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Recent questions tagged integers


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\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers
0 answers 45 views
\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers abcde \(=a+b+c+d+e\) \(\max (\max (a, b, c, d, e))=?\) ...
by Pieter Gold Status
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asked in Mathematics May 5
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Does MathsGee have a Number Line: Integers simulation?
1 answer 42 views
Does MathsGee have a Number Line: Integers simulation?Does MathsGee have a Number Line: Integers simulation? ...
by Pieter Gold Status
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asked in Physics & Chemistry May 1
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Write down the number of integers that satisfy the inequality \(-11\leq 3m-8\leq 4\)
1 answer 124 views
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What are all sets of three positive consecutive even integers such that twice the sum of the two is less than three several times the third?
0 answers 64 views
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Prove the following theorem:
1 answer 67 views
Prove the following theorem:Prove the following theorem: Let \(n\) and \(m\) be integers. Then i. if \(n\) and \(m\) are both even, then \(n+m\) is even, ii. if \(n\) and \(m\) ...
by MathsGee Platinum
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asked in Mathematics Jan 8
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Simplify \(\frac{1}{7} \times \frac{9}{16} \times \frac{16}{9} \times \frac{16}{9} \times \frac{9}{16}=\)
1 answer 132 views
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Are there lots of integer solutions for the mysterious equation, or just a few? \[ n! + n = n^n\]
1 answer 106 views
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Show that \(x^{2}-6 x+11>0\) for all real values of \(x\).
1 answer 103 views
Show that \(x^{2}-6 x+11>0\) for all real values of \(x\).Show that \(x^{2}-6 x+11>0\) for all real values of \(x\). ...
by MathsGee Platinum
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asked in Mathematics Nov 9, 2021
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Find the value of \(x\) such that \[ \frac{1+x}{x}=\sqrt{5} \] Giving your answer in the form \(a+b \sqrt{5}\) where \(a\) and \(b\) are rational numbers.

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Factorise completely: \(75 x-12 x^{3}\)
1 answer 70 views
Factorise completely: \(75 x-12 x^{3}\)Factorise completely: \(75 x-12 x^{3}\) ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Nov 9, 2021
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Factorise completely: \(x-16 x^{3}\)
1 answer 73 views
Factorise completely: \(x-16 x^{3}\)Factorise completely: \(x-16 x^{3}\) ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Nov 9, 2021
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Given \(y=2^{x}\) - Express \(4^{x}\) in terms of \(y\).
1 answer 89 views
Given \(y=2^{x}\) - Express \(4^{x}\) in terms of \(y\).Given \(y=2^{x}\) (a) Express \(4^{x}\) in terms of \(y\). (b) Hence, or otherwise, solve \(4^{x}-6\left(2^{x}\right)-16=0\) ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Nov 9, 2021
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Express \(8^{2 x-5}\) in the form \(2^{y}\), giving \(y\) in the form \(a x+b\), where \(a\) and \(b\) are constants.
1 answer 124 views
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Express \(9^{3 x+2}\) in the form \(3^{y}\), giving \(y\) in the form \(a x+b\), where \(a\) and \(b\) are constants.
1 answer 126 views
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Determine the value of m
1 answer 47 views
Determine the value of mIf $m$ is the largest integer for which $m^{200} < 5^{300}$, determine the value of $m$ ...
by Claudia Bronze Status
(5,894 points)
asked in Mathematics Oct 7, 2021
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\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)
1 answer 206 views
\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) A. \(\frac{-9}{8}\) B. ...
by Siyavula Bronze Status
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asked in Mathematics Sep 11, 2021
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\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\alpha+\beta\)
1 answer 179 views
\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\alpha+\beta\)\(\alpha\) and \(\beta\) are the roots of the equation \(2 x^{2}-3 x+4=0\). Find \(\alpha+\beta\) A. \(-2\) B. \(-\frac{3}{2}\) C. \(\frac{3}{2}\) D. ...
by Siyavula Bronze Status
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asked in Mathematics Sep 11, 2021
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What is the prime factorization of 136?
1 answer 107 views
What is the prime factorization of 136?What is the prime factorization of 136? ...
by MathsGee Platinum
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asked in Mathematics Sep 10, 2021
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Prove that there exist 3 indices $p, q$ and $r$ such that $p<q<r$ and
1 answer 177 views
Prove that there exist 3 indices $p, q$ and $r$ such that $p<q<r$ andProve that there exist 3 indices $p, q$ and $r$ such that $p&lt;q&lt;r$ and $$ \begin{gathered} a_{p} \leq a_{q} \leq a_{r} \\ b_{p} \leq b_{q} \leq ...
by MathsGee Platinum
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asked in Mathematics Aug 9, 2021
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When are two complex numbers equal?
1 answer 270 views
When are two complex numbers equal?When are two complex numbers equal? ...
by MathsGee Platinum
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asked in Mathematics Aug 8, 2021
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Can integers be written as rational numbers?
1 answer 90 views
Can integers be written as rational numbers? Write each of the following as a rational number. 7 0 -8 ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jul 29, 2021
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A(n) __________________ is an arrangement of numbers in rows and columns.
0 answers 86 views
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Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n$.
1 answer 186 views
Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n$.Let $P(n)$ and $S(n)$ denote the product and the sum, respectively, of the digits of the integer $n$. For example, $P(23)=6$ and $S(23)=5$. Suppose $N ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jul 16, 2021
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Express $b \times b \times b \times b \times b$ in exponential form:
1 answer 171 views
Express $b \times b \times b \times b \times b$ in exponential form:Express $b \times b \times b \times b \times b$ in exponential form: ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jun 27, 2021
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How many positive integers $n$ satisfy the inequality $2000<\sqrt{n(n+1)}<2016 ?$
0 answers 181 views
How many positive integers $n$ satisfy the inequality $2000<\sqrt{n(n+1)}<2016 ?$How many positive integers $n$ satisfy the inequality $2000&lt;\sqrt{n(n+1)}&lt;2016 ?$ ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jun 26, 2021
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For how many integers $n$ is $72\left(\frac{3}{2}\right)^{n}$ equal to an integer?
0 answers 133 views
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Two positive integers $m$ and $n$ satisfy the equation $m^{2} n=2016$. How many different values of $m$ are possible?
0 answers 157 views
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How many integers satisfy the equation $2^{x}(6-x)=8 x ?$
0 answers 93 views
How many integers satisfy the equation $2^{x}(6-x)=8 x ?$How many integers satisfy the equation $2^{x}(6-x)=8 x ?$ ...
by Edzai Zvobwo Bronze Status
(9,010 points)
asked in Mathematics Jun 26, 2021
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How many odd integers are there between $\frac{17}{4}$ and $\frac{47}{2}$ ?
0 answers 112 views
How many odd integers are there between $\frac{17}{4}$ and $\frac{47}{2}$ ?How many odd integers are there between $\frac{17}{4}$ and $\frac{47}{2}$ ? ...
by Edzai Zvobwo Bronze Status
(9,010 points)
asked in Mathematics Jun 26, 2021
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How are complex numbers related to real numbers?
1 answer 176 views
How are complex numbers related to real numbers?How are complex numbers related to real numbers? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jun 19, 2021
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For how many integers $x$ is the fraction $\frac{4 x-17}{5 x+9}$ also an integer?
0 answers 245 views
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If ${ }^{n} P_{r}:{ }^{n} C_{r}=126$ then find $n$ and $r$.
0 answers 108 views
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Find the number of rectangles and squares in an 8 by 8 chess board respectively.
0 answers 418 views
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For how many integers $n$ is the fraction $\frac{2 n^{2}+1}{n^{2}-1}$ also an integer?
0 answers 2K views
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When is the expression $\sqrt{a}$ real?
1 answer 77 views
When is the expression $\sqrt{a}$ real?When is the expression $\sqrt{a}$ real? ...
by Maths Genie Bronze Status
(5,562 points)
asked in Mathematics Jun 14, 2021
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Solve for $x$: $9^{x+1}=27^{x}$
1 answer 112 views
Solve for $x$: $9^{x+1}=27^{x}$Solve for $x$: $9^{x+1}=27^{x}$ ...
by Student SIlver Status
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asked in Mathematics Jun 14, 2021
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Express $9^{x-1}+3^{2 x}$ as a single power expression.
1 answer 116 views
Express $9^{x-1}+3^{2 x}$ as a single power expression.Express $9^{x-1}+3^{2 x}$ as a single power expression. ...
by Student SIlver Status
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asked in Mathematics Jun 14, 2021
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If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$
1 answer 240 views
If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$ 1) $-1$ 2) 1 3) 2 4) $-2$ ...
by Student SIlver Status
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asked in Mathematics Jun 12, 2021
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Difference between the corresponding roots of $x^{2}+a x+b=0$ and $x^{2}+b x+a=0$ is same and $a \neq b$, then
1 answer 117 views
Difference between the corresponding roots of $x^{2}+a x+b=0$ and $x^{2}+b x+a=0$ is same and $a \neq b$, thenDifference between the corresponding roots of $x^{2}+a x+b=0$ and $x^{2}+b x+a=0$ is same and $a \neq b$, then 1) $a+b+4=0$ 2) $a+b-4=0$ 3) $a-b-4=0$ ...
by MathsGee Platinum
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asked in Mathematics Jun 9, 2021
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If $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $\mathrm{z}$ lies
1 answer 110 views
If $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $\mathrm{z}$ liesIf $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $\mathrm{z}$ lies 1) either on the real axis or on a ...
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asked in Mathematics Jun 9, 2021
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The number of complex number $z$ such that $|z-1|=|z+1|=|z-i|$ equals
1 answer 238 views
The number of complex number $z$ such that $|z-1|=|z+1|=|z-i|$ equalsThe number of complex number $z$ such that $|z-1|=|z+1|=|z-i|$ equals 1) 1 2) 2 3) $\infty$ 4) 0 ...
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asked in Mathematics Jun 9, 2021
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If $z^{2}+z+1=0$, where $z$ is a complex number, then the value of
1 answer 182 views
If $z^{2}+z+1=0$, where $z$ is a complex number, then the value ofIf $z^{2}+z+1=0$, where $z$ is a complex number, then the value of $\begin{aligned}\left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^ ...
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asked in Mathematics Jun 9, 2021
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Let $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equals
1 answer 128 views
Let $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equalsLet $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equals 1) $\frac{\pi}{4}$ 2) $\frac{5 \pi}{4}$ 3) $\f ...
by MathsGee Platinum
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asked in Mathematics Jun 9, 2021
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$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+A r g w=\pi$ then $z$ equals
1 answer 104 views
$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+A r g w=\pi$ then $z$ equals$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+A r g w=\pi$ then $z$ equals 1) $\bar{w}$ 2) $-\bar{w}$ 3) w ...
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asked in Mathematics Jun 9, 2021
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Let $n$ be a positive integer. Show that $\left(1+\frac{1}{n+1}\right)^{n+1}>\left(1+\frac{1}{n}\right)^{n}$.
0 answers 179 views
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Let $n>1$ be an integer. Show that $$ n !<\left(\frac{n+1}{2}\right)^{n} $$
1 answer 152 views
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