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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How would you write the aspect ratio when height is greater than width?

If you have an image that is sized 200x100 you would say the aspect ratio is "2:1" correct? You can figure that out with width/height correct? What if the size was 100x200? Would you say the aspect ratio is "1:2"? If so how do you do the math to get…
1.21 gigawatts
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Can I execute this division at this point?

I realize this is basic, but this little doubt has been around with me for quite a while: I have this: $$\frac{(2n+3)n+1}{(2n+1)(2n+3)}$$ I need it to end up with this shape: $$\frac{n+1}{2n+3}$$ At first, I thought "well, I simply remove the…
Saturn
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Compute base price of each item in a list of items given the total sales tax

I'm having a disagreement with a client that I think is relatively simple mathematics, but I'd like a third party to confirm or dispute my assertions. Here's the situation: We have a list of N final prices p1, ..., pN. A final price is tax-inclusive…
John Feminella
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The roots of the cubic $x^3+qx+r=0$ are $a,b,c$. How can I find the equation whose roots are $la+mbc,lb+mca,lc+mab$

The roots of the cubic $x^3+qx+r=0$ are $a,b,c$. How can I find the equation whose roots are $la+mbc,lb+mca,lc+mab$? Can anyone help me to solve this problem?
abdakchi
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Finding the Coefficient of $(x^3 + 2y^2)^n$ containing $x^{18} y^{12}$

I was helping somebody when I scratched my head because of this question. It goes like this: If the middle term of the expansion of $(x^3 + 2y^2)^n$ is $C x^{18} y^{12},$ find C. My work: I let $u = x^3$ and $v = 2y^2.$ Then doing this: $$(u)^6 =…
fitzmerl duron
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Indicator function for multiplies of $n$.

From something I saw in of Jack'D Aurizio's answer a while ago. What is reasoning on why the construction of this function works, the connection of indicator variables and roots of unity? How to to derive it from…
Ahmed S. Attaalla
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Fourth root of a biquadratic

Three roots of the equation $x^4-px^3+qx^2-rx+s=0$ are $\tan A$, $\tan B$ & $tan C$ where $A$, $B$, $C$ are the angles of a triangle.The fourth root of the biquadratic is $(p-r)$/$(1-q+s)$ $(p-r)$/$(1+q-s)$ $(p+r)$/$(1-q+s)$ $(p+r)$/$(1+q-s)$ I…
Gem
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Value of an exponential function

What is the value of the exponential function $y=e^{x^{x}-1}$ at $x=0$? I graphed the function on desmos and the value at $x=0$ is $1$. However, I do not know how to show this analytically.
okabe42
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Why is $x^{p/q}$ ill-defined for $x<0$.

This is probably a duplicate but I can't find, if you do let me know and I will delete. Why is $x^{p/q}$ ill-defined for $x<0$. I can see that it is, $(-1)^{1/3} \neq (-1)^{2/6}$, but why? I define $x^{p/q}=\sqrt[q]{x^p}=(\sqrt[q]{x})^p$. Also…
Ahmed S. Attaalla
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How to show that x, y and z are equal?

I would really appreciate help with this system of equations: $$ \left\{ \begin{array}{c} x^2 +3y=-2 \\ y^2 +3z=-2 \\ z^2+3x=-2 \end{array} \right. $$ It seems quite obvious that $x, y$ and $z$ are all equal and then the equation can be solved…
suomynona
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Find all solutions to $|x^2-2|x||=1$

Firstly, we have that $$\left\{ \begin{array}{rcr} |x| & = & x, \ \text{if} \ x\geq 0 \\ |x| & = & -x, \ \text{if} \ x<0 \\ \end{array} \right.$$ So, this means that $$\left\{ \begin{array}{rcr} |x^2-2x| & = & 1, \ \text{if} \ x\geq…
Parseval
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Why the graph of $f(x)=ax+b$ is a straight line?

I am going to teach 10th grade students for the first time and while preparing my lecture i was just curious to know about this so as i can explain it to my students Thanks
J. Deff
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what does "solve the equation for x" mean?

I'm not expert for the mathematics, and familiar with this. But when I learn the math in high school, I've got the sort of the below equation things from teacher or books. Solve the equation for $x$: $$(x^2 + 6x -7)(2x^2 - 5x-3) = 0$$ After…
excelman
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Why does parenthesis before exponents not apply to squaring a binomial?

This must be a stupid question with an obvious answer that is hidden from me. No one I have found even mentions a conflict. lets say I want to find the square $(2 + 3)^2 = 2^2 + 2\times2\times3 + 3^2$ Why do I not simplify first? Parenthesis first? …
mLovelady85
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Computing $x^{2017}+\frac1{x^{2017}}$ given the value of $x+\frac1x$.

If $x+\dfrac{1}{x}=2017$, then the value of $x^{2017}+\dfrac{1}{x^{2017}}$ is, A) $2017^{2016(\sqrt{5}-\sqrt{3})}$ B) $2017^{2016(\sqrt{3}-\sqrt{2})}$ C) $2017^{2\sqrt{3}}$ D) $2017^{3\sqrt{2}}$ E) None of the above Progress: We could make use of…
Jack Frost
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