Tag: maths

Questions Related to maths

If $\sqrt[3]{8x+6} = -3$, calculate the value of $x$.

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

  1. $-4.125$

  2. $-2.625$

  3. $-1.875$

  4. $-1.125$

Show answer
Correct Option: A
Explanation:

Given $\sqrt [ 3 ]{ 8x+6 } =-3$

Cubing on both sides, we get
$8x+6=(-3)^3$
$\Rightarrow 8x+6=-27\ \Rightarrow x=(-27-6)/8=-33/8\ \Rightarrow x=-4.125$

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

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

  1. $-0.969$

  2. $-0.875$

  3. $0$

  4. $0.875$

Show answer
Correct Option: B
Explanation:
Given is $\sqrt [ 4 ]{ \dfrac { x+1 }{ 2 }  } = \dfrac { 1 }{ 2 } $
Now Raising the power to $4$ on both sides, we get
$\dfrac { x+1 }{ 2 } = { \left (\dfrac {1}{2}\right) }^{ 4 }\\ \Rightarrow \dfrac { x+1 }{ 2 } =\dfrac { 1 }{ 16 } \\ \Rightarrow 16x+16=2\\ \Rightarrow x=-0.875$

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

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

  1. $\dfrac{3}{14}$

  2. $\dfrac{1}{3}$

  3. $\dfrac{6}{13}$

  4. $\dfrac{3}{4}$

  5. $\dfrac{9}{7}$

Show answer
Correct Option: E
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 } $
$\Rightarrow 5\times 2x=3\times (x+3)\ \Rightarrow 10x=3x+9\ \Rightarrow x=\dfrac {9}{7}$

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?

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

  1. $5 + 180 m$

  2. $ 225 + 5 m$

  3. $ 180 + 5 m$

  4. $ 180 - 5 m$

Show answer
Correct Option: C
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 $

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

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

  1. $1.375$

  2. $2.118$

  3. $2.599$

  4. $5.125$

Show answer
Correct Option: A
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.

If $\dfrac {2}{3x + 12} = \dfrac {2}{3}$, then the value of $x + 4 $ is

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

  1. $\dfrac {1}{2}$

  2. $1$

  3. $\dfrac {3}{2}$

  4. $2$

Show answer
Correct Option: B
Explanation:

Given $\dfrac { 2 }{ 3x+12 } =\dfrac { 2 }{ 3 } $

$\Rightarrow 3(2)=2(3x+12)$
$\Rightarrow 6=6x+24$
$\Rightarrow 6x=-18$
$\Rightarrow x=-3$
Therefore $x+4=-3+4=1$

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

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

  1. $0.984$

  2. $0.996$

  3. $1.004$

  4. $1.016$

Show answer
Correct Option: D
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$

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.

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

  1. $75$

  2. $225$

  3. $350$

  4. $500$

Show answer
Correct Option: D
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 $IJKL=500$.

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

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

  1. $0.71$

  2. $3.57$

  3. $5.8$

  4. $45$

Show answer
Correct Option: D
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 } $
$\Rightarrow 5x\times 2=9(x+5)\\ \Rightarrow 10x=9x+45\\ \Rightarrow x=45$

Find the value of $\dfrac {4}{y} + 4$ given that $\dfrac {4}{y} + 4 = \dfrac {20}{y} + 20$

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

  1. $-1$

  2. $0$

  3. $1$

  4. $4$

Show answer
Correct Option: B
Explanation:
The value of $\frac{20}{y}+20=5\left ( \frac{4}{y}+4 \right )$
Given $\frac{4}{y}+4=5\left ( \frac{4}{y}+4 \right )$
This when possible then value of $\frac{4}{y}+4=0$