Matilda Webb
2022-05-07
Answered

Factor 35 into its prime factors.

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parentalite50bqd

Answered 2022-05-08
Author has **13** answers

The factors for $35$ are all numbers between $-35$ and $35$, which divide $35$ evenly.

Check numbers between $-35$ and $35$

Find the factor pairs of $35$ where $x\cdot y=35$.

$\begin{array}{cc}x& y\\ 1& 35\\ 5& 7\\ -1& -35\\ -5& -7\end{array}$

List the factors for $35$.

$-35,-7,-5,-1,1,5,7,35$

asked 2021-06-03

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

$g(x)=3-\frac{{x}^{2}}{4}$

asked 2022-02-01

What is the standard form of $y={(x+4)}^{3}-{(2x+3)}^{2}$ ?

asked 2022-03-26

Could you describe this function as "logarithmic"?

$f\left(x\right)=\frac{1}{\sqrt{x}}$

As x increases, the value of$f\left(x\right)$ decreases, but the decrease tapers off quickly as $x$ gets larger, and if you plot the graph of $f\left(x\right)$ , the shape looks kind of like an upside-down logarithm. Would it be correct to describe this function as declining logarithmically, as $x$ increases?

As x increases, the value of

asked 2022-06-24

How to prove if log is rational/irrational

I'm an English major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook.

Within the first chapter of the book's practice problems, they ask us multiple times to prove that some log function is either rational or irrational.

Specific cases make more sense than others, but I would really appreciate any advice on how to approach these problems. Not how to carry them out algebraically, but what thought constructs are necessary to consider a log being (ir)rational.

For example, in the case of ${\sqrt{2}}^{2{\mathrm{log}}_{2}3}$, proving that $2{\mathrm{log}}_{2}3$ is irrational (and therefore ${a}^{b}$, when $a=\sqrt{2}$ and $b=2{\mathrm{log}}_{2}3$ is rational) is not an easily solvable problem. I understand the methods of proofs, but the rules of logs are not intuitive to me.

A section from my TF's solution is not something I would know myself to construct:

Since $2<3$ we know that ${\mathrm{log}}_{2}3$ is positive (specifically it is greater than 1), and hence so is $2{\mathrm{log}}_{2}3$. Therefore, we can assume that a and b are two positive integers. Now $2{\mathrm{log}}_{2}3=a/b$ implies ${2}^{2{\mathrm{log}}_{2}3}={2}^{a/b}$. Thus

${2}^{a/b}={2}^{2{\mathrm{log}}_{2}3}={2}^{{\mathrm{log}}_{2}{3}^{2}}={3}^{2}=9\text{,}$

and hence ${2}^{a}={9}^{b}$

Any advice on approaching thought construct to logs would be greatly appreciated!

I'm an English major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook.

Within the first chapter of the book's practice problems, they ask us multiple times to prove that some log function is either rational or irrational.

Specific cases make more sense than others, but I would really appreciate any advice on how to approach these problems. Not how to carry them out algebraically, but what thought constructs are necessary to consider a log being (ir)rational.

For example, in the case of ${\sqrt{2}}^{2{\mathrm{log}}_{2}3}$, proving that $2{\mathrm{log}}_{2}3$ is irrational (and therefore ${a}^{b}$, when $a=\sqrt{2}$ and $b=2{\mathrm{log}}_{2}3$ is rational) is not an easily solvable problem. I understand the methods of proofs, but the rules of logs are not intuitive to me.

A section from my TF's solution is not something I would know myself to construct:

Since $2<3$ we know that ${\mathrm{log}}_{2}3$ is positive (specifically it is greater than 1), and hence so is $2{\mathrm{log}}_{2}3$. Therefore, we can assume that a and b are two positive integers. Now $2{\mathrm{log}}_{2}3=a/b$ implies ${2}^{2{\mathrm{log}}_{2}3}={2}^{a/b}$. Thus

${2}^{a/b}={2}^{2{\mathrm{log}}_{2}3}={2}^{{\mathrm{log}}_{2}{3}^{2}}={3}^{2}=9\text{,}$

and hence ${2}^{a}={9}^{b}$

Any advice on approaching thought construct to logs would be greatly appreciated!

asked 2022-02-03

How do you write a polynomial in standard form, then classify it by degree and number of terms $y}^{3}-4y+6-{y}^{2$ ?

asked 2021-09-19

Solve the equation.

$\frac{4}{5x+2}-\frac{12}{15x+6}=0$

asked 2021-06-23

Use the strategy for solving word problems modeling the verbal conditions of the problem with a linear inequality. On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90. What must you get on the final to earn an A in the course?