# Algebra 1 Questions & Answers

Recent questions in Algebra I
Zhyar Hoshyar Wali 2022-05-25
istupilo8k 2022-05-24 Answered

### The standard form of a linear firs-order DE is$\frac{dy}{dx}+P\left(x\right)y=Q\left(x\right)$I think the equation is separable if and only if $P\left(x\right)$ and $Q\left(x\right)$ are constants, but I'm not sure. (Haven't found any counterexamples but also can't seem to prove it.) Can anyone confirm or deny that this is correct?

Pitrellais 2022-05-24 Answered

### How to find an irrational number in $\mathbb{Q}\cap \left[0,1\right]$?

Despiniosnt 2022-05-24 Answered

### $EXP=\left\{\begin{array}{ll}{n}^{3}\left(\frac{⌊\frac{n+1}{3}⌋+24}{50}\right)& n\le 15\\ {n}^{3}\left(\frac{n+14}{50}\right)& 15\le n\le 36\\ {n}^{3}\left(\frac{⌊\frac{n}{2}⌋+32}{50}\right)& 36\le n\le 100\end{array}$In this equation there are 3 systems of equations, but there are inequalities next to them. Does this mean that for example we use the top equation when$n\le 15\phantom{\rule{0ex}{0ex}}$and so on?

seiyakou2005n1 2022-05-24 Answered

### E.g. the equation is$u\left(x\right)=f\left(x\right){u}^{\prime }\left(x\right)$Is there a general form of solving such an equation?If not, is there a general form for $f\left(x\right)$ being a linear function?

Alani Conner 2022-05-23 Answered

### For which value(s) of parameter m is there a solution for this system$\left\{\begin{array}{l}mx+y=m\\ mx+2y=1\\ 2x+my=m+1\end{array}$when does this system of equations have a solution?

Case Nixon 2022-05-23 Answered

### Suppose that $x$, $y$ and $z$ are three integers (positive,negative or zero) such that we get the following relationships simultaneously1. $x+y=1-z$and2. ${x}^{3}+{y}^{3}=1-{z}^{2}$Find all such $x$, $y$ and $z$.

Nicholas Cruz 2022-05-23 Answered

### Show that every irrational number in $\mathbb{R}$ is the limit of a sequence of rational numbers. Every rational number in $\mathbb{R}$ is the limit of a sequence of irrational numbers.

Cara Duke 2022-05-23 Answered

### Graph the following system of inequalities. Show (by shading in) the feasible region.$x+2y\le 12$$2x+y\le 12$$x\ge 0,y\ge 0$

Eliaszowyr1 2022-05-23 Answered

### A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes. The size of the high-quality version is 4.6 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 2668 MB. How many downloads of the standard version were there?

Kozankaht2 2022-05-23 Answered

### Proof that $2\sqrt{2}+\sqrt{7}$ is an irrational number.

rs450nigglix2 2022-05-23 Answered

### Simultaneous equation difficulty minus$\left(1\right)×3$$\left(3\right)-\left(2\right)$$21x=-7$$3x=-1$

zato1kom7 2022-05-23 Answered

### Proving $\sqrt{2}+\sqrt{3}$ is irrational

Isaiah Farrell 2022-05-23 Answered

### Solve $\frac{1}{{x}^{2}-1}⩾\frac{1}{x+1}$

Brooke Ayala 2022-05-23 Answered

### I want to know how many ways there are to choose $l$ elements in order from a set with $d$ elements, allowing repetition, such that no element appears more than 3 times. I've thought of the following recursive function to describe this:$C\left({n}_{1},{n}_{2},{n}_{3},0\right)=1$$C\left({n}_{1},{n}_{2},{n}_{3},l\right)={n}_{1}C\left({n}_{1}-1,{n}_{2},{n}_{3},l-1\right)+{n}_{2}C\left({n}_{1}+1,{n}_{2}-1,{n}_{3},l-1\right)+{n}_{3}C\left({n}_{1},{n}_{2}+1,{n}_{3}-1,l-1\right)$The number of ways to choose the elements is then $C\left(0,0,d,l\right)$. Clearly there can be at most ${3}^{l}$ instances of the base case $C\left({n}_{1},{n}_{2},{n}_{3},0\right)=1$. Additionally, if ${n}_{i}=0$, that term will not appear in the expansion since zero times anything is zero.It isn't too hard to evaluate this function by hand for very small l or by computer for small l, but I would like to find an explicit form. However, while I know how to turn recurrence relations with only one variable into explicit form by expressing them as a system of linear equations (on homogeneous coordinates if a constant term is involved) in matrix form, I don't know how a four variable equation such as this can be represented explicitly. There's probably a simple combinatorical formulation I'm overlooking. How can this function be expressed explicitly?

Brooke Webb 2022-05-23 Answered

2022-05-22

### why is 4/3 πr^3 a monomial

Brennen Fisher 2022-05-22 Answered

### choosing $h$and $k$ such that this system:$\left\{\begin{array}{l}{x}_{1}+h{x}_{2}=2\\ 4{x}_{1}+8{x}_{2}=k\end{array}$Has (a) no solution, (b) a unique solution, and (c) many solutions.First i made an augmented matrix, then performed row reduction:$\left[\begin{array}{ccc}1& h& 2\\ 4& 8& k\end{array}\right]\sim \left[\begin{array}{ccc}1& h& 2\\ 0& 8-4h& k-8\end{array}\right]$Continuing row reduction, i get:$\sim \left[\begin{array}{ccc}1& 0& \frac{k-8}{2\left(h-2\right)}+\frac{k}{4}\\ 0& 1& \frac{k-8}{8-4h}\end{array}\right]$how to go about solving the problem with the matrix i end up with?

Despiniosnt 2022-05-22 Answered

### Prove that the function:is discontinuous at every irrational number using both the precise definition of a limit and the fact that every nonempty open interval of real numbers contains both irrational and rational numbers.

Rachel Villa 2022-05-22 Answered

### Consider the differential system$\left\{\begin{array}{ll}& {y}^{\prime }\left(t\right)=ay\left(t{\right)}^{3}+bz\left(t\right)\\ & {z}^{\prime }\left(t\right)=cz\left(t{\right)}^{5}-by\left(t\right)\end{array}$with $t>0$$y\left(0\right)={y}_{0},z\left(0\right)={z}_{0},\phantom{\rule{1em}{0ex}}a<0,\phantom{\rule{1em}{0ex}}c<0,\phantom{\rule{1em}{0ex}}b\in \mathbb{R}$the question is to prouve that this system admits a unique solution on $\left[0,+\mathrm{\infty }\right]$?

When you are a high school student or someone already enrolled in college, even those simple research projects will include Algebra 1 equations, which means that getting some help cannot be avoided. Thankfully, you can access Algebra 1 problems and answers free of charge, which will let you see what Algebra 1 practice problems can be used for certain questions. Just remember to check calculations twice as these can easily get complex. The majority of Algebra 1 answers will be familiar to most students dealing with financial concepts as it is not related to advanced Math problems in most scenarios.