Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\sqrt[4]{\dfrac{x+1}{2}} = \dfrac{1}{2}$, then find $x $.

  1. $-0.969$
  2. $-0.875$
  3. $0$
  4. $0.875$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given is $\sqrt [ 4 ]{ \dfrac { x+1 }{ 2 }  } = \dfrac { 1 }{ 2 } $
Now Raising the power to $4$ on both sides, we get
$\dfrac { x+1 }{ 2 } = { \left (\dfrac {1}{2}\right) }^{ 4 }\\ \Rightarrow \dfrac { x+1 }{ 2 } =\dfrac { 1 }{ 16 } \\ \Rightarrow 16x+16=2\\ \Rightarrow x=-0.875$
Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\dfrac{5}{x+3} = \dfrac{1}{x}+\dfrac{1}{2x}$, calculate the value of $x$.

  1. $\dfrac{3}{14}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{6}{13}$
  4. $\dfrac{3}{4}$
  5. $\dfrac{9}{7}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Given, $\dfrac { 5 }{ x+3 } =\dfrac { 1 }{ x } +\dfrac { 1 }{ 2x } $

Taking RHS:
$\dfrac { 1 }{ x } +\dfrac { 1 }{ 2x } $
LCM of these is $2x$
$\Rightarrow \dfrac { 2 }{ 2x } +\dfrac { 1 }{ 2x } \ \Rightarrow \dfrac { 3 }{ 2x } $
Now taking LHS:
$\dfrac { 5 }{ x+3 } $
It is given, LHS $=$ RHS
$\dfrac { 5 }{ x+3 } =\dfrac { 3 }{ 2x } $
$\Rightarrow 5\times 2x=3\times (x+3)\ \Rightarrow 10x=3x+9\ \Rightarrow x=\dfrac {9}{7}$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

One of the requirements for becoming a court reporter is the ability to type  $225$  words per minute. Donald can currently type  $180$  words per minute, and believes that with practice he can increase his typing speed by  $5$  words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type  $m $ months from now?

  1. $5 + 180 m$
  2. $ 225 + 5 m$
  3. $ 180 + 5 m$
  4. $ 180 - 5 m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With $ m $ months, Donald can type $5m $ more words per  minutes on top of $ 180 $ words.

So, total number of words Donald believes that he will be able to type $ m $ months from now $ = 180 + 5m $

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\sqrt[3]{5j - 7} = -\cfrac{1}{2}$, calculate the value of $j$.

  1. $1.375$
  2. $2.118$
  3. $2.599$
  4. $5.125$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $\sqrt [ 3 ]{ 5j-7 } =\dfrac { -1 }{ 2 } $

On cubing on both sides, we get
$5j-7=\dfrac { -1 }{ 8 } $
$\Rightarrow 5j=\dfrac { 55 }{ 8 } $
$\Rightarrow j=\dfrac { 11 }{ 8 } $
$\Rightarrow  j = 1.375$
Hence, option A is correct.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $\sqrt[5]{\cfrac{g-1}{4}} = \cfrac{1}{3}$, then find the value of $g$.

  1. $0.984$
  2. $0.996$
  3. $1.004$
  4. $1.016$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, $\sqrt [ 5 ]{ \dfrac { g-1 }{ 4 }  } =\dfrac { 1 }{ 3 } $

$ \Rightarrow  $ $\cfrac{g-1}{4} = \cfrac { 1 }{ { 3 }^{ 5 } } =\cfrac { 1 }{ 243 } $
$ \Rightarrow  $ $ g-1 = \cfrac{4}{243}$
$ \Rightarrow  $ $ g = 1 + \cfrac{4}{243} = 1.016$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

The area of square $ABCD$ is three-fourths the area of parallelogram $EFGH$. The area of parallelogram $EFGH$ is one-third the area of trapezoid $IJKL$. If square $ABCD$ has an area of $125$ square feet, calculate the area of trapezoid $IJKL$, in square feet.

  1. $75$
  2. $225$
  3. $350$
  4. $500$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, area of square $ABCD$ is three fourth of area of parallelogram $EFGH$,

And the area of parallelogram $EFGH$ is one-third of the area of trapezoid $IJKL$ and area of square $ABCD$ is $125$.
Let the area of trapezoid $IJKL$ is $x$
Then  area of  parallelogram $EFGH =$ $\dfrac{1}{3}x$
And  area of square $ABCD=$ $\dfrac{3}{4}$ area of  parallelogram $EFGH=$ $\dfrac{3}{4}\times \dfrac{1}{3}x=\dfrac{1}{4}x$
But area of square $ABCD =125$
$\therefore \dfrac{1}{4}x=125$
$\Rightarrow x=500$
So, area of trapezoid $IJKL=500$.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Find the value of $x: \dfrac {1}{x} + \dfrac {4}{5x} = \dfrac {2}{x + 5}$

  1. $0.71$
  2. $3.57$
  3. $5.8$
  4. $45$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given  $\dfrac { 2 }{ x+5 } =\dfrac { 1 }{ x } +\dfrac { 4 }{ 5x } $
Taking RHS:

$\dfrac { 1 }{ x } +\dfrac { 4 }{ 5x } $

LCM is $5x$
$\Rightarrow \dfrac { 5 }{ 5x } +\dfrac { 4 }{ 5x } \\ \Rightarrow \dfrac { 9 }{ 5x } $
Now taking LHS:
$\dfrac { 2 }{ x+5 } $
LHS $=$ RHS
$\dfrac { 2 }{ x+5 } =\dfrac { 9 }{ 5x } $
$\Rightarrow 5x\times 2=9(x+5)\\ \Rightarrow 10x=9x+45\\ \Rightarrow x=45$