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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$\$10$ and $\$100$ bill equation

My question: A cashier has a total of $114$ bills, made up of tens and hundreds. The total value of the money is $\$6450.00$. How much of each kind does he have? He has [BLANK] tens and [BLANK] hundreds. I'm pretty sure there is an algebra equation…
Dan
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positive integer ordered pair $(x,y,z)$ in factorial equations

[1] Total no. of positive integer ordered pairs in $x!+y!+z! = x!\cdot y!$ [2] Total no. of positive integer ordered pairs in $x!+y!+z! = x!\cdot y!\cdot z!$ [3] If $x!\cdot y! = x!+y!+2^z$, Then no. of positive integer ordered pairs $(x,y,z)$…
juantheron
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If Bob makes $\$9.00$ an hour, how long does it take for him to make $\$1.00$?

I divided 9 by 60 (for 60 seconds in an hour) and that came out to $0.15$. Then I do $0.15x = 1$ which is $6.666...$. Does that mean it takes those many seconds for him to make a dollar?
David G
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Finding the linear equations of a piecewise defined function

Given the following graph: I know the trick of finding the linear equation of the function between $A$ to $B$ is the intersection with $Y$ is the constant and the slope is $-\frac{10}{30}$ which means that the linear equation is $y = -\frac{1}{3}x…
Georgey
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If $3^n+81$ is a perfect square, then positive integer value $n$ is

If $3^n+81$ is a perfect square, Then calculation of a positive integer value of $n$. $\bf{My\; Try}::$ When $n≤4,$ then easy to know that $3^n+81$ is not a perfect square. Now let $n=k+4(k∈Z^{+}),$ then $3^{n}+81=81(3^{k}+1).$ So $3^{n}+81$ is a…
juantheron
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Solve $x^2+(-7-4i)x+9+15i=0.$

Solve $$x^2+(-7-4i)x+9+15i=0.$$ Using the quadratic formula, I get $$\frac12 (7+4i \pm \sqrt{-4i})$$ but that's not correct. How do you solve this? I get no help from looking at wolfram alpha.
jacob
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moving particle gone crazy

Let's say that a point particle moves along a line? We can come with a function describing the speed of the particle. It is not hard to imagine what would the motion of the particle look like if our speed function is given by a linear function. My…
Adam
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Equations with unknowns and powers

$a + b +c = 17$ $a^2 + b^2 + c^2 = 101$ $a^3 + b^3 + c^3 = 623$ How does one go about solving this? Thanks
Dan
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Can you solve for a value within a floor function?

I'm writing some software which performs activities using an exponential back-off delay e.g. performs an action at t = 1, 2, 4, 8, 16 etc, assuming a base of 2. I want the base to adjust dynamically depending upon available resources so the…
Cam Price-Austin
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$(ab)^2=(bc)^4=(ca)^x=abc$ Then what is the value of $x$?

Given that $(ab)^2=(bc)^4=(ca)^x=abc$ Then what is the value of $x$? $2(\log a+\log b)=4(\log b+\log c)=x(\log c+\log a)=\log a+\log b+\log c$ Then I am lost, any other easier way to solve?
Myshkin
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Can $a^2+b+2$ and $b^2+4a$ both be perfect squares?

Are there any positive integers $a$ and $b$ so that $a^2+b+2$ and $b^2+4a$ are both perfect squares?
marshall
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How to go from $\lim_{n\to \infty}\frac{81}4(\frac{n(n+1)}{2})^2-\frac{54n(n+1)}{2n^2}$ to $\lim_{n\to \infty} \frac{81}4(\frac1n+1)^2-27(\frac1n+1)$?

It was a question in a calculus textbook and I didn't know how he did the algebra between these steps $$ \lim_{n\to \infty} \frac{81}{4}\left(\frac{n(n+1)}{2}\right)^2-\frac{54}{n^2}\frac{n(n+1)}{2} $$ $$ \lim_{n\to \infty}…
Out Of Bounds
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A Problem on Geometric Progression

Let $a_1,a_2,...$ be in G.P. where $a_1 = a$ and common ratio $r$ are positive integers. If $\log_8 a_1 + \log_8 a_2 + ... + \log_8 a_{12} = 2014$, the the number of order pairs $(a,r)$ is (A) 44 (B) 45 (C) 46 (D) 47 I have tried the…
aghost
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How to apply the remainder theorem for multi-variable polynomials?

In our math class, we were taught that for a polynomial $f(x)$ $$f(\alpha) \equiv f(x) \pmod {x-\alpha} $$ That's all very well. But, what about polynomials in more than variable? Specifically, how can I apply the remainder theorem for a…
Gerard
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Calculate Interior Dimensions Using Cubic Feet

I have been tasked to calculate the interior dimensions of a product given some non-traditional values. Given the following numerical information how would one go about calculating the interior dimensions of an object (let's say a food storage…
Dennis
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