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.

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Homework: Stuck on last step of simplifying

This is for homework, and I could really use help on the last step. This is the original equation. I'm working on simplifying it. My math book is for Intermediate Algebra. $$ \dfrac{ 5x }{ x^2-25 } - \dfrac{5}{x+5} $$ I created the common…
monkey
  • 133
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Not understanding this division problem

$\frac{52}{x}=13$ It says to next step $\frac{52}{13}=x$ Ok, I can do future problems like this, but is there a rule that explains this? What just happened to both sides of the equal sign?
Liger86
  • 427
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(Precalculus) Can someone explain the working out in this picture?

According to the picture, $x^2 - 4x + 4 = 32 + 4$ is written as $(x - 2)^2 = 36$. Can someone please show me the steps so I can learn to do this manually? I don't understand how $x^2 - 4x + 4 = 36$ is rewritten as $(x - 2)^2 = 36$. What's the…
Sophia
  • 33
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(Highschool Pre-calculus) Solving quadratic via completing the square

I'm trying to solve the following equation by completing the square: $x^2 - 6x = 16$ The correct answer is -6,1. This is my attempt: $x^2 - 6x = 16$ $(x - 3)^2 = 16$ $(x - 3)^2 = 25$ $\sqrt(x -3)^2 = \sqrt(25)$ $x - 3 = \pm5$ $x =\pm5 - 3$ $x =…
Sophia
  • 45
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finding the zeros of a polynomial that have irrational zeros

$x^3-5x^2+x+8=0$ I know that the zeros are approx. $-1.07$, $1.72$, and $4.34$ by looking by using a graphing calculator, but how do I find the zeros without? Rational roots theorem does not work here!
user121357
  • 31
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Matrix Multiplication

If I had any $m\times n$-matrix, where $m$ and $n$ are variables, what can I multiply this matrix by? Can it be multiplied by itself? By a square matrix? Another $m\times n$-matrix? Or can it be multiplied by a scalar?
PrecalcNewb
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Determining the domain of a function

What is the domain of: $$\left(\frac{5x+4}{x^2+9x+8}\right)^{1/3}$$ I got $(-\infty, -8) \cup (-8,-1) \cup (-1, \infty).$ But according to Wolfram Alpha it is $(-8, -1) \cap [-4/5, \infty)$. Could someone please tell me why I am wrong? The way I got…
user120920
  • 303
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What is this operation? Where can I learn more about it?

This is probably very basic, but I need to learn more about this: What is this operation? (a, b) operation (c, d) = (a * c - b * d, a * d + b * c) And where can I learn more about the topic? Thanks.
Jason
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Quadratic formula - math error

I'm attempting a past paper and I have been asked to compute the derivative for $(x^2-2x+2)$ and from this I calculated $2x-2$. Once I completed this, I was then asked to find and classify the stationary point. I usually use quadratic formulas to…
user119325
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Prove that for every $x\in[0,1]$, this is true $\sqrt{1+2x}\geq x+1-(1/(2x^2))$

Prove that for every $x\in[0,1]$, this is true $\sqrt{1+2x}\geq x+1-(\frac{1}{2x^2})$ i proved that $x+1-\sqrt{1+2x}>0$ by: $(x+1)^2 -1-2x=x^2$ so $x+1>\sqrt{1+2x}$ but then don't know how to proceed for this question Thank you in advance
lotofdots
  • 81
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Calculate adjusted / reciprocal values from a sequence of numbers

tl;dr (summary) I'm a beginner in mathematics. My question is: is there a formula to calculate the right column in the following table based on the values of the left column? $$ \begin{array}{|c|c|} \hline {\rm AwardedCount} & {\rm CalculatedScore}…
A.L
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minimum of $x^2+y^2$

Find minimum of the expression $$x^2+y^2$$ knowing that $x, y, a$ are real numbers ( $a$ fixed real number) so $$x^2-y^2+2xy=a.$$ My solution is: $$ x^2-y^2+2xy=a <=>(x+y)^2-2y^2=a<=>(x+y+y\sqrt{2})(x+y-y\sqrt{2})=a.$$ I wrote for $a$ nonzero :…
medicu
  • 4,482
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A question on indices

I am solving a 7th grade text book and came across this question. $81^x = 1/(125^y)$ where $x$ and $y$ are integers. Find $12xy$. The answer given is $0$. While I can understand that when $x$ & $y$ are $0$ the above equation is satisfied, I can't…
Ramana
  • 61
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$f(x)=\sqrt{(x-1)^2+(x^2-5)^2}\;\;,\;\; g(x)=\sqrt{(x+2)^2+(x^2+1)^2},\forall x\in \mathbb{R}$, Then Max $\left\{f(x)-g(x)\right\}$

Let $f(x)=\sqrt{(x-1)^2+(x^2-5)^2}\;\;,\;\; g(x)=\sqrt{(x+2)^2+(x^2+1)^2},\forall x\in \mathbb{R}$. Find the Minimum of function $\left\{f(x)+g(x)\right\}$ and the maximum of function $\left\{f(x)-g(x)\right\}$. $\bf{My\; Try}$:: For Minimum of …
juantheron
  • 53,015
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remainder when $(x+1)^n$ is divided by $(x-1)^3$, where $n\in \mathbb{N}$

Calculation of remainder when $(x+1)^n$ is divided by $(x-1)^3$, where $n\in \mathbb{N}$ $\bf{My\; Try}::$ Using Division Algorithm:: $p(x) = q(x)\cdot g(x)+r(x)$ Now Let $r(x) = ax^2+bx+c$ So $(x+1)^n=q(x)\cdot…
juantheron
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