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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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Solving Mixture word problems?

I am having very difficult times in understanding the following and related mixture problems.Can anybody guide me the easy and nice trick that is useful in understanding,visualizing and solving these types of problems? following are few of…
Edison
  • 329
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How to compute this sum

I'm trying to remove the summation sign from this formula, is this possible? $$1+\sum_{k=1}^{500}(4(2k+1)^2-12k)$$
Timo Willemsen
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How do I show that if $a_1\neq a_2$, then $\left (\frac{a_1+a_2}{2} \right )^{2}> a_1a_2$.

How do I show that if $a_1\neq a_2$, then $\left (\frac{a_1+a_2}{2} \right )^{2}> a_1a_2$. My work: $(a_1-a_2)^{2}> 0\Rightarrow a_1^2-2a_1a_2 +a_2^2>0\Rightarrow a_1^2+a_2^2> 2a_1a_2\Rightarrow \frac{a_1^2+a_2^2}{2}> a_1a_2$. Why isn't this…
OGC
  • 2,305
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$x^x = y$, express $x$ in terms of $y$

$x^x = y$ Express $x$ in terms of $y$. I'm particularly interested in the solution where $x$ is real, but complex would be interesting too. Any ideas? Thanks.
Mysterious Entity
  • 31
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How can I solve the equation $n\log_2n = 10^6$?

I was solving some exercises and the most of them I found the algebraic properties on the web. But in the equation $n\log_2 n = 10^6$ I have no idea, I tried several ways to solve the equation and none of them worked. Thanks!
user136913
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Simplifying a radical with fraction and sum

What are the steps to simplify $(1+(\frac{1}{2}(x^3-\frac{1}{x^3})^2))^ \frac{1}{2}$ to $\frac{1}{2}(x^3+\frac{1}{x^3})$ ?
BC Dozier
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Solving $3x - 40 \cdot 2 = x + 5$

What did I do wrong? Start problem got rid of the 2 on the left side by reversing the multiplication simplified - got rid of the two on the left side and divided on the right to get 2.5 undoing the subtraction of 40 by adding 40 to both…
user3402545
  • 74
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How to divide polynomials?

The title says it all : How to divide polynomials? I don't understand the method below taught in my school. Would any of you mind explaining it or even better, suggest an alternative way to solve this?
user123399
  • 289
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Explicit solution to $100(y + \frac{100}{10-y}) = x + 1000$

$$ 100\left(y + \frac{100}{10-y}\right) = x + 1000 $$ I'm looking to have the equation in the form $y(x) = ...$ Seems pretty simple, but I'm just not seeing it. The answer is: $$ y(x) = \frac{1}{200}\sqrt{x^2 + 4000x} − x $$ Wolfram|Alpha…
David Chouinard
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no. of Strictly monotonic function in $f:\{1,2,3,4\}\rightarrow \{5,6,7,8,9\}$

Of all the mapping that can be defined from $f:\{1,2,3,4\}\rightarrow \{5,6,7,8,9\}$ a mapping is randomly selected. The chance that the selected mapping is strictly monotonic, is My Try: Total no. of function from $A$ to $B$ in $f:A\rightarrow B$,…
juantheron
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Find $x_n$ if $x_1,x_2,\ldots,x_n$ is a set of positive numbers that satisfy $\frac{x_n+2}{2}=\sqrt{2S_n}$.

Find $x_n$ if $x_1,x_2,\ldots,x_n$ is a set of positive numbers that satisfy $\frac{x_n+2}{2}=\sqrt{2S_n}$. Here $S_n$ denotes $x_1+x_2+\ldots+x_n$. Also $n\in\mathbb N_{>0}$. It's easy to see that $x_1=2$. I've substituted $x_n$ with…
user26486
  • 11,331
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Relationship between coefficients of a polynomials and its roots.

The roots of the equation $x^4 -3x^2 + 5x - 2 = 0$ are $\alpha$, $\beta$, $\gamma$ and $\delta$. $\alpha^n + \beta^n + \gamma^n + \delta^n$ is denoted by $S(n)$. Find values of $S(2)$ and $S(4)$ and of $S(3)$ and $S(5)$. Hence, find the value of…
George
  • 2,556
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Reducing a fraction by dividing top and bottom

I am trying to cancel out to reduce this: $$\frac{ 6xh + 3h^2 + 5h }{ h }$$ Is it possible to cancel out the h's to become this; $$\frac{ 6x + 3 + 5 }{ h }$$ While the $3$ goes into the $6x$? So the final answer is $2x + 5$?
user3247128
  • 181
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Having problem in finding values of variables

I was trying to find the values of two unknown variables using two equations.When I simplified both the equations, both of them were the same. What should be the value of the variables in such a case?
user2857
3
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1 answer

Find the domain and the solution

I am trying to understand the solution of this problem. $$ \dfrac{(2x-8)}{(x+5)} \leq0 $$ The domain is $ \mathbb{R}\ - \{-5\}$ and the solution is $-5 \lt x \leq 4 $ However, I can't figure why $-5$ is not included in the solution. I did a…
Francis
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