Question

Solve
i] 3/7+x=17/7
ii] The solution of 2x – 3 = 7 is _____________.
iii] The additive identity for rational numbers is _____________.
iv] Each of the angles of a square is _____________.
v] The angles of a quadrilateral are in ratio 1:2:3:4. Which angle has the largest measure?
vi] A perfect square number between 30 and 40 is _____________.
vii] What will be the number of zero in the square of the number 50?
viii] The one’s digit of the cube of 53 is _____________.
ix] By what number should 81 be divided to get perfect cube?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

i] $\sf\:\frac{3}{7}+x=\frac{17}{7}$

$\sf\dashrightarrow\:\frac{3+7x}{7}=\frac{17}{7}$

$\sf\dashrightarrow\:7(3+7x)=17 \times 7$

$\sf\dashrightarrow\:21+49x=119$

$\sf\dashrightarrow\:49x=119-21$

$\sf\dashrightarrow\:49x=98$

$\sf\:\dashrightarrow~x=$$\small\red{\tt\pmb{\frac{98}{49}}}$

Verifying :

$\sf\:\frac{3}{7}+x=\frac{17}{7}$

$\sf\to\:\frac{3}{7}+\frac{98}{49}=\frac{17}{7}$

$\sf\to\:\frac{21+98}{49}=\frac{17}{7}$

$\sf\to\:\frac{119}{49}=\frac{17}{7}$

$\sf\to\:119\times 7=17 \times 49$

$\sf\to\:833=833$

Hence Verified!~

‎_________________________

ii] The solution of 2x – 3 = 7 is _____ .

$\sf\:2x-3=7$

$\sf\dashrightarrow\:2x=7+3$

$\sf\dashrightarrow\:2x=10$

$\sf\dashrightarrow\:x=\cancel{\frac{10}{2}}$

$\sf\dashrightarrow\:x=$$\small\red{\tt\pmb{5}}$

Verifying :

$\sf\:2x-3=7$

$\sf\to\:2(5)-3=7$

$\sf\to\:10-3=7$

$\sf\to\:7=7$

Hence Verified!~

_________________________‎

iii] The additive identity for rational numbers is $\small\red{\tt\pmb{0}}$.

⠀⠀⠀⠀⠀⠀ ⋆ Additive identity is the number which when added to the number gives the same number. Only 0 is used as the additive identity, because adding 0 to any number we get the same given number.

‎ _________________________

iv] Each of the angles of a square is $\small\red{\tt\pmb{90°}}$.

Proof :

⋆ Sum of all the angles of a quadrilateral = 360°

We know all the four angles in the quadrilateral measures same.

$\sf\therefore\:x+x+x+x=360°$

$\sf\to\:4x=360°$

$\sf\to\:x=\cancel{\frac{360}{4}}$

$\sf\to\:x=$$\small\red{\tt\pmb{90°}}$

Hence proved!~

_________________________‎

v] The angles of a quadrilateral are in ratio 1:2:3:4. Which angle has the largest measure ?

Given :

• Ratio of angles in a quadrilateral = 1:2:3:4

Assumption :

Let the ,

• $\sf\:1^{st}~angle~=~x$
• $\sf\:2^{nd}~angle~=~2x$
• $\sf\:3^{rd}~angle~=~3x$
• $\sf\:4^{th}~angle~=~4x$

Solution :

As done in the question number iv] ,

⋆ Sum of all the angles of a quadrilateral = 360°

$\sf\therefore\:x+2x+3x+4x=360°$

$\sf\dashrightarrow\:10x=360°$

$\sf\dashrightarrow\:x=\cancel{\frac{360}{10}}$

$\bf\dashrightarrow\:x=36°$

Henceforth,

• $\sf\:1^{st}~angle~=~36°$
• $\sf\:2^{nd}~angle~=~2x = 2\times 36=72°$
• $\sf\:3^{rd}~angle~=~3x = 3\times 36=108°$
• $\sf\:4^{th}~angle~=~4x=4\times 36=144°$

$\sf\:Required~largest~angle~is$$\small\red{\tt\pmb{144°}}$

Verification :

Verifying if we got the correct values for all the angles.

$\sf\:x+2x+3x+4x=360°$

$\sf\to\:36+72+108+144=360°$

$\sf\to\:360°=360°$

Hence Verified!~

_________________________‎

vi] A perfect square number between 30 and 40 is $\small\red{\tt\pmb{36}}$.

Given :

• The numbers between 30 and 40.

To find :

• Need to calculate a perfect square number between 30 and 40.

Solution :

⋆ Perfect square number is a number that is an square of an integer.

Since ,

⠀⠀⠀⠀1 × 1 = 1

⠀⠀⠀⠀2 × 2 = 4

⠀⠀⠀⠀3 × 3 = 9

⠀⠀⠀⠀4 × 4 = 16

⠀⠀⠀⠀5 × 5 = 25

⠀⠀⠀⠀6 × 6 = 36

⠀⠀⠀⠀7 × 7 = 49

Thus, $\small\red{\tt\pmb{36}}$ is the only perfect square number between 30 and 40.

_________________________

vii] What will be the number of zero in the square of the number 50?

‎

⋆ Since 50 has only 1 zero , so its square will have $\small\red{\tt\pmb{2}}$ zeros.

_________________________

viii] The one’s digit of the cube of 53 is $\small\red{\tt\pmb{7}}$

⋆ The given number has 3 at units place so, its cube will end with 7.

_________________________

ix] By what number should 81 be divided to get perfect cube ?

⋆ Perfect cube is a number that is obtained by multiplying the same integer three times.

Here,

⠀⠀⠀⠀81 = 3 × 3 × 3 × 3

⠀⠀⠀⠀= 3³ × 3

Here, the prime factor 3 is not grouped as a triplet. Hence, we divide 81 by 3, so that the obtained number becomes a perfect cube.

⠀⠀⠀⠀⠀⠀⠀⠀[ 3 × 3 × 3 = 27 ]

$\sf\:Required~number~is$$\small\red{\tt\pmb{3}}$.

_________________________

❒‎ Final answers :

⠀⠀⠀⠀⠀⠀⠀⠀i] 98/49

⠀⠀⠀⠀⠀⠀⠀⠀ii] 5

⠀⠀⠀⠀⠀⠀⠀⠀iii] 0

⠀⠀⠀⠀⠀⠀⠀⠀iv] 90°

⠀⠀⠀⠀⠀⠀⠀⠀v] 144°

⠀⠀⠀⠀⠀⠀⠀⠀vi] 36

⠀⠀⠀⠀⠀⠀⠀⠀vii] 2

⠀⠀⠀⠀⠀⠀⠀⠀viii] 7

⠀⠀⠀⠀⠀⠀⠀⠀ix] 3

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