ must be a perfect cube. For example $\sqrt[3]{10+6\sqrt{3}}$ where…
Hashem
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Simplify $\frac{\sqrt{x^2 + x}}{x}$

How does this simplification work? $\frac{\sqrt{x^2 + x}}{x} =\sqrt{1 + 1/x} $
Maik Klein
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Tricky SAT testproblem

edit: NO, it is not a^2 * b^3 = 432, see photo proof attached, but I did missread the question :) This SAT test question has me stuck: If a and b are positive integers and ${({a^{(1/2)}} \cdot {b^{(1/3)}})^6} = 432$ what is the value of $ab$? (a)…
Robin
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Simplifying $\frac1{1+x}+\frac2{1+x^2}+\frac4{1+x^4}+\frac8{1+x^8}+\frac{16}{x^{16}-1}$

We need to simplify $$\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{x^{16}-1}$$ The last denominator can be factored and we can get all the other denominators as factors of $x^{16}-1$. I tried handling the expressions…
rah4927
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Need help solving exponential equation $2\mathrm{e}^x=5-\mathrm{e}^{-x}$

I need help solving $2\mathrm{e}^x=5-\mathrm{e}^{-x}$. I've tried many ways of solving it but I keep getting the wrong answer. By the way, my book says the solutions are $x=-1.518$ and $x=0.825$ Thanks!
Xerif917
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Finding $a$ and $b$ from $a^3+b^3$ and $a^2+b^2$

Question 1 Two numbers are such that the sum of their cubes is 14 and the sum of their squares is 6. Find the sum of the two numbers. I did $a^2+b^2=6$ and $a^3+b^3=14$ Find $a$ and $b$, two numbers. but got lost when trying to algebraicly solve…
user143525
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