332354 + Interview Questions in Secondary School in Math

1.	Using properties of Rational numbers find ½×⅚+⅓×¼
Answer» ANSWER: $\frac{1}{2}$ Step-by-step EXPLANATION: $(\frac{1}{2} * \frac{5}{6} ) +( \frac{1}{3} * \frac{1}{4} )$ = $\frac{5}{12} + \frac{1}{12}$ = $\frac{6}{12}$ = $\frac{1}{2}$

1.

Using properties of Rational numbers find ½×⅚+⅓×¼

Answer»

ANSWER:

$\frac{1}{2}$

Step-by-step EXPLANATION:

$(\frac{1}{2} * \frac{5}{6} ) +( \frac{1}{3} * \frac{1}{4} )$

= $\frac{5}{12} + \frac{1}{12}$

= $\frac{6}{12}$

= $\frac{1}{2}$

Discussion

2.	Write zero on 3a upon 7 - 1
Answer» PLEASE WRITE PROPERLY

2.

Write zero on 3a upon 7 - 1

Answer»

PLEASE WRITE PROPERLY

Discussion

3.	is 56351 a perfect square .if not find a perfect square number just less than 56351 and a perfect square number just less than 56351
Answer» Answer: 12238289292929929 Step-by-step EXPLANATION: bannananjakakskskskz

3.

is 56351 a perfect square .if not find a perfect square number just less than 56351 and a perfect square number just less than 56351

Answer»

Answer:

12238289292929929

Step-by-step EXPLANATION:

bannananjakakskskskz

Discussion

4.	The equivalent common fraction to recurring decimal fraction 0.6666... is
Answer» Answer: Step-by-step EXPLANATION: COMMON Repeating Decimals and Their Equivalent Fractions Repeating DECIMAL Equivalent Fraction 0.6666... 2/3 0.1666... 1/6 0.8333... 5/6 0.1111... 1/9

4.

The equivalent common fraction to recurring decimal fraction 0.6666... is

Answer»

Answer:

Step-by-step EXPLANATION:

COMMON Repeating Decimals and Their Equivalent Fractions

Repeating DECIMAL Equivalent Fraction

0.6666... 2/3

0.1666... 1/6

0.8333... 5/6

0.1111... 1/9

Discussion

5.	(3) x2 + 5x = -(3 - )
Answer» Step-by-step explanation: 3*2+5x =-3 6+5x=-3 5x= -3-6 x=-9/5 ANS

5.

(3) x2 + 5x = -(3 - )

Answer»

Step-by-step explanation:

3*2+5x =-3

6+5x=-3

5x= -3-6

x=-9/5 ANS

Discussion

6.	The formula for circumference of the circle
Answer» ANSWER: circumference of a circle=2πr or πd i *HOPE* it *will* *benefit* *you. PLEASE* *LIKE* at *least*...

6.

The formula for circumference of the circle

Answer»

ANSWER:

circumference of a circle=2πr or πd

i HOPE it will benefit you.

PLEASE LIKE at least...

Discussion

7.	Find the sunof the following8+9+10=
Answer» 27 85 28 4. 55 Hope it HELPS....XD

7.

Find the sunof the following8+9+10=

Answer»

27
85
28

4. 55

Hope it HELPS....XD

Discussion

8.	हल का अर्थ कल का अर्थ
Answer» ☆1. SOLUTION ☆ ☆2. TOMORROW ☆ $pls \\ mark \: as \: brainliest \infty \infty \infty \infty \infty \infty$

8.

हल का अर्थ कल का अर्थ

Answer»

☆1. SOLUTION ☆

☆2. TOMORROW ☆

$pls \\ mark \: as \: brainliest \infty \infty \infty \infty \infty \infty$

Discussion

9.	Sina/1-cosa =1+cosa-sina/sina-1+cosa
Answer» ANSWER: HI......... GOOD AFTERNOON

9.

Sina/1-cosa =1+cosa-sina/sina-1+cosa

Answer»

ANSWER:

HI.........

GOOD AFTERNOON

Discussion

10.	Factorise x to the power 12 is equal to 1
Answer» STEP-by-step explanation: Break the problem down to the exponents you can handle. Ideally, Difference of Squares or sum and difference of CUBES can be used. An explanation is given below on how to go about it. Explanation: Factoring x 12 − 1 can be tricky but can be broken down and worked it out step by step. Let US recollect some rules. Difference of squares a 2 − b 2 = ( a − b ) ( a + b ) Difference of cubes a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) Sum of cubes a 3 + b 3 = ( a + b ) ( a 2 − a b + b 2 ) Now let us come to our problem. x 12 − 1 Let us make x^12 into SOMETHING which we can recognize easily. x 12 = x 6 ⋅ 2 = ( x 6 ) 2 We have used a m n = ( a m ) n ( x 6 ) 2 − 1 2 Now it is of form a 2 − b 2 ( x 6 − 1 ) ( x 6 + 1 ) Let us factorize x 6 − 1 x 6 − 1 = ( x 3 ) 2 − 1 2 Rewriting x 6 to get into a 2 − b 2 form x 6 − 1 = ( x 3 − 1 ) ( x 3 + 1 ) x 6 − 1 = ( x − 1 ) ( x 2 + x + 1 ) ( x + 1 ) ( x 2 − x + 1 ) Now to factorize ( x 6 + 1 ) x 6 + 1 = ( x 2 ) 3 + 1 3 Rewriting x 6 to get it into a 3 + b 3 form x 6 + 1 = ( x 2 + 1 ) ( x 4 − x 2 + 1 ) Factors of ( x 6 − 1 ) ( x 6 + 1 ) = ( x − 1 ) ( x 2 + x + 1 ) ( x + 1 ) ( x 2 − x + 1 ) ( x 2 + 1 ) ( x 4 − x 2 + 1 ) Rearranging ( x − 1 ) ( x + 1 ) ( x 2 + 1 ) ( x 2 − x + 1 ) ( x 2 + x + 1 ) ( x 4 − x 2 + 1 ) Answer. Answer link

10.

Factorise x to the power 12 is equal to 1

Answer»

STEP-by-step explanation:

Break the problem down to the exponents you can handle. Ideally, Difference of Squares or sum and difference of CUBES can be used. An explanation is given below on how to go about it.

Explanation:

Factoring

x

12

−

1

can be tricky but can be broken down and worked it out step by step.

Let US recollect some rules.

Difference of squares

a

2

−

b

2

=

(

a

−

b

)

(

a

+

b

)

Difference of cubes

a

3

−

b

3

=

(

a

−

b

)

(

a

2

+

a

b

+

b

2

)

Sum of cubes

a

3

+

b

3

=

(

a

+

b

)

(

a

2

−

a

b

+

b

2

)

Now let us come to our problem.

x

12

−

1

Let us make x^12 into SOMETHING which we can recognize easily.

x

12

=

x

6

⋅

2

=

(

x

6

)

2

We have used

a

m

n

=

(

a

m

)

n

(

x

6

)

2

−

1

2

Now it is of form

a

2

−

b

2

(

x

6

−

1

)

(

x

6

+

1

)

Let us factorize

x

6

−

1

x

6

−

1

=

(

x

3

)

2

−

1

2

Rewriting

x

6

to get into

a

2

−

b

2

form

x

6

−

1

=

(

x

3

−

1

)

(

x

3

+

1

)

x

6

−

1

=

(

x

−

1

)

(

x

2

+

x

+

1

)

(

x

+

1

)

(

x

2

−

x

+

1

)

Now to factorize

(

x

6

+

1

)

x

6

+

1

=

(

x

2

)

3

+

1

3

Rewriting

x

6

to get it into

a

3

+

b

3

form

x

6

+

1

=

(

x

2

+

1

)

(

x

4

−

x

2

+

1

)

Factors of

(

x

6

−

1

)

(

x

6

+

1

)

=

(

x

−

1

)

(

x

2

+

x

+

1

)

(

x

+

1

)

(

x

2

−

x

+

1

)

(

x

2

+

1

)

(

x

4

−

x

2

+

1

)

Rearranging

(

x

−

1

)

(

x

+

1

)

(

x

2

+

1

)

(

x

2

−

x

+

1

)

(

x

2

+

x

+

1

)

(

x

4

−

x

2

+

1

)

Answer.

Answer link

Discussion

11.	I cannont understand this problem explain it brief please
Answer» ANSWER: where is the PROBLEM????????

11.

I cannont understand this problem explain it brief please

Answer»

ANSWER:

where is the PROBLEM????????

Discussion

12.	Is-150,a term of the Ap 17,12,7,2.....?
Answer» Answer: No NEVER. Step-by-step explanation: USE the formula of AP. Put first term,d and NTH term . Find n.( n will be a fraction which is never POSSIBLE))

12.

Is-150,a term of the Ap 17,12,7,2.....?

Answer»

Answer:

No NEVER.

Step-by-step explanation:

USE the formula of AP.

Put first term,d and NTH term .

Find n.( n will be a fraction which is never POSSIBLE))

Discussion

13.	The product of two rational number is 5/6 if one of them is -15 16 find the other
Answer» Step-by-step EXPLANATION: LET the no. be =X. then - 15/16 × x =5/6 solve it x= - 8/9

13.

The product of two rational number is 5/6 if one of them is -15 16 find the other

Answer»

Step-by-step EXPLANATION:

LET the no. be =X. then

- 15/16 × x =5/6

solve it

x= - 8/9

Discussion

14.	How many metres of ribbon can be made from a piece of cloth 1 m × 1 m of width 10 cm
Answer» Answer: 1000cm Step-by-step EXPLANATION: =100×100÷10 =1000cm

14.

How many metres of ribbon can be made from a piece of cloth 1 m × 1 m of width 10 cm

Answer»

Answer:

1000cm

Step-by-step EXPLANATION:

=100×100÷10

=1000cm

Discussion

15.	What is a international system of 123,115,027
Answer» ANSWER: SORRY i NEED POINTS

15.

What is a international system of 123,115,027

Answer»

ANSWER:

SORRY i NEED POINTS

Discussion

16.	If and are the zeroes of a polynomial p(x)= 6x2+x-2, find the value of 1+1−1
Answer» ANSWER: HURRAH! thois IA sanswer Step-by-step EXPLANATION:

16.

If and are the zeroes of a polynomial p(x)= 6x2+x-2, find the value of 1+1−1

Answer»

ANSWER:

HURRAH! thois IA sanswer

Step-by-step EXPLANATION:

Discussion

17.	Cm is equal to 0282 16162 24242 32 frequency e 67108
Answer» Answer: 345544434 errr33444444 rrrrrr

17.

Cm is equal to 0282 16162 24242 32 frequency e 67108

Answer»

Answer:

345544434 errr33444444 rrrrrr

Discussion

18.	What is its 100th term of the sequence 5, 12, 19, 26
Answer» GIVEN: A.P. = 5, 12, 19, 26 TO FIND: What is the 100th term of an A.P. ? SOLUTION: We have given the A.P. = 5, 12, 19, 26 a = 5 Common difference = d2 – d1 ➾ 12 – 5 = 7 d = 7 No. of terms = n = 100 We know that the formula for finding the nth term of an A.P. is:- $\large{\boxed{\bf{\star \: a_n = a + (n-1) d \: \star}}}$ According to question:- On putting the given values in the formula, we GET $\rm{\dashrightarrow a_n = 5 + (100-1)7 }$ $\rm{\dashrightarrow a_n = 5 + 99 \times 7}$ $\rm{\dashrightarrow a_n = 5 + 693 }$ $\bf{\dashrightarrow a_n = 698 }$ ❝ Hence, the nth term of an A.P. is 698 ❞ ______________________ ✯ Extra Information ✯ ⇛Sum of n terms = SN = n/2 [2a + (n–1)d] ⇛ Sum of n terms = Sn = n/2 [a + an]

18.

What is its 100th term of the sequence 5, 12, 19, 26

Answer»

TO FIND:

What is the 100th term of an A.P. ?

SOLUTION:

We have given the A.P. = 5, 12, 19, 26

a = 5

Common difference = d2 – d1

➾ 12 – 5 = 7

d = 7

No. of terms = n = 100

We know that the formula for finding the nth term of an A.P. is:-

$\large{\boxed{\bf{\star \: a_n = a + (n-1) d \: \star}}}$

According to question:-

On putting the given values in the formula, we GET

$\rm{\dashrightarrow a_n = 5 + (100-1)7 }$

$\rm{\dashrightarrow a_n = 5 + 99 \times 7}$

$\rm{\dashrightarrow a_n = 5 + 693 }$

$\bf{\dashrightarrow a_n = 698 }$

❝ Hence, the nth term of an A.P. is 698 ❞

______________________

✯ Extra Information ✯

⇛Sum of n terms = SN = n/2 [2a + (n–1)d]

⇛ Sum of n terms = Sn = n/2 [a + an]

Discussion

19.	Find the quotient and remainder when a is divided by b if a=17 b= -3
Answer» Step-by-step EXPLANATION: a=17 B= -3 when a is divided by b, quotient = -5, REMAINDER = 2

19.

Find the quotient and remainder when a is divided by b if a=17 b= -3

Answer»

Step-by-step EXPLANATION:

a=17 B= -3

when a is divided by b, quotient = -5, REMAINDER = 2

Discussion

20.	BRAINLIESTdraw the graph of the lines 4x+3y=24 write the coordinates of the point where this line meets the x-axis and y-axis also shade the triangle formed and finds it area with graph
Answer» ANSWER: FRIEND,this is your answer

20.

BRAINLIESTdraw the graph of the lines 4x+3y=24 write the coordinates of the point where this line meets the x-axis and y-axis also shade the triangle formed and finds it area with graph

Answer»

ANSWER:

FRIEND,this is your answer

Discussion

21.	Solve the quadraticsequation by factorisation method 7x² - 10x + 3 = 0
Answer» Answer:7x²-10x+3=0 7x²-7x-3x+3=0 7x(x-1)-3(x-1)=0 (7x-3)(x-1)=0 7x=3,x=1 x=3/7,x=1 Step-by-step explanation: Hope it helps you FRND....

21.

Solve the quadraticsequation by factorisation method 7x² - 10x + 3 = 0

Answer»

Answer:7x²-10x+3=0

7x²-7x-3x+3=0

7x(x-1)-3(x-1)=0

(7x-3)(x-1)=0

7x=3,x=1

x=3/7,x=1

Step-by-step explanation:

Hope it helps you FRND....

Discussion

22.	A^4-18a^2-16=0plz slove this quadratic equation??
Answer» Answer: a^4-18a^2-16=0 d=260=b^2-4ac a^2=(18+ $\sqrt{388}$ )/2 or a^2=(18- $\sqrt{388}$ )/2 this would be rejected as a SQ cannot be negative thus a= root of (18+ $\sqrt{388}$ )/2

22.

A^4-18a^2-16=0plz slove this quadratic equation??

Answer»

Answer:

a^4-18a^2-16=0

d=260=b^2-4ac

a^2=(18+ $\sqrt{388}$ )/2 or a^2=(18- $\sqrt{388}$ )/2 this would be rejected as a SQ cannot be negative

thus a= root of (18+ $\sqrt{388}$ )/2

Discussion

23.	Here is the two triangle 1st triangle is abc and next pqr thena=b,thenp=?
Answer» <P>ANSWER: ➡ p = R . Step-by-step EXPLANATION:

23.

Here is the two triangle 1st triangle is abc and next pqr thena=b,thenp=?

Answer»

<P>ANSWER: ➡ p = R .

Step-by-step EXPLANATION:

Discussion

24.	If x-y=2 and xy=15,find x3+y3
Answer» Step-by-step explanation: Please CHECK the QUESTION, we cannot FIND x3+y3 as the VALUE is in x-y=2

24.

If x-y=2 and xy=15,find x3+y3

Answer»

Step-by-step explanation:

Please CHECK the QUESTION, we cannot FIND x3+y3 as the VALUE is in x-y=2

Discussion

25.	If z=1+i,then z² If z=1+i,then z²
Answer» ANSWER: z² = 1 + i² + 2i Step-by-step EXPLANATION: Mark it as brainliest and follow me . ...

25.

If z=1+i,then z² If z=1+i,then z²

Answer»

ANSWER:

z² = 1 + i² + 2i

Step-by-step EXPLANATION:

Mark it as brainliest and follow me . ...

Discussion

26.	Which figure is formed by three non-collinear points
Answer» $\text{[math]}$ ⠀⠀⠀ $\huge\underline\mathfrak\pink{♡AnSwer♡}$ $\text{[math]}$ ⠀⠀⠀ ❍ A "ᴛʀɪᴀɴɢʟᴇ" ɪꜱ ᴀ ғɪɢᴜʀᴇ ғᴏʀᴍᴇᴅ ʙʏ ᴛʜʀᴇᴇ ꜱᴇɢᴍᴇɴᴛꜱ ᴊᴏɪɴɪɴɢ ᴛʜʀᴇᴇ ɴᴏɴᴄᴏʟʟɪɴᴇᴀʀ ᴘᴏɪɴᴛꜱ. $\text{[math]}$ $♡ B૨αเɳℓเεรƭ ρℓεαรε ♡$ ⠀⠀⠀ $\huge \mathfrak \red{♡ThAnKs...!!♡ }$

26.

Which figure is formed by three non-collinear points

Answer»

$\text{[math]}$

⠀⠀⠀ $\huge\underline\mathfrak\pink{♡AnSwer♡}$

$\text{[math]}$ ⠀⠀⠀ ❍ A "ᴛʀɪᴀɴɢʟᴇ" ɪꜱ ᴀ ғɪɢᴜʀᴇ ғᴏʀᴍᴇᴅ ʙʏ ᴛʜʀᴇᴇ ꜱᴇɢᴍᴇɴᴛꜱ ᴊᴏɪɴɪɴɢ ᴛʜʀᴇᴇ ɴᴏɴᴄᴏʟʟɪɴᴇᴀʀ ᴘᴏɪɴᴛꜱ.

$\text{[math]}$ $♡ B૨αเɳℓเεรƭ ρℓεαรε ♡$

⠀⠀⠀ $\huge \mathfrak \red{♡ThAnKs...!!♡ }$

Discussion

27.	Find the zeroes of X2 +13x+1
Answer» $\blue{\bold{\underline{\underline{Answer:}}}}$ $\green{\tt{\therefore{Value\:of\:x=\frac{-13\pm\sqrt{165}}{2}}}}\\$ $\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$ $\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt:\implies {x}^{2} + 13x + 1 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt:\implies Zeroes =?$ • ACCORDING to given QUESTION : $\tt \circ \: a = 1 \: \: \: \: \: \: b = 13 \: \: \: \: \: \: c = 1 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies D= {b}^{2} - 4ac \\ \\ \tt: \implies D= {13}^{2} - 4 \times 1 \times 1 \\ \\ \tt: \implies D = 169 - 4 \\ \\ \green{\tt: \implies D = 165} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ \tt: \implies x = \frac{ - 13 \pm \sqrt{165} }{2 \times 1} \\ \\ \green{\tt: \implies x = \frac{ - 13 \pm \sqrt{165} }{2} }$

27.

Find the zeroes of X2 +13x+1

Answer»

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=\frac{-13\pm\sqrt{165}}{2}}}}\\$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt:\implies {x}^{2} + 13x + 1 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt:\implies Zeroes =?$

• ACCORDING to given QUESTION :

$\tt \circ \: a = 1 \: \: \: \: \: \: b = 13 \: \: \: \: \: \: c = 1 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies D= {b}^{2} - 4ac \\ \\ \tt: \implies D= {13}^{2} - 4 \times 1 \times 1 \\ \\ \tt: \implies D = 169 - 4 \\ \\ \green{\tt: \implies D = 165} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies x = \frac{ - b \pm \sqrt{D} }{2a} \\ \\ \tt: \implies x = \frac{ - 13 \pm \sqrt{165} }{2 \times 1} \\ \\ \green{\tt: \implies x = \frac{ - 13 \pm \sqrt{165} }{2} }$

Discussion

28.	Plz Answer this anyone please
Answer» ANSWER: this is your answer hope it will HELP you! MARK me as a brainlist PLS

28.

Plz Answer this anyone please

Answer»

ANSWER:

this is your answer hope it will HELP you! MARK me as a brainlist PLS

Discussion

29.	Find the root of 1/x+4 - 1/x-7 =11/3
Answer» ANSWER: $hope \: it \: helps \: u \\ mark \: it \: as \: branlist \\ follow \: me \: pls$

29.

Find the root of 1/x+4 - 1/x-7 =11/3

Answer»

ANSWER:

$hope \: it \: helps \: u \\ mark \: it \: as \: branlist \\ follow \: me \: pls$

Discussion

30.	14. To stitch a shirt, 2 m 35 cm length of cloth is required. How much length of cloth is neededto stitch 11 such shirts?please help me
Answer» ANSWER: SEE the ATTACHEMENT...

30.

14. To stitch a shirt, 2 m 35 cm length of cloth is required. How much length of cloth is neededto stitch 11 such shirts?please help me

Answer»

ANSWER:

SEE the ATTACHEMENT...

Discussion

31.	Can someone pls solve this?In the following diagram, ABCD is a square while points P and Q lie on sides BC and CDrespectively such that APQ is an equilateral triangle. What is the ratio of the area of squareABCD to that of equilateral triangle APO?Solution: 4th option. 2 + root 3 / root 3
Answer» GIVEN: ABCD is a square. APQ is an equilateral triangle. To find: Ratio of area of square ABCD : Area of triangle APQ Solution: Please have a look at the labeling of the diagram as shown in the figure attached. Let side of square = x Let side of equilateral triangle = a In $\triangle ABP$ : AB = a BP = x and Hypotenuse, AP = s According to pythagorean THEOREM: $\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AP^{2} = AB^{2} + BP^{2}\\\Rightarrow s^2=a^{2} +x^{2} ........ (1)$ In $\triangle PQC$ : QC = PC = x - a and Hypotenuse, PQ = s According to pythagorean theorem: $\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow PQ^{2} = QC^{2} + PC^{2}\\\Rightarrow s^2=(a-x)^{2} +(a-x)^{2} ........ (2)$ Equating (1) and (2): $a^{2}+ x^{2} = (a-x)^2+(a-x)^2\\\Rightarrow a^{2}+ x^{2} = 2a^2+2x^2-4ax\\\Rightarrow x^{2} -4ax+a^2=0$ It is a quadratic equation. The solution of a quadratic equation $AX^2+BX+C=0$ is given as: $X=\dfrac{-B\pm \sqrt{B^2-4AC}}{2A}$ SOLVING the above quadratic equation: $x=\dfrac{4a\pm\sqrt{16a^2-4a^2}}{2}\\\Rightarrow x=\dfrac{4a\pm\sqrt{12a^2}}{2}\\\Rightarrow x=2a\pm\sqrt{3}a\\\\\Rightarrow x=a(2\pm\sqrt{3})\\$ Value $x=a(2-\sqrt3)$ will make $a-x$ as negative which is not possible so only one value $x=a(2+\sqrt3)$ is possible. Putting in equation (1) to find $s^2$ : $s^2=a^2+(a(2-\sqrt3))^2\\\Rightarrow s^2=a^2+(a^2(4+3-4\sqrt3))\\\Rightarrow s^2=a^2(8-4\sqrt3)$ The required ratio: $\dfrac{\text{Area of Square}}{\text{Area of Equilateral Triangle}}= \dfrac{a^2}{\dfrac{\sqrt3}{4}s^2}\\\Rightarrow \dfrac{4a^2}{\sqrt3 s^2}\\\Rightarrow \dfrac{4a^2}{4\sqrt3 (2-\sqrt3)a^2}\\\Rightarrow \dfrac{1}{\sqrt3 (2-\sqrt3)} \times \dfrac{2+\sqrt3}{2+\sqrt3}\\\Rightarrow \dfrac{2+\sqrt3}{\sqrt3 \times (4-3)}\\\Rightarrow \dfrac{2+\sqrt3}{\sqrt3}$ So, the required ratio is: $\dfrac{2+\sqrt3}{\sqrt3}$

31.

Can someone pls solve this?In the following diagram, ABCD is a square while points P and Q lie on sides BC and CDrespectively such that APQ is an equilateral triangle. What is the ratio of the area of squareABCD to that of equilateral triangle APO?Solution: 4th option. 2 + root 3 / root 3

Answer»

GIVEN:

ABCD is a square.

APQ is an equilateral triangle.

To find:

Ratio of area of square ABCD : Area of triangle APQ

Solution:

Please have a look at the labeling of the diagram as shown in the figure attached.

Let side of square = x

Let side of equilateral triangle = a

In $\triangle ABP$ :

AB = a

BP = x and

Hypotenuse, AP = s

According to pythagorean THEOREM:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AP^{2} = AB^{2} + BP^{2}\\\Rightarrow s^2=a^{2} +x^{2} ........ (1)$

In $\triangle PQC$ :

QC = PC = x - a and

Hypotenuse, PQ = s

According to pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow PQ^{2} = QC^{2} + PC^{2}\\\Rightarrow s^2=(a-x)^{2} +(a-x)^{2} ........ (2)$

Equating (1) and (2):

$a^{2}+ x^{2} = (a-x)^2+(a-x)^2\\\Rightarrow a^{2}+ x^{2} = 2a^2+2x^2-4ax\\\Rightarrow x^{2} -4ax+a^2=0$

It is a quadratic equation.

The solution of a quadratic equation $AX^2+BX+C=0$ is given as:

$X=\dfrac{-B\pm \sqrt{B^2-4AC}}{2A}$

SOLVING the above quadratic equation:

$x=\dfrac{4a\pm\sqrt{16a^2-4a^2}}{2}\\\Rightarrow x=\dfrac{4a\pm\sqrt{12a^2}}{2}\\\Rightarrow x=2a\pm\sqrt{3}a\\\\\Rightarrow x=a(2\pm\sqrt{3})\\$

Value $x=a(2-\sqrt3)$ will make $a-x$ as negative which is not possible so only one value $x=a(2+\sqrt3)$ is possible.

Putting in equation (1) to find $s^2$ :

$s^2=a^2+(a(2-\sqrt3))^2\\\Rightarrow s^2=a^2+(a^2(4+3-4\sqrt3))\\\Rightarrow s^2=a^2(8-4\sqrt3)$

The required ratio:

$\dfrac{\text{Area of Square}}{\text{Area of Equilateral Triangle}}= \dfrac{a^2}{\dfrac{\sqrt3}{4}s^2}\\\Rightarrow \dfrac{4a^2}{\sqrt3 s^2}\\\Rightarrow \dfrac{4a^2}{4\sqrt3 (2-\sqrt3)a^2}\\\Rightarrow \dfrac{1}{\sqrt3 (2-\sqrt3)} \times \dfrac{2+\sqrt3}{2+\sqrt3}\\\Rightarrow \dfrac{2+\sqrt3}{\sqrt3 \times (4-3)}\\\Rightarrow \dfrac{2+\sqrt3}{\sqrt3}$

So, the required ratio is:

$\dfrac{2+\sqrt3}{\sqrt3}$

Discussion

32.	The relation "is is father of" overthe set of family members is the relationa] Reflexive 6] Symmetricc] Transitived] None
Answer» if can't UNDERSTAND SORRY!!

Discussion

33.	A^2 + 4b2 + 6a + 4b + 10 = 0, find /
Answer» $Given \:a^{2}+4b^{2}+6a+4b+10=0$ $\implies a^{2}+6a+9 + 4b^{2}+4b+1 = 0$ $\implies [a^{2}+2\times a \times 3 + 3^{2} ]+[(2b)^{2}+2\times 2b\times 1 + 1^{2}] = 0$ $\implies ( a + 3 )^{2} + ( 2b + 1 )^{2} = 0$ /* By ALGEBRAIC IDENTITY */ $\boxed{\pink{ x^{2} + 2xy + y^{2} = ( x + y )^{2} }}$ $a + 3 = 0 \: and \: 2b + 1 = 0$ $\implies a = -3 \: and \: 2b = - 1$ $\implies a = -3 \: and \: b = \frac{- 1}{2}$ $Now , \red{ Value \: of \: \frac{a}{b} }$ $= \frac{(-3)}{\frac{-1}{2}}$ $= (-3) \times \frac{2}{(-1)}$ $= 6$ THEREFORE., $\red{ Value \: of \: \frac{a}{b} } \green { = 6}$ ••♪

33.

A^2 + 4b2 + 6a + 4b + 10 = 0, find /

Answer»

$Given \:a^{2}+4b^{2}+6a+4b+10=0$

$\implies a^{2}+6a+9 + 4b^{2}+4b+1 = 0$

$\implies [a^{2}+2\times a \times 3 + 3^{2} ]+[(2b)^{2}+2\times 2b\times 1 + 1^{2}] = 0$

$\implies ( a + 3 )^{2} + ( 2b + 1 )^{2} = 0$

/* By ALGEBRAIC IDENTITY */

$\boxed{\pink{ x^{2} + 2xy + y^{2} = ( x + y )^{2} }}$

$a + 3 = 0 \: and \: 2b + 1 = 0$

$\implies a = -3 \: and \: 2b = - 1$

$\implies a = -3 \: and \: b = \frac{- 1}{2}$

$Now , \red{ Value \: of \: \frac{a}{b} }$

$= \frac{(-3)}{\frac{-1}{2}}$

$= (-3) \times \frac{2}{(-1)}$

$= 6$

THEREFORE.,

$\red{ Value \: of \: \frac{a}{b} } \green { = 6}$

••♪

Discussion

34.	What is the output from the following machine when the input is 4 the topic is Function machine pls help
Answer» Step-by-step EXPLANATION: ANSWER IS –1 THANKS AND MARK ME AS BRAINLIEST.

34.

What is the output from the following machine when the input is 4 the topic is Function machine pls help

Answer»

Step-by-step EXPLANATION:

ANSWER IS –1

THANKS AND MARK ME AS BRAINLIEST.

Discussion

35.	Here is the two triangle 1st triangle is abc and next pqr here a=b,thenp=?
Answer» ANSWER: when I GET HOME and LET me KNOW

35.

Here is the two triangle 1st triangle is abc and next pqr here a=b,thenp=?

Answer»

ANSWER:

when I GET HOME and LET me KNOW

Discussion

36.	A = {∅ ,{∅ },2,{2,∅ },3}, which of the following is true?a) {{∅ ,{∅ }} ∈ A b) {2} ∈ A c) ∅ ⊂ A d) 3 ⊂ A
Answer» ANSWER: C Step-by-step EXPLANATION: PIE is SUBSET to any SET

36.

A = {∅ ,{∅ },2,{2,∅ },3}, which of the following is true?a) {{∅ ,{∅ }} ∈ A b) {2} ∈ A c) ∅ ⊂ A d) 3 ⊂ A

Answer»

ANSWER:

C

Step-by-step EXPLANATION:

PIE is SUBSET to any SET

Discussion

37.	State true or false The Roman number CDLXIV is 765 in Hindu Arabic
Answer» ANSWER: No Step-by-step EXPLANATION: It's WRONG... ...... ... .. . ........ ...

37.

State true or false The Roman number CDLXIV is 765 in Hindu Arabic

Answer»

ANSWER:

No

Step-by-step EXPLANATION:

It's WRONG...

......

...

..

.

........

...

Discussion

38.	If x2 - x - 1 = 0, then the value of x3 - 2x + 1 issolve with complete process
Answer» FIRST STEP is to split the middle term from x²-x-1 and then when u find the value of x then PUT it in x³-2x+1. two values will come after splitting so put both values and u will get one of the ANSWERS from the given options. pls mark me the brainliest

38.

If x2 - x - 1 = 0, then the value of x3 - 2x + 1 issolve with complete process

Answer»

FIRST STEP is to split the middle term from x²-x-1 and then when u find the value of x then PUT it in x³-2x+1. two values will come after splitting so put both values and u will get one of the ANSWERS from the given options.

pls mark me the brainliest

Discussion

39.	3. Write the following rationals in decimal form using Theorem 1.513/2515/1623/2(3) 5(2)7218/3(2) 5(2)143/110
Answer» Answer: 13/25 x 4/4 = 72/100 = 0.7215/16 = 15/2^4 = 15 / 2^4 x 5^4 /5^ 4 =15 x 625 /10^4 = 13.4375. Step-by-step EXPLANATION: MAY this ANSWER will help you PLZ mark has BRAINLIEST

39.

3. Write the following rationals in decimal form using Theorem 1.513/2515/1623/2(3) 5(2)7218/3(2) 5(2)143/110

Answer»

Answer:

13/25 x 4/4 = 72/100 = 0.7215/16 = 15/2^4 = 15 / 2^4 x 5^4 /5^ 4 =15 x 625 /10^4 = 13.4375.

Step-by-step EXPLANATION:

MAY this ANSWER will help you PLZ mark has BRAINLIEST

Discussion

40.	The value of(5-√5) (5 +√5) is
Answer» ANSWER: 20 is the answer for the GIVEN PROBLEM

40.

The value of(5-√5) (5 +√5) is

Answer»

ANSWER:

20 is the answer for the GIVEN PROBLEM

Discussion

41.	X2-4x+3) x3-6x2+11x-6(divide?
Answer» Answer: Q(X)=x−7 R(x)= x 2 +x+1 17x+1 Step-by-step explanation: PLS MARK me as brainlist.

41.

X2-4x+3) x3-6x2+11x-6(divide?

Answer»

Answer:

Q(X)=x−7

R(x)=

x

2

+x+1

17x+1

Step-by-step explanation:

PLS MARK me as brainlist.

Discussion

42.	(-8)+(-4) ___ (-8)-(-4) question is which symbol its answer >,< or =
Answer» Answer: < Step-by-step explanation: (- 8) + (- 4) = - 8 - 4 = -12 (- 8) - (- 4) = - 8 + 4 = - 4 :- -12 < - 4 because in NEGATIVE - 4 comes first so it is small tha -12. EG :- 4 > 3 > 2 > 1 > 0 > -1 > -2 > -3 > -4 > -5 <-6 > -7 > -8 > -9 > -10 > -11 > -12......

42.

(-8)+(-4) ___ (-8)-(-4) question is which symbol its answer >,< or =

Answer»

Answer:

<

Step-by-step explanation:

(- 8) + (- 4) = - 8 - 4 = -12

(- 8) - (- 4) = - 8 + 4 = - 4

:- -12 < - 4

because in NEGATIVE - 4 comes first so it is small tha -12.

EG :- 4 > 3 > 2 > 1 > 0 > -1 > -2 > -3 > -4 > -5 <-6 > -7 > -8 > -9 > -10 > -11 > -12......

Discussion

43.	Plese solve it urgent Don't spam
Answer» Step-by-step explanation: Here, B = 100° ( being Alternate angle ) Also, b + a = 180 ° ( being co interior angle) 100 + a = 180 a = 80 ° Again, D = 100° ( being vertically Opposite angle) Now, C = B ( being crossponding angle of //) c = 100°

43.

Plese solve it urgent Don't spam

Answer»

Step-by-step explanation:

Here,

B = 100° ( being Alternate angle )

Also,

b + a = 180 ° ( being co interior angle)

100 + a = 180

a = 80 °

Again,

D = 100° ( being vertically Opposite angle)

Now,

C = B ( being crossponding angle of //)

c = 100°

Discussion

44.	Thezeroesx²-3of quadratic polynomial
Answer» *HOPE* it helps *you...... PLZ* *mark* my *answer* as a brainliest..✌ and also foll**ow me...

44.

Thezeroesx²-3of quadratic polynomial

Answer»

HOPE it helps you......

PLZ mark my *answer*** as a

brainliest..✌

and also follow me...

Discussion

45.	Hcf and lcm 12 and 17 using primefactorization
Answer» ANSWER: L can't UNDERSTAND your QUESTION

45.

Hcf and lcm 12 and 17 using primefactorization

Answer»

ANSWER:

L can't UNDERSTAND your QUESTION

Discussion

46.	Please answer me very urgent
Answer» CORRECT ANSWER is PARALLEL

46.

Please answer me very urgent

Answer»

CORRECT ANSWER is PARALLEL

Discussion

47.	Pls.....help me it is 10th maths-1 Question
Answer» ANSWER: HEY there PLS MARK as BRAINLIEST

47.

Pls.....help me it is 10th maths-1 Question

Answer»

ANSWER:

HEY there PLS MARK as BRAINLIEST

Discussion

48.	Define limt of a function at a point and give two examples
Answer» Step-by-step explanation: Informally, a function F assigns an output f(x) to every INPUT x. We say the function has a limit L at an input p: this means f(x) gets CLOSER and closer to L as x moves closer and closer to p. More specifically, when f is applied to any input sufficiently close to p, the output VALUE is forced ARBITRARILY close to L.

48.

Define limt of a function at a point and give two examples

Answer»

Step-by-step explanation:

Informally, a function F assigns an output f(x) to every INPUT x. We say the function has a limit L at an input p: this means f(x) gets CLOSER and closer to L as x moves closer and closer to p. More specifically, when f is applied to any input sufficiently close to p, the output VALUE is forced ARBITRARILY close to L.

Discussion

49.	Hcf and lcm 120 and 288 using primefactorization
Answer» Answer: In some questions the highest common factor (HCF) or lowest common multiple (LCM) of two large numbers may need to be found. It would take a long time to write out all the factors and multiples of 24 and 180 and COMPARE the lists and it would be easy to make a mistake. A more efficient method is to use prime factors. USING prime factors to find the HCF and LCM Numbers can be broken down into prime factors using prime factor trees. When the prime factors of two numbers are known, they can be compared to calculate HCFs and LCMs. This can be a more efficient method than listing the factors and multiples of large numbers. Example Find the HCF and LCM of 24 and 180. Start by writing 24 and 180 as the product of their prime factors. Factor trees of 24 and 180 The product of prime factors for 24 is: 2 \times 2 \times 2 \times 3 The product of prime factors for 180 is: 2 \times 2 \times 3 \times 3 \times 5 To find the HCF, find any prime factors that are in common between the products. Each product contains two 2S and one 3, so use these for the HCF. HCF = 2 \times 2 \times 3 = 12 Cross any numbers used so far off from the products. The product of prime factors for 24 is: \cancel2\times\cancel2\times2\times\cancel3 The product of prime factors for 180 is: \cancel2\times\cancel2\times\cancel3\times3\times5 To find the LCM, multiply the HCF by all the numbers in the products that have not YET been used. LCM = 12 \times 2 \times 3 \times 5 = 360

49.

Hcf and lcm 120 and 288 using primefactorization

Answer»

Answer:

In some questions the highest common factor (HCF) or lowest common multiple (LCM) of two large numbers may need to be found.

It would take a long time to write out all the factors and multiples of 24 and 180 and COMPARE the lists and it would be easy to make a mistake.

A more efficient method is to use prime factors.

USING prime factors to find the HCF and LCM

Numbers can be broken down into prime factors using prime factor trees. When the prime factors of two numbers are known, they can be compared to calculate HCFs and LCMs. This can be a more efficient method than listing the factors and multiples of large numbers.

Example

Find the HCF and LCM of 24 and 180.

Start by writing 24 and 180 as the product of their prime factors.

Factor trees of 24 and 180

The product of prime factors for 24 is: 2 \times 2 \times 2 \times 3

The product of prime factors for 180 is: 2 \times 2 \times 3 \times 3 \times 5

To find the HCF, find any prime factors that are in common between the products. Each product contains two 2S and one 3, so use these for the HCF.

HCF = 2 \times 2 \times 3 = 12

Cross any numbers used so far off from the products.

The product of prime factors for 24 is: \cancel2\times\cancel2\times2\times\cancel3

The product of prime factors for 180 is: \cancel2\times\cancel2\times\cancel3\times3\times5

To find the LCM, multiply the HCF by all the numbers in the products that have not YET been used.

LCM = 12 \times 2 \times 3 \times 5 = 360

Discussion

50.	Please help me with this question urgently
Answer» ANSWER: aaggee PEECHE aaggee peeche aaggee peeche Step-by-step EXPLANATION:

50.

Please help me with this question urgently

Answer»

ANSWER:

aaggee PEECHE

aaggee peeche

Step-by-step EXPLANATION:

Discussion

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