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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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polynomials $P(x)$ with integer coefficients such that $P(1)\cdot P(9)\cdot P(8) = 1988$

Calculation of polynomials $P(x)$ with integer coefficients such that $P(1)\cdot P(9)\cdot P(8) = 1988$ $\bf{My\; Try}::$ Given $P(1)\cdot P(9)\cdot P(8) = 1988 = 2^2\cdot 7 \cdot 71$ and Let $P(x) = a_{0}+a_{1}x+a_{2}x^2+...........+a_{n}x^n$ Now I…
juantheron
  • 53,015
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votes
1 answer

Sequence of nonzero digits with sum dividing decimal representation

Is there an infinite sequence of nonzero digits $a_1,a_2,\ldots$ such that $$a_1+a_2+\ldots+a_n\mid\overline{a_1a_2\ldots a_n}$$ for all $n\geq 1$, where $\overline{a_1a_2\ldots a_n}$ denotes the number in decimal representation?
Kunal
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How do you find the value of an equation with nested fractions?

Am stuck on this problem in electronics as I have ran into a bit of algebra. Am generally not too bad with algebra but I cant for the life of me solve this equation: $V=IR$ $P=IV$ So $V = \frac{P}I$ We know that $I = \frac{V}R$ So, given that…
user2901512
  • 2,080
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1 answer

Algebra; if one variable doubles how does it affect another one?

First, the "connection" between the radius r (in meters) in a satellites trajectory and orbital period time is given by the following equation: $$\frac{r^3}{T^2}= \frac{k}{4\pi^2} $$ $K$ is a constant equal to $3.98 \cdot 10^{14}$. I solved for…
Algific
  • 1,899
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How to isolate y?

I've got an equation: $$-4y=12-3x$$ I want to simply isolate the y variable so i could get rid of the -4 coefficient of the y variable. What can I do to isolate the y variable? I've done the following but i'm not sure: $$ y =…
user227546
  • 143
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Find a simplified form for $n!+(n-1)!+(n-2)!+(n-3)!+ \dots +1!$ .

Find a simplified form for $n!+(n−1)!+(n−2)!+(n−3)!+\dots+1!$ . By simplified, I mean that there should not be "..." in the equation. If there isn't one, prove it. Thanks! Edit 1: Is it possible not to have $\sum$ in it?
asdf
  • 571
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4 answers

How do you factor an equation over the set of complex numbers?

A problem that is an example of this is $x^2+16$. I have to know how to factor this over the set of complex numbers. How do you do that? I used to know it's just been a long time.
chromedude
  • 229
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4 answers

Rules for Factorisation?

Basically presented with this, simplify \begin{aligned} {\Bigl(\sqrt{x^2 + 2x + 1}\Big) + \Bigl(\sqrt{x^2 - 2x + 1}\Big)} \end{aligned} Possible factorisations into both \begin{aligned} {\Bigl({x + 1}\Big)^2}, {\Bigl({x - 1}\Big)^2}…
Ben L
  • 41
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3 answers

time speed distance

Two horses start simultaneously towards each other and meet after $3h 20 min$. How much time will it take the slower horse to cover the whole distance if the first arrived at the place of departure of the second $5 hours$ later than the second…
RbG
  • 469
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votes
6 answers

How can $|x|= -x$, when $x<0$?

Why is the following true? $$ |x|= \begin{cases} x,&x\ge 0\\ -x,&x<0 \end{cases} $$ Isn't the modulus of a number always positive? According to the above formula $|-4|=-4$ because $4<0$, which is incorrect. Please explain this to me. Thank you.
Tamás
  • 239
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1 answer

$50^{th}$ digit from the left in the expansion of $(\sqrt{50}+7)^{50}$.

The $50^{th}$ digit from the left in the expansion of $(\sqrt{50}+7)^{50}$ after the decimal point. $\underline{\bf{My\; Try}}::$ Let $\left(\sqrt{50}+7\right)^{50} = I+f$, where $I = $Integer part and $f = $ fractional part. and $0\leq f<1$ Now Let…
juantheron
  • 53,015
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votes
2 answers

Can the quadratic equation apply to functions?

I'd like to know if the approach I took below (solving quadratic formula for function $u$) was valid. Solve for $\theta$: $2\cos \theta = 3\cos^2 \theta - 1$ Let $u = \cos \theta$: $0 = 3u^2 - 2u - 1$ Apply quadratic formula: $u = \frac{1\pm…
Kip
  • 587
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2 answers

How do you factor $x^3 - 8 = 0$?

I factored $x^3 - 8 = 0$ and I only got $x = 2$, but the answer said it's $x=2$ and $x=-1 \pm \sqrt{3}i$? How do you get $x=-1 \pm\sqrt{3}i$?
Joshua Ree
  • 471
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4 answers

Solving $a(x+2)=\pi-cy$ for $x$, arrived at an answer different from the one in the book

In an algebra review book, one exercise asked to solve for $x$: $$a(x+2)=\pi-cy$$ I arrived at the following: $$x=\frac{\pi-cy}{a}-2$$ The book stated the correct answer is: $$x=\frac{\pi-cy-2a}{a}$$ I see that technically I ignored the PEMDAS…
measureallthethings
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Minimisation of fraction

If it is given that $x+y=C$ and $w+z=D$ then how to find the least and maximum value of the expression $x/w + y/z$? $C$ and $D$ are positive integer constants. $x, y, w, z$ are variables taking positive integer values. Also take the case when 0…
Suy
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