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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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Simple algebraic logic question

$2x^2 + 3y^2=0$. This is possible only when both the value of $x$ and $y$ are zero. But the thing is I fail to understand the significance of this equation. Why would such an equation exist or why we create them?
Four Seasons
  • 864
6
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4 answers

How find $a$ such that $x^2-\sqrt{a-x}=a$ has exactly two real solutions

Consider the equation $$ x^2-\sqrt{a-x}=a.$$ I wish to determine the values of $a$ for which the above equation has exactly two real solutions (for $x$). My idea: $$a-x=(x^2-a)^2=x^4-2ax^2+a^2\Longrightarrow f(x)=x^4-2ax^2+x+a^2-a=0$$ and we must…
math110
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How to solve the equation $8(12x + 15) + 13(2x - 11) = 123$

I'm doing some revision again and I need a bit of help. I've doing some a bit of equations from a textbook and I'm not sure how to solve it. You need to find the $x$ so how would you solve $8(12x + 15) + 13(2x - 11) = 123.$ I know you should…
user61406
6
votes
1 answer

Is there any easy way to simplify the following term?

$[p (p+1) (p+2) (p+3) (p+q)^3] - 4[ p^2 (p+1) (p+2) (p+q)^2 (p+q+3) ] +6[ p^3 (p+1) (p+q) (p+q+2) (p+q+3)] -3[ p^4 (p+q+1) (p+q+2) (p+q+3)]$ After the simplification , the result will be: $3pq \cdot (p^2q + pq^2+2p^2-2pq+2q^2)$ I have tried to…
time
  • 1,595
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2 answers

Really easy algebra problem

Can somebody show me how to go about solving the following (really easy) equation for $\alpha$ please? $$\displaystyle 0 = \sum_{n=1}^{N}\left( \frac{y_n}{\alpha} + \frac{1-y_n}{1-\alpha}\right)$$
rbell
  • 69
6
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3 answers

If $x$ is a nonnegative real number, find the minimum value of $\sqrt{x^2 +4} + \sqrt{x^2 -24x+153}$

If $x$ is a nonnegative real number, then find the minimum value of $$\sqrt{x^2 +4} + \sqrt{x^2 -24x+153}$$ How can I approach this? Thanks
yambourg
  • 207
6
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2 answers

Solve the equation $\frac{1}{x^2+11x-8} + \frac{1}{x^2+2x-8} + \frac{1}{x^2-13x-8} = 0$

Problem Solve the equation $$\frac{1}{x^2+11x-8} + \frac{1}{x^2+2x-8} + \frac{1}{x^2-13x-8} = 0$$ What I've tried First I tried factoring the denominators but only the second one can be factored as $(x+4)(x-2)$. Then I tried substituting $y = x^2 -…
DandelionDreams
  • 81
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Is it possible to express the product of two real numbers in terms of their difference?

Some motivation: I have a (simplified) function $f(x) = \frac{k}x$, where $k$ is some real constant and $x$ is a real number. The result of the function, however, is always truncated to an integer for application purposes. Since I also use the…
Basil
  • 161
6
votes
2 answers

Solving for a variable that's an exponent

How would you figure out this? $x^y = z$ How do you find out $y$ if you know $x$ and $z$ ?
Xplane
  • 267
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1 answer

Find $( \dotsb ((2017 \diamond 2016) \diamond 2015) \diamond \dotsb \diamond 2) \diamond 1$ given ...

For positive real numbers $a$ and $b,$ let $$a \diamond b = \frac{\sqrt{a^2 + 4ab + b^2 - 2a - 2b + 9}}{ab + 6}.$$Find $$( \dotsb ((2017 \diamond 2016) \diamond 2015) \diamond \dotsb \diamond 2) \diamond 1.$$ I can't find any quick way to do…
Mike Smith
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6
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1 answer

Algebra - Find the equation of the line perpendicular to 3x+2y-4=0 going through point (2,-3)

I was wondering if you could help... I have Math homework, I was hoping if you could check my answer. Find the equation of the line perpendicular to $3x+2y-4=0$ going through point $(2,-3)$. $y=\large\frac{-3x+4}{2}$ $y =…
Jay
6
votes
4 answers

How to solve for $y$ in $x = \frac{\sqrt[3]{9y-5}}{\sqrt[3]{11}}$

I am trying to solve the following for $y$ but am lost. I tried to multiply by $\sqrt[3]{121}/\sqrt[3]{121}$ but don't think that is how to do it. $$x = \frac{\sqrt[3]{9y-5}}{\sqrt[3]{11}}$$
BDGapps
  • 141
6
votes
5 answers

Simplify $ \frac{1}{x-y}+\frac{1}{x+y}+\frac{2x}{x^2+y^2}+\frac{4x^3}{x^4+y^4}+\frac{8x^7}{x^8+y^8}+\frac{16x^{15}}{x^{16}+y^{16}} $

Please help me find the sum $$ \frac{1}{x-y}+\frac{1}{x+y}+\frac{2x}{x^2+y^2}+\frac{4x^3}{x^4+y^4}+\frac{8x^7}{x^8+y^8}+\frac{16x^{15}}{x^{16}+y^{16}} $$
Matema Tika
  • 869
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3 answers

Mechanics of Horizontal Stretching and Shrinking

I know $y=2f(x)$ doubles the $y$ value in vertical shifting, and I know that $y=(1/2)f(x)$ halves the $y$ value. But, why does $y=f(2x)$ halve the $x$ value, and why does $y=f((1/2)x)$ double the $x$ value in horizontal shifting? I looked at the…
Carlton Reid III
  • 63
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votes
3 answers

What is the mental-math behind this tiny bit? (If I use normal fraction calculation I get it, but mentally!)

For being a guy who dreams of studying medicine one day, it hurts me to ask such a question because it makes me feel like a total idiot. Anyways... $$1 - \frac{1}{1+x^2} = \frac{x^2}{1+x^2}$$ I can go from the left part to the right part, but not…
Algific
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