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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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Proving $\sqrt{ab} = \sqrt a\sqrt b$

I am currently in high school and we are studying radicals. I had asked my math teacher why $\sqrt{ab}=\sqrt{a}\sqrt{b}$ (for all a,b>0) and he tries to prove it by arguing that $a^{1/2}*b^{1/2}=(ab)^{1/2}$ (an exponent law). However, I find this…
MathematicsStudent1122
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Why is the slope of a line defined the way it is.

This may seem like a silly question but why is it $ \dfrac{y_2 - y_1}{ x_2 - x_1} $ instead of $ \dfrac{x_2 - x_1}{ y_2 - y_1} $ . It is a rate of change so why is it defined they way it is?
Blair Davidson
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A simple proof that $\bigl(1+\frac1n\bigr)^n\leq3-\frac1n$?

The inequality $$ e_n:=\left(1+\frac1n\right)^n\leq3-\frac1n, $$ where $n\in\mathbb{N}_+$, is certainly true, because we know, how LHS is connected with $e$. The other argument is the standard proof of boundedness of $(e_n)$, which uses the binomial…
Przemysław Scherwentke
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How do I solve $\vert x\vert^{x^2-2x} = 1$?

I have the exponential equation $\vert x\vert^{x^2-2x} = 1$, but how do I solve it?
pirsquare
  • 721
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Is there a shorter/faster way to show these two expressions are equal?

I want to know if the two expressions are equivalent: $\frac{1}{2}(k+2)(2a+(k+1)b)$ $\frac{1}{2}(k+1)(2a+kb)+(a+(k+1)b)$ My attempt: First, I decided to start with 2 as 1 looks complicated to me (expanding it is time consuming). Since 1 has…
mauna
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3 answers

A 3-minute algebra problem

I have just taken advance math test level 2 and there are several problems that have been bugging me. This is the first question: If $x,y>0$, then determine the value of $x$ that satisfies the system of equations: \begin{align} x^2+y^2-xy&=3\\…
Anastasiya-Romanova 秀
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Can asymptotes be imaginary?

I'm currently learning about asymptotes and I'm trying to work out the following example: $$f(x)=\frac{1}{x^2+1}$$ To find the vertical asymptotes, the book I'm following says that after factoring completely, you should set each factor of the…
Andreas Grech
  • 1,005
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How to use $x + \frac{1}{x} = 7$ to compute $x^2 + \frac{1}{x^2}$.

I am not sure how to approach this question: You know that $x + \frac{1}{x} = 7$. Compute $x^2 + \frac{1}{x^2}$. I have tried adding $x + \frac{1}{x}$ to get $\frac{x^2 +1}{x}$ but can't see if this was useful or not. I need help in getting…
mikoyan
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$a/b=c$, how to move the numerator to the right side of the equation

Given an equation of the form $a/b=c$, how do you move $a$, the numerator, over to the other side so that you get $b =c?$ (where $?$ denotes my ignorance of what the right side should look like).
Matt Munson
  • 1,537
11
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4 answers

equation $x^2+ax+6a = 0$ has integer roots, Then integer values of $a$ is

If the equation $x^2+ax+6a = 0$ has integer roots, Then integer values of $a$ is $\bf{My\; Try}::$ Let $\bf{\alpha,\beta}$ be two roots of given equation $x^2+ax+6a = 0$ So $\bf{\alpha+\beta = -a}$ and $\bf{\alpha \cdot \beta = 6a}$ and…
juantheron
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I need "intuition" about fraction exponents, like $4^{1.2}$. What exactly is it meant to do with number $4$?

$4^3$ is $4\cdot 4\cdot 4$ Then $4^{1.2}$ is what, $4\cdot\dotso$?? What happens to the number with a fraction exponent when we try to represent it only using numbers and basic operations (like $+$, $-$, $\div$, and $\cdot$)? $4^{1.2} = 4*4^{0.2}$;…
JeX
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Is it possible that a clock's three hands divide the clock face into 3 equal parts?

And is there a proof/disproof out of intuition? Here we ignore the structure of the clock and suppose the hands move with constant speed.
arax
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Why is $\sqrt{4} = 2$ and Not $\pm 2$?

I've always been told that if $\ x^2 = 4,$ $ =>x = \pm2$ But recently, Prof. mentioned that if $x = \sqrt{4}$, Then $x = +2(only)$ I am very skeptical about this because they both mean the same thing and still yield different results! So how is the…
Graviton
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What is $(26+15(3)^{1/2})^{1/3}+(26-15(3)^{1/2})^{1/3}$?

$$(26+15\cdot\sqrt3)^{1/3}+(26-15\cdot\sqrt3)^{1/3}$$ I'm trying to get the result of this number. Through some algebra I found that it is close to $52^{1/3}$. Through some observation I found that it is a root of this cubic equation $x^3-3x-52=0$…
Eesu
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7th class question my daughter asked and need answer if possible

My daughter has asked me to solve this question but I am unable to than I thought to post it here may be someone help. Q : The watchman works 4 days a week and has a rest on the fifth day. He had been resting on sunday and began working on Monday.…
Pirzada
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