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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Simplifying a square root of a square

Simplify: $$(x^2+6x+9)^{-\frac{1}{2}} \cdot (x+3)^2$$ The answer is $x+3$, but I don't understand how? There is no restriction, should it not be as follows? $$\frac{1}{\sqrt{(x+3)^2}} \cdot (x+3)^2$$ $$\frac{1}{|x+3|} \cdot (x+3)^2$$ So shouldn't…
Jason
  • 3,563
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Feedback on solution to $30/(4x+5)=95$

The problem is $$\frac{30}{4x+5} = 95$$ I multiplied $95$ by $(4x+5)$ and then eventually got: $$-445 = 380x$$ and dividing by $380$ gives $x = -1.17$. Is this correct?
suineG
  • 31
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Solution of equation $\frac{x\cdot 2014^{\frac{1}{x}}+\frac{1}{x}\cdot 2014^x}{2} = 2014$

Solution of equation $\displaystyle \frac{x\cdot 2014^{\frac{1}{x}}+\frac{1}{x}\cdot 2014^x}{2} = 2014$ $\bf{My\; Try::}$ Clearly Here $x>0$, Now Using $\bf{A.M\geq G.M}$ So Here $\displaystyle x\cdot 2014^{\frac{1}{x}}>0$ and $\displaystyle…
juantheron
  • 53,015
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Solve $3^x+3^{(3x+1)}=108$

I was helping a high school student with their homework and I ran across the following problem: solve $$3^x+3^{(3x+1)}=108.$$ I was unable to find any "elementary way" to do this (by which I mean something a high school student would be comfortable…
recmath
  • 2,738
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Solving an exponential

I was practicing some exponential equations. I made up the following equation and cannot seem to solve it: $3^{2x}+5x=12$. I noticed most equations do not have the $x$ in the 5. I keep getting $x=\sqrt{\ln 12\over 2\ln 15}$. How is this type of…
Tyrone
  • 31
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Writing statement as algebraic expression

Write "a number decreased by the sum of the number and eight" as an algebraic expression. Let $x$ represent the number. Then simplify. algebraic expression: $x-(8+x)$ simplified: $-8$ Is this correct? Thanks.
Emi Matro
  • 5,013
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Simplifying an expression with algebraic indices

I don't know why but I just can't simplify this expression and its driving me mad!! Could someone please help me with the steps? $\frac {2^n 9^{2n+1}}{6^{n-2}}$ I know the answer is 4 x $3^{3n + 4}$ I just can't get there. Thanks in advance :)
Dani
  • 171
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How long will it take to fill a water tank with two inlet pipes and one outlet?

E11/40. I can see here that I work the fill rate out as: $\large\frac13 + \frac14 - \frac18 =$ Overall fill rate of $\large\frac{11}{24}$ tank per hour. If I multiply $60$ minutes by $\large\frac{24}{11}$ I get the correct result of $131$ minutes,…
user1495024
  • 263
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The fundamental theorem of algebra

In some places (including this), the fundamental theorem of algebra is said to state that for a polynomial of degree d, there are at most d roots. Now, how is this equivalent to stating the existence of at least one root-the way the fundamental…
kalkanistovinko
  • 379
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4 answers

Finding the value of $m-n$ if $m+n=7$, $mn=12$

Finding the value of $m-n$ if $m+n=7$, $mn=12$ I tried the following, As we know, $a^2+b^2=(a-b)^2+2ab$ But, where do I put $m+n$ value? Please help. I am stuck.
Abhishekstudent
  • 1,211
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2 answers

Solving this Exponential Equation

This is the equation that I need help with. The fact that there is that extra $1$ is throwing me off. If you move the $4^x$ term over and take the $\log$ of both sides, then you have a $\log$ with a polynomial inside. $$5^x - 4^x = 1$$
John
  • 31
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Work with algebra

$2{x}^2 + 3{y}^2 = {a}^2$ What is the maximum value of $3x+2y$ ? Not knowing calculus and how to graph a ellipse may make this harder. But is there a way to get around calculus? Please determine the answer in terms of $a$.
most venerable sir
  • 1,689
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1 answer

A unfamiliar question

I'm sure asking this kinda problem is stupid but somehow I have never seen such problems before. $2{x}^2 + 3{y}^2 =0$ what is $3x+2y$?
most venerable sir
  • 1,689
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Can you show me where the "1/2" comes from?

I'm struggling with a math assignment: $$\frac12 \cos(x)·(3+2\sin(2x))−\cos(x)=0 ⇔ \cos(x)\left(\color{red}{\frac12}+\sin(2x)\right)=0$$ According to my knowledge it needs to be: $$\frac12 \cos(x)·(3+2\sin(2x))−\cos(x)=0 ⇔…
Bob Dolman
  • 31
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votes
1 answer

Sum of all real solutions for $x$ to the equation $\displaystyle (x^2+4x+6)^{{(x^2+4x+6)}^{\left(x^2+4x+6\right)}}=2014.$

Find the sum of all real solutions for $x$ to the equation $\displaystyle (x^2+4x+6)^{{(x^2+4x+6)}^{\left(x^2+4x+6\right)}}=2014.$ $\bf{My\; Try::}$ Let $y=x^2+4x+6 = (x+2)^2+2\geq 2$. So our exp. equation convert into $\displaystyle y^{y^{y}} =…
juantheron
  • 53,015
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