332354 + Interview Questions in Secondary School in Math

1.	Kim invested $20,000 in an account that pays nominal interest rate of 6% compounded continuously. How many years, to the nearest tenth (one decimal) will it take for Kim's account to reach a value of $35,000?
Answer» Answer: It WIL take 12 year to reach the VALUE of 35,000

1.

Kim invested $20,000 in an account that pays nominal interest rate of 6% compounded continuously. How many years, to the nearest tenth (one decimal) will it take for Kim's account to reach a value of $35,000?

Answer»

Answer:

It WIL take 12 year to reach the VALUE of 35,000

Discussion

2.	If 10^2y=25, then wat is 10^-y
Answer» {10)^y }² = 5² => if POWERS are EQUAL , BASES are equal => 10^y = 5 => then , • 10^-y = 1 / 10^y = 1/5 { same as , 2^-1 = 1/2 }

2.

If 10^2y=25, then wat is 10^-y

Answer»

{10)^y }² = 5²

=> if POWERS are EQUAL , BASES are equal

=> 10^y = 5

=> then ,

• 10^-y = 1 / 10^y = 1/5

{ same as , 2^-1 = 1/2 }

Discussion

3.	Fatheya and Fatema, along with 30 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Fatheya will be called to perform first and Fatema will be called second?
Answer» Answer: 1/870 Step-by-step explanation: Total= 30 people Fatheya has 1/30 chance to be called first (1 out of 30) Fatema has then 1/29 chance to be called first after Fatheya was called (ONE out of 29) The probability of the scenario happening is 1/301/29= 1/870 Answer: 1/870*

3.

Fatheya and Fatema, along with 30 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Fatheya will be called to perform first and Fatema will be called second?

Answer»

Answer:

1/870

Step-by-step explanation:

Total= 30 people

Fatheya has 1/30 chance to be called first (1 out of 30)

Fatema has then 1/29 chance to be called first after Fatheya was called (ONE out of 29)

The probability of the scenario happening is 1/30*1/29= 1/870

Answer: 1/870

Discussion

4.	The value of [2-3(2-3)^3]^3
Answer» Hii Your ANSWER is -8 HOPE it will HELP you

4.

The value of [2-3(2-3)^3]^3

Answer»

Hii

Your ANSWER is

-8

HOPE it will HELP you

Discussion

5.	CALIFICO CON ESTRELLA: En una clínica de la ciudad se clasifica cada una de las urgencias de acuerdo con si gravedad :(L: leve ; U: urgente). En un día de la semana se reportaron 35 casos de urgencia de los 1.200 que se presentan al mes. POR FA RESPONDER
Answer» ANSWER: COULD you ASK it in ENGLISH?

5.

CALIFICO CON ESTRELLA: En una clínica de la ciudad se clasifica cada una de las urgencias de acuerdo con si gravedad :(L: leve ; U: urgente). En un día de la semana se reportaron 35 casos de urgencia de los 1.200 que se presentan al mes. POR FA RESPONDER

Answer»

ANSWER:

COULD you ASK it in ENGLISH?

Discussion

6.	Please explain the answer with proper written steps
Answer» ANSWER: (B) 108 Step-by-step explanation: √225 = 15 √(154 + 15) = √169 = 13 √{10 + √[25 + √(x + 13)]} = 4 {10 + √[25 + √(x + 13)]}² = 4² 10 + √[25 + √(x + 13)] = 16 √[25 + √(x + 13)] = 16 - 10 √[25 + √(x + 13)] = 6 {√[25 + √(x + 13)]}² = 6² 25 + √(x + 13) = 36 √(x + 13) = 36 - 25 √(x + 13) = 11 [√(x + 13)]² = 11² x + 13 = 121 x = 108

6.

Please explain the answer with proper written steps

Answer»

ANSWER:

(B) 108

Step-by-step explanation:

√225 = 15

√(154 + 15) = √169 = 13

√{10 + √[25 + √(x + 13)]} = 4

{10 + √[25 + √(x + 13)]}² = 4²

10 + √[25 + √(x + 13)] = 16

√[25 + √(x + 13)] = 16 - 10

√[25 + √(x + 13)] = 6

{√[25 + √(x + 13)]}² = 6²

25 + √(x + 13) = 36

√(x + 13) = 36 - 25

√(x + 13) = 11

[√(x + 13)]² = 11²

x + 13 = 121

x = 108

Discussion

7.	A box in the shape of a rectangular prism is shown. The box contains 1/2 inch number cubes.What is the volume of the box?
Answer» Step-by-step EXPLANATION: V = l×b×h = 5+(1/2)×1+(1/2)×2+(1/2) = 11/2×3/2×5/2 = 165/8 = 21+(5/8)

7.

A box in the shape of a rectangular prism is shown. The box contains 1/2 inch number cubes.What is the volume of the box?

Answer»

Step-by-step EXPLANATION:

V = l×b×h

= 5+(1/2)×1+(1/2)×2+(1/2)

= 11/2×3/2×5/2

= 165/8

= 21+(5/8)

Discussion

8.	From the figure and statement provided, select the proper TO PROVE statement.If two parallel planes are cut by a third plane, the lines of intersection are parallel.MN = ABAB + BC = ACm is parallel to lAB = BCa is parallel to b
Answer» ANSWER: Answer is 5) A is PARALLEL to B!

8.

From the figure and statement provided, select the proper TO PROVE statement.If two parallel planes are cut by a third plane, the lines of intersection are parallel.MN = ABAB + BC = ACm is parallel to lAB = BCa is parallel to b

Answer»

ANSWER:

Answer is 5) A is PARALLEL to B!

Discussion

9.	If (x,y)is the solution to the system of equations above, what is the value of y?Please answer, I will mark the brainliest
Answer» $☺️☺️☺️☺️☺️☺️☺️$ $☺hi HEARTIE here☺️$ ➻❥T꙰H꙰A꙰N꙰K꙰Y꙰O꙰U꙰➻❥ ♡ＬＯＶＥＹＯＵＲＳＥＬＦ♡ ❤️❤️ MARK me brainliest❤️❤️ $☺️☺️☺️☺️☺️☺️☺️$

9.

If (x,y)is the solution to the system of equations above, what is the value of y?Please answer, I will mark the brainliest

Answer»

$☺️☺️☺️☺️☺️☺️☺️$

$☺hi HEARTIE here☺️$

➻❥T꙰H꙰A꙰N꙰K꙰Y꙰O꙰U꙰➻❥

♡ＬＯＶＥＹＯＵＲＳＥＬＦ♡

❤️❤️ MARK me brainliest❤️❤️

$☺️☺️☺️☺️☺️☺️☺️$

Discussion

10.	How to do grouped frequency tables .STEP BY STEP
Answer» Step-by-step explanation: Creating a GROUPED Frequency Distribution Find the LARGEST and smallest values. Compute the RANGE = Maximum - Minimum. Select the number of classes desired. ... Find the class width by DIVIDING the range by the number of classes and rounding up. ... Pick a suitable starting point less than or EQUAL to the minimum value.

10.

How to do grouped frequency tables .STEP BY STEP

Answer»

Step-by-step explanation:

Creating a GROUPED Frequency Distribution

Find the LARGEST and smallest values.

Compute the RANGE = Maximum - Minimum.

Select the number of classes desired. ...

Find the class width by DIVIDING the range by the number of classes and rounding up. ...

Pick a suitable starting point less than or EQUAL to the minimum value.

Discussion

11.	How many additional blocks are required to make the cube whole?
Answer» Answer: If you're asked to make the cube whole, then the answer is 45. If you're asked to make the BLOCK whole, then the answer is 20. This is just ONE of many riddles and puzzles that are circulating on sites like Facebook and Instagram during the coronavirus pandemic. I HOPE you like it STAY home and stay safe

11.

How many additional blocks are required to make the cube whole?

Answer»

Answer:

If you're asked to make the cube whole, then the answer is 45. If you're asked to make the BLOCK whole, then the answer is 20. This is just ONE of many riddles and puzzles that are circulating on sites like Facebook and Instagram during the coronavirus pandemic.

I HOPE you like it

STAY home and stay safe

Discussion

12.	Please I need help, I will mark the brainliest to the brainliest answer lolmx-6y=102x-ny=5In the system of equations above, m and n are constant.If the system has infinitely many solutions, what is the value of m/n?
Answer» ANSWER: m=16 n=(-3) Step-by-step EXPLANATION:

12.

Please I need help, I will mark the brainliest to the brainliest answer lolmx-6y=102x-ny=5In the system of equations above, m and n are constant.If the system has infinitely many solutions, what is the value of m/n?

Answer»

ANSWER:

m=16

n=(-3)

Step-by-step EXPLANATION:

Discussion

13.	Please make a concept map of chapter 1 number system class 9
Answer» i HOPE this HELPS you you ... ..

13.

Please make a concept map of chapter 1 number system class 9

Answer»

i HOPE this HELPS you you

...

..

Discussion

14.	Please explain with proper written steps
Answer» 9 Step-by-step explanation: Given: $\sqrt{<klux>X</klux> + 16} - \sqrt{x} = 2$ To FIND: The value of x Solution: $\sqrt{x + 16} - \sqrt{x} = 2 \\ \\ \sqrt{x + 16} - 2 = \sqrt{x} \\ \\ \text{[Squaring both side]} \\ \\ {( \sqrt{x + 16} - 2) }^{2} = {( \sqrt{x}) }^{2} \\ \\ {( \sqrt{x + 16}) }^{2} + {(2)}^{2} - 2.2. \sqrt{x + 16} = x \\ \\ x + 16 + 4 - 4 \sqrt{x+16} = x \\ \\\cancel{x} + 20 - 4 \sqrt{x+ 16}=\cancel{x}\\\\ 20 = 4 \sqrt{x+16} \\ \\\cancel{20} = \cancel{4} \sqrt{x + 16} \\ \\ 5 = \sqrt{x + 16} \\ \\ \text{[Squaring both side]} \\ \\ {(5)}^{2} = {( \sqrt{x + 16}) }^{2} \\ \\ 25 = x + 16 \\ \\ 25 - 16 = x\\ \\ x = 9$ THEREFORE, The REQUIRED value of x is 9. Important Formula ${x}^{2}+{y}^{2}+2xy={(x + y)}^{2}\\\\{x}^{2}+{y}^{2}-2xy={(x - y)}^{2}\\\\(x + y)(x - y)={x}^{2}-{y}^{2}\\\\$

14.

Please explain with proper written steps

Answer»

9

Step-by-step explanation:

Given:

$\sqrt{<klux>X</klux> + 16} - \sqrt{x} = 2$

To FIND:

The value of x

Solution:

$\sqrt{x + 16} - \sqrt{x} = 2 \\ \\ \sqrt{x + 16} - 2 = \sqrt{x} \\ \\ \text{[Squaring both side]} \\ \\ {( \sqrt{x + 16} - 2) }^{2} = {( \sqrt{x}) }^{2} \\ \\ {( \sqrt{x + 16}) }^{2} + {(2)}^{2} - 2.2. \sqrt{x + 16} = x \\ \\ x + 16 + 4 - 4 \sqrt{x+16} = x \\ \\\cancel{x} + 20 - 4 \sqrt{x+ 16}=\cancel{x}\\\\ 20 = 4 \sqrt{x+16} \\ \\\cancel{20} = \cancel{4} \sqrt{x + 16} \\ \\ 5 = \sqrt{x + 16} \\ \\ \text{[Squaring both side]} \\ \\ {(5)}^{2} = {( \sqrt{x + 16}) }^{2} \\ \\ 25 = x + 16 \\ \\ 25 - 16 = x\\ \\ x = 9$

THEREFORE, The REQUIRED value of x is 9.

Important Formula

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

Discussion

15.	Consider circle C with diameter DE.The equation of circle C is (x-5, x-7, x+5, x+7) + (y-5, y-7, y+5, y+7) = 12, 80, 144, 160
Answer» ANSWER: DUDE you don't tell what to find out in the question PLZZ tell what to find Step-by-step explanation: plzz mark as brainilist PLZZZ

15.

Consider circle C with diameter DE.The equation of circle C is (x-5, x-7, x+5, x+7) + (y-5, y-7, y+5, y+7) = 12, 80, 144, 160

Answer»

ANSWER:

DUDE you don't tell what to find out in the question PLZZ tell what to find

Step-by-step explanation:

plzz mark as brainilist PLZZZ

Discussion

16.	How many numbers of the form 34a5b are divisible by 36?A]3B] 2C] 5
Answer» Step-by-step EXPLANATION: since digital sum of a number divisible by 36 is equal to 9. and even number at it's unit place. also 0 or multiple of 4 at hundred place (not at all, only in this CASE) => 3+4+a+5+B = 9 => 12+a+b = 9 => 1+2+a+b = 9 => a+b+3 = 9 => a+b = 6 => (a,b) = (0,6),(4,2) therefore four numbers are formed (1) 34056 (3) 34452 thus option(B) 2 is correct.

16.

How many numbers of the form 34a5b are divisible by 36?A]3B] 2C] 5

Answer»

Step-by-step EXPLANATION:

since digital sum of a number divisible by 36

is equal to 9.

and even number at it's unit place.

also 0 or multiple of 4 at hundred place

(not at all, only in this CASE)

=> 3+4+a+5+B = 9

=> 12+a+b = 9

=> 1+2+a+b = 9

=> a+b+3 = 9

=> a+b = 6

=> (a,b) = (0,6),(4,2)

therefore four numbers are formed

(1) 34056

(3) 34452

thus option(B) 2 is correct.

Discussion

17.	How do you simplify ratios (step by step)
Answer» Answer: EXAMPLE: Simplify the ratio 6 : 10 The factors of 6 are: 1, 2, 3, 6. The factors of 10 are: 1, 2, 5, 10. Then the greatest common factor of 6 and 10 is 2. Divide both terms by 2. 6 ÷ 2 = 3. 10 ÷ 2 = 5. Rewrite the ratio using the results. The simplified ratio is 3 : 5. 6 : 10 = 3 : 5 in simplest form. I HOPE you like it Stay home and stay safe Hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii please mark me as brainlist

17.

How do you simplify ratios (step by step)

Answer»

Answer:

EXAMPLE: Simplify the ratio 6 : 10

The factors of 6 are: 1, 2, 3, 6.

The factors of 10 are: 1, 2, 5, 10.

Then the greatest common factor of 6 and 10 is 2.

Divide both terms by 2.

6 ÷ 2 = 3.

10 ÷ 2 = 5.

Rewrite the ratio using the results. The simplified ratio is 3 : 5.

6 : 10 = 3 : 5 in simplest form.

I HOPE you like it

Stay home and stay safe

Hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii please mark me as brainlist

Discussion

18.	Brian and Colin are marking exam papers. Each set takes Brian 40 minutes and Colin 1 hour. Express the times Brian and Colin take as a ratio.How do i answer this question ?
Answer» ANSWER: The ratio is SIMPLY ALSO called division 1 HOUR = 60 minutes The ratio of the times TAKEN by Brian and Colin is 40:60(or 40/60 = 2/3) = 2:3 Step-by-step explanation:

18.

Brian and Colin are marking exam papers. Each set takes Brian 40 minutes and Colin 1 hour. Express the times Brian and Colin take as a ratio.How do i answer this question ?

Answer»

ANSWER:

The ratio is SIMPLY ALSO called division

1 HOUR = 60 minutes

The ratio of the times TAKEN by Brian and Colin is 40:60(or 40/60 = 2/3) = 2:3

Step-by-step explanation:

Discussion

19.	RootFind the squareof the following:484With solution
Answer» ANSWER: What to FIND,, SQUARE or square ROOT?

19.

RootFind the squareof the following:484With solution

Answer»

ANSWER:

What to FIND,, SQUARE or square ROOT?

Discussion

20.	The ratio of speeds of A is to B is 2: 3 and therefore A takes 20 minutes less time than B takes. What is the ratioof time taken by A and B?(a) 2:3(b) 2:5(c) 3:2(d) 3:5
Answer» ANSWER: 2:3 is the CORRECT answer

20.

The ratio of speeds of A is to B is 2: 3 and therefore A takes 20 minutes less time than B takes. What is the ratioof time taken by A and B?(a) 2:3(b) 2:5(c) 3:2(d) 3:5

Answer»

ANSWER:

2:3 is the CORRECT answer

Discussion

21.	Answer me of 6 parts of poygos then I will mark you as a brainliest.
Answer» Answer: Step-by-step explanation: Regular polygons include equilateral triangles, squares and MANY other shapes. The parts of polygons include the sides, interior angles and EXTERIOR angles. There is also the vertex, the spot where two sides MEET, and the diagonals, or lines connecting VERTICES #bisma

21.

Answer me of 6 parts of poygos then I will mark you as a brainliest.

Answer»

Answer:

Step-by-step explanation:

Regular polygons include equilateral triangles, squares and MANY other shapes. The parts of polygons include the sides, interior angles and EXTERIOR angles. There is also the vertex, the spot where two sides MEET, and the diagonals, or lines connecting VERTICES

#bisma

Discussion

22.	2 ND persons to land on the moon
Answer» *Edwin Eugene Aldrin, Jr.* Edwin Eugene Aldrin, Jr.Buzz Aldrin (born Edwin Eugene Aldrin, Jr., January 20, 1930) is an AMERICAN engineer and former ASTRONAUT. As the Lunar Module PILOT on Apollo 11, he was one of the first TWO HUMANS to land on the Moon, and the second person to walk on it.

22.

2 ND persons to land on the moon

Answer»

Edwin Eugene Aldrin, Jr.

Edwin Eugene Aldrin, Jr.Buzz Aldrin (born Edwin Eugene Aldrin, Jr., January 20, 1930) is an AMERICAN engineer and former ASTRONAUT. As the Lunar Module PILOT on Apollo 11, he was one of the first TWO HUMANS to land on the Moon, and the second person to walk on it.

Discussion

23.	What is the LCM OF 72 ,102
Answer» ANSWER: The answer is 1224 Step-by-step EXPLANATION:

23.

What is the LCM OF 72 ,102

Answer»

ANSWER:

The answer is 1224

Step-by-step EXPLANATION:

Discussion

24.	I need to know how to do ratio questions .
Answer» ANSWER: Depends on what you need to know. Step-by-step EXPLANATION: I am happy to HELP U THO

24.

I need to know how to do ratio questions .

Answer»

ANSWER:

Depends on what you need to know.

Step-by-step EXPLANATION:

I am happy to HELP U THO

Discussion

25.	Factorise the following sum : 2-50x^2
Answer» ANSWER: The answer is (2)(1 + 5X)(1 - 5x) Step-by-step EXPLANATION:

25.

Factorise the following sum : 2-50x^2

Answer»

ANSWER:

The answer is (2)(1 + 5X)(1 - 5x)

Step-by-step EXPLANATION:

Discussion

26.	Solve: x(x+2)(x^2-1)=-1
Answer» ANSWER: The answer is (x^2 + 2X)(x^2 - 1) = -1 x^4 - x^2 + 2x^3 - 2x = p(x) (-1)^4 - (-1)^2 + 2(-1)^3 - 2(-1) =p(-1) 1 - 1 - 2 + 2 = 0 0 = 0 p(-1) = 0 HENCE SOLVED Step-by-step explanation:

26.

Solve: x(x+2)(x^2-1)=-1

Answer»

ANSWER:

The answer is (x^2 + 2X)(x^2 - 1) = -1

x^4 - x^2 + 2x^3 - 2x = p(x)

(-1)^4 - (-1)^2 + 2(-1)^3 - 2(-1) =p(-1)

1 - 1 - 2 + 2 = 0

0 = 0

p(-1) = 0

HENCE SOLVED

Step-by-step explanation:

Discussion

27.	200+300+10+1000=? answer this I will give you brainliestThanks for the answer
Answer» ANSWER: 1510 is a answer . ............

27.

200+300+10+1000=? answer this I will give you brainliestThanks for the answer

Answer»

ANSWER:

1510 is a answer .

............

Discussion

28.	7tan2A-7cosec2A Pls.helpmMe
Answer» Answer: As you have not said to prove the above PROBLEM with something Instead you could take A as 30° to SOLVE to get a VALUE So, take 7 common from the above TERMS and SUBSTITUTE the value of A And finally you will end with the answer of getting the value as 7(√3-1÷2)

28.

7tan2A-7cosec2A Pls.helpmMe

Answer»

Answer:

As you have not said to prove the above PROBLEM with something

Instead you could take A as 30° to SOLVE to get a VALUE

So, take 7 common from the above TERMS and SUBSTITUTE the value of A

And finally you will end with the answer of getting the value as 7(√3-1÷2)

Discussion

29.	On dividing p(x) by g(x),quotient q(x) and remainder r(x) =14x-10 is obtained. Then p(x) is
Answer» ANSWER: CHECK your QUESTION once again..

29.

On dividing p(x) by g(x),quotient q(x) and remainder r(x) =14x-10 is obtained. Then p(x) is

Answer»

ANSWER:

CHECK your QUESTION once again..

Discussion

30.	The sum of two integers is minus 15 If one of them is 8,find the other
Answer» ANSWER: -23 Step-by-step explanation: let the other INTEGER be X 8+X=-15 X=-15-8 X=-23 hope it helped. pls mark as the BRAINLIEST ANS ❤️❤️❤️... pls follow me...

30.

The sum of two integers is minus 15 If one of them is 8,find the other

Answer»

ANSWER:

-23

Step-by-step explanation:

let the other INTEGER be X

8+X=-15

X=-15-8

X=-23

hope it helped.

pls mark as the BRAINLIEST ANS ❤️❤️❤️...

pls follow me...

Discussion

31.	Sebastian has 121212 more trophies than Megan. Megan has ttt trophies. How many trophies does Sebastian have?
Answer» ANSWER: Step-by-step EXPLANATION: SEBASTIAN- s, MEGAN- ttt Sebastian has 121212 more TROPHIES than Megan s=ttt+121212 Sebastian has: ttt+121212 trophies

31.

Sebastian has 121212 more trophies than Megan. Megan has ttt trophies. How many trophies does Sebastian have?

Answer»

ANSWER:

Step-by-step EXPLANATION:

SEBASTIAN- s, MEGAN- ttt

Sebastian has 121212 more TROPHIES than Megan

s=ttt+121212

Sebastian has: ttt+121212 trophies

Discussion

32.	Find a rational and irrational no. between two positive number a and b
Answer» ANSWER: Hi frnd here's the answer to the GIVEN question For RATIONAL NUMBERS a+b/2 For IRRATIONAL NUMBERS is √ab Step-by-step explanation: hope it helped. pls MARK as the brainliest ANS ❤️❤️❤️.. pls follow me...

32.

Find a rational and irrational no. between two positive number a and b

Answer»

ANSWER:

Hi frnd here's the answer to the GIVEN question

For RATIONAL NUMBERS a+b/2

For IRRATIONAL NUMBERS is √ab

Step-by-step explanation:

hope it helped.

pls MARK as the brainliest ANS ❤️❤️❤️..

pls follow me...

Discussion

33.	S.P. of an article sold at Rs 264 at 12%. Find the cost price of the article.
Answer» Answer: ₹235.71 Step-by-step EXPLANATION: S.P.= ₹264, PROFIT= 12%, COST=x x+12%=₹264 x1.12=₹264 x=₹264/1.12 x=₹235.71 Answer: Cost price is ₹235.71*

33.

S.P. of an article sold at Rs 264 at 12%. Find the cost price of the article.

Answer»

Answer:

₹235.71

Step-by-step EXPLANATION:

S.P.= ₹264, PROFIT= 12%, COST=x

x+12%=₹264
x*1.12=₹264
x=₹264/1.12
x=₹235.71

Answer: Cost price is ₹235.71

Discussion

34.	Prove that cos2A+cos4A+cos6A+cos8A=4cosA cos2A cos5A
Answer» $\\ \large{ \bold{ \underline{TO \: \: PROVE} : - }} \\ \\$ $\\ \implies { \bold{ cos(2A)+cos(4A)+cos(6A)+cos(8A)=4cos(A) cos(2A) cos(5A) }} \\$ $\\ \large{ \bold{ \underline{Solution} : - }} \\$ • Let's take L.H.S. – $\\ \: \: \: \: { \bold{ = \: cos(2A) + cos(4A) + cos(6A) + cos(8A) }} \\$ • We know that – $\\ \\ \: \: \: \large \bigstar \: \: { \red{ \boxed{ \bold{ cos(C) + cos(D) = 2cos( \frac{C + D}{2} ) cos( \frac{C - D}{2} ) }}}} \\ \\$ • Now APPLYING formula – $\\ \: \: \: \: { \bold{ = \: 2 cos( \frac{2A + 4A}{2} ) cos( \frac{2A - 4A}{2} ) + 2 cos( \frac{6A + 8A}{2} ) cos( \frac{6A - 8A}{2} ) }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( \frac{ 6A}{ 2} ) cos( \frac{ - 2A }{2} ) + 2 cos( \frac{14A}{2} ) cos( \frac{ - 2A}{2} ) }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( 3A) cos( - A ) + 2 cos(7A ) cos( - A ) }} \\$ • Using IDENTITY – $\\ \\ \: \: \: \large \bigstar \: \: \: { \red{ \boxed{ \bold{ cos( - \theta) = cos( \theta) }}}} \\ \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( 3A) cos( A ) + 2 cos(7A ) cos( A ) }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ cos(3A ) \: + cos(7A )\: ] }} \\$ • Now again applying formula – $\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( \frac{3A +7A }{2} ) \: cos( \frac{3A - 7A}{2} )\: ] }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( \frac{10A }{2} ) \: cos( \frac{ - 4A}{2} )\: ] }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( 5A ) \: cos( - 2A )\: ] }} \\$ $\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( 5A ) \: cos( 2A )\: ] }} \\$ $\\ \: \: \: \: { \bold{ = \: 4 cos( A ) \: cos( 2A )\: cos( 5A ) }} \\$ $\\ \: \: \: \: { \bold{ = R.H.S. }} \\$ ADDITIONAL information :– $\\ \: \: \: \large \bigstar \: \: { \red { \bold{ sin(C) + sin(D) = 2sin( \frac{C+ D}{2} ) cos( \frac{ C - D}{2} ) }}} \\$ $\\ \: \: \: \large \bigstar \: \: { \red { \bold{ sin(C) - sin(D) = 2cos( \frac{C + D}{2} ) sin( \frac{C - D}{2} ) }}} \\$ $\\ \: \: \: \large \bigstar \: \: { \red { \bold{ cos(C) + cos(D) = 2cos( \frac{C + D}{2} ) cos( \frac{C - D}{2} ) }}} \\$ $\\ \: \: \: \large \bigstar \: \: { \red { \bold{ cos(C) - cos(D) = 2sin( \frac{C + D}{2} ) sin( \frac{D - C}{2} ) }}} \\$

34.

Prove that cos2A+cos4A+cos6A+cos8A=4cosA cos2A cos5A

Answer»

$\\ \large{ \bold{ \underline{TO \: \: PROVE} : - }} \\ \\$

$\\ \implies { \bold{ cos(2A)+cos(4A)+cos(6A)+cos(8A)=4cos(A) cos(2A) cos(5A) }} \\$

$\\ \large{ \bold{ \underline{Solution} : - }} \\$

• Let's take L.H.S. –

$\\ \: \: \: \: { \bold{ = \: cos(2A) + cos(4A) + cos(6A) + cos(8A) }} \\$

• We know that –

$\\ \\ \: \: \: \large \bigstar \: \: { \red{ \boxed{ \bold{ cos(C) + cos(D) = 2cos( \frac{C + D}{2} ) cos( \frac{C - D}{2} ) }}}} \\ \\$

• Now APPLYING formula –

$\\ \: \: \: \: { \bold{ = \: 2 cos( \frac{2A + 4A}{2} ) cos( \frac{2A - 4A}{2} ) + 2 cos( \frac{6A + 8A}{2} ) cos( \frac{6A - 8A}{2} ) }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( \frac{ 6A}{ 2} ) cos( \frac{ - 2A }{2} ) + 2 cos( \frac{14A}{2} ) cos( \frac{ - 2A}{2} ) }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( 3A) cos( - A ) + 2 cos(7A ) cos( - A ) }} \\$

• Using IDENTITY –

$\\ \\ \: \: \: \large \bigstar \: \: \: { \red{ \boxed{ \bold{ cos( - \theta) = cos( \theta) }}}} \\ \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( 3A) cos( A ) + 2 cos(7A ) cos( A ) }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ cos(3A ) \: + cos(7A )\: ] }} \\$

• Now again applying formula –

$\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( \frac{3A +7A }{2} ) \: cos( \frac{3A - 7A}{2} )\: ] }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( \frac{10A }{2} ) \: cos( \frac{ - 4A}{2} )\: ] }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( 5A ) \: cos( - 2A )\: ] }} \\$

$\\ \: \: \: \: { \bold{ = \: 2 cos( A ) [ 2cos( 5A ) \: cos( 2A )\: ] }} \\$

$\\ \: \: \: \: { \bold{ = \: 4 cos( A ) \: cos( 2A )\: cos( 5A ) }} \\$

$\\ \: \: \: \: { \bold{ = R.H.S. }} \\$

ADDITIONAL information :–

$\\ \: \: \: \large \bigstar \: \: { \red { \bold{ sin(C) + sin(D) = 2sin( \frac{C+ D}{2} ) cos( \frac{ C - D}{2} ) }}} \\$

$\\ \: \: \: \large \bigstar \: \: { \red { \bold{ sin(C) - sin(D) = 2cos( \frac{C + D}{2} ) sin( \frac{C - D}{2} ) }}} \\$

$\\ \: \: \: \large \bigstar \: \: { \red { \bold{ cos(C) + cos(D) = 2cos( \frac{C + D}{2} ) cos( \frac{C - D}{2} ) }}} \\$

$\\ \: \: \: \large \bigstar \: \: { \red { \bold{ cos(C) - cos(D) = 2sin( \frac{C + D}{2} ) sin( \frac{D - C}{2} ) }}} \\$

Discussion

35.	Write the sum without actual addition 1+3+5+7____+19
Answer» Answer: WITHOUT ACTUAL ADDITION of odd no. TILL 19 we will GET 100

35.

Write the sum without actual addition 1+3+5+7____+19

Answer»

Answer:

WITHOUT ACTUAL ADDITION of odd no. TILL 19 we will GET 100

Discussion

36.	0.1and 0.12find three irrational number
Answer» Hii Your ANSWER is 0.22,222,2222 0.666,6666,66666 0.5,55,555,5555 Hope it will HELP you

36.

0.1and 0.12find three irrational number

Answer»

Hii

Your ANSWER is

0.22,222,2222

0.666,6666,66666

0.5,55,555,5555

Hope it will HELP you

Discussion

37.	Prove that is an irrational
Answer» Hii Your ANSWER is here HOPE it will HELP you

37.

Prove that is an irrational

Answer»

Hii

Your ANSWER is here

HOPE it will HELP you

Discussion

38.	Find roots of x²+5x+5=0 by quadratic formula
Answer» A Quadratic Equation $\sf x^2+5x+<klux>5</klux>=0$ We have to find the roots of given equation By using quadratic formula $\boxed{\sf{x= \dfrac{-<klux>B</klux>\pm\sqrt{b{}^{2}-4ac}}{2a}}}$ Now we have , Coefficient of $\sf x^2$ (a) = 1 Coefficient of x (b) = 5 CONSTANT term (C) = 5 Now find the roots $\sf\bullet a= 1\ \ , \ \bullet \ b= 5 \ \ , \ \bullet\ c= 5$ $\longmapsto\sf x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{(5)^2-4\times 1\times 5}}{2\times 1}\\ \\ \\ \longmapsto\sf x= \dfrac{-5 \pm \sqrt{25-20}}{2}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{5}}{2}\\ \\ \\ \longmapsto\sf x = \dfrac{-5-\sqrt{5}}{2} \ \ or \ \dfrac{-5+\sqrt{5}}{2}$ So the roots of given equation is $\bigstar{\boxed{\sf{ \dfrac{-5-\sqrt{5}}{2}}}}$ $\bigstar{\boxed{\sf{ \dfrac{-5+\sqrt{5}}{2}}}}$

38.

Find roots of x²+5x+5=0 by quadratic formula

Answer»

A Quadratic Equation

$\sf x^2+5x+<klux>5</klux>=0$

We have to find the roots of given equation

By using quadratic formula

$\boxed{\sf{x= \dfrac{-<klux>B</klux>\pm\sqrt{b{}^{2}-4ac}}{2a}}}$

Now we have ,

Coefficient of $\sf x^2$ (a) = 1

Coefficient of x (b) = 5

CONSTANT term (C) = 5

Now find the roots

$\sf\bullet a= 1\ \ , \ \bullet \ b= 5 \ \ , \ \bullet\ c= 5$

$\longmapsto\sf x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{(5)^2-4\times 1\times 5}}{2\times 1}\\ \\ \\ \longmapsto\sf x= \dfrac{-5 \pm \sqrt{25-20}}{2}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{5}}{2}\\ \\ \\ \longmapsto\sf x = \dfrac{-5-\sqrt{5}}{2} \ \ or \ \dfrac{-5+\sqrt{5}}{2}$

So the roots of given equation is

$\bigstar{\boxed{\sf{ \dfrac{-5-\sqrt{5}}{2}}}}$

$\bigstar{\boxed{\sf{ \dfrac{-5+\sqrt{5}}{2}}}}$

Discussion

39.	Prove that 5+
Answer» Step-by-step EXPLANATION: please SEND attachment I didn't get what to PROVE

39.

Prove that 5+

Answer»

Step-by-step EXPLANATION:

please SEND attachment

I didn't get what to PROVE

Discussion

40.	Three consecutive multiples of 7
Answer» ANSWER: the SUM of three consecutive multiple of 7 is 777

40.

Three consecutive multiples of 7

Answer»

ANSWER:

the SUM of three consecutive multiple of 7 is 777

Discussion

41.	Find the value of K for which the roots of quadratic equation are equal (k-4) x^2 + (k-4)x +4.
Answer» Step-by-step EXPLANATION: HOPE it helps plz THANK

41.

Find the value of K for which the roots of quadratic equation are equal (k-4) x^2 + (k-4)x +4.

Answer»

Step-by-step EXPLANATION:

HOPE it helps

plz THANK

Discussion

42.	The part between any two points on the circle is called
Answer» Answer: the PART between any two POINTS on the CIRCLE is CALLED a CHORD.

42.

The part between any two points on the circle is called

Answer»

Answer:

the PART between any two POINTS on the CIRCLE is CALLED a CHORD.

Discussion

43.	If the ratio of the roots of the equation axsquare +bx+c=0 be equal to the ratio of the roots of a1xsquare+b1x+c1=0 then b/b1 whole square
Answer» ANSWER: BACH hbhtvfjvhbbyb igj

43.

If the ratio of the roots of the equation axsquare +bx+c=0 be equal to the ratio of the roots of a1xsquare+b1x+c1=0 then b/b1 whole square

Answer»

ANSWER:

BACH hbhtvfjvhbbyb igj

Discussion

44.	Why is 1 not included in prime factorization give examples
Answer» Answer: The answer is 1 is NEITHER a PRIME NUMBER nor a composite number Step-by-step EXPLANATION: So why 1 is not included in the prime factorization

44.

Why is 1 not included in prime factorization give examples

Answer»

Answer:

The answer is 1 is NEITHER a PRIME NUMBER nor a composite number

Step-by-step EXPLANATION:

So why 1 is not included in the prime factorization

Discussion

45.	Find the values of 25÷√40-√80 to correct to there places of decimal being given that √2=1.4142,√3=1.732,√5=2.236and √10=3.162
Answer» Answer: If √2=1.414, √3=1.732,√5 =2.236,√10=3.162 find the VALUE of the following CORRECT to 3 places of DECIMAL. √40-- √20

45.

Find the values of 25÷√40-√80 to correct to there places of decimal being given that √2=1.4142,√3=1.732,√5=2.236and √10=3.162

Answer»

Answer:

If √2=1.414, √3=1.732,√5 =2.236,√10=3.162 find the VALUE of the following CORRECT to 3 places of DECIMAL. √40-- √20

Discussion

46.	A 7-pack of granola bars costs $1.82. What is the unit price?
Answer» ANSWER: $0.26 Step-by-step explanation: 7 PACK = 1.82 1 pack = 1.82/7 answer = 0.26

46.

A 7-pack of granola bars costs $1.82. What is the unit price?

Answer»

ANSWER:

$0.26

Step-by-step explanation:

7 PACK = 1.82

1 pack = 1.82/7

answer = 0.26

Discussion

47.	4/(216)^-2/3 +1/(256)^-3/4 +2/(243)^-1/5
Answer» Answer: 4256609.2 Step-by-step EXPLANATION:

47.

4/(216)^-2/3 +1/(256)^-3/4 +2/(243)^-1/5

Answer»

Answer:

4256609.2

Step-by-step EXPLANATION:

Discussion

48.	36/........... =-4/9=_84/..........
Answer» Answer: 36/-72 =-4/9_84/ - 189 I hope you LIKE it STAY HOME and stay safe Hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii please mark me as BRAINLIST

48.

36/........... =-4/9=_84/..........

Answer»

Answer:

36/-72 =-4/9_84/ - 189

I hope you LIKE it

STAY HOME and stay safe

Hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii please mark me as BRAINLIST

Discussion

49.	What is the square root of √0.000729
Answer» ANSWER: Step-by-step EXPLANATION: √0.000729 = 0.027. HOPE THIS HELPS.

49.

What is the square root of √0.000729

Answer»

ANSWER:

Step-by-step EXPLANATION:

√0.000729 = 0.027.

HOPE THIS HELPS.

Discussion

50.	The circumference of a circular track is 154m. Find the diameter of the track take x 22/7
Answer» ANSWER: As we KNOW the circumference of the circle is $\pi$ d 154= $\pi$ d 154=22/7·d 154×7/22=d 7x7=d 49=d So our diameter is 49m. THANK YOU If my answer was REALLY helpfull to you then hit that like and don't forget to make me Brainlist ok PLZZ

50.

The circumference of a circular track is 154m. Find the diameter of the track take x 22/7

Answer»

ANSWER:

As we KNOW the circumference of the circle is $\pi$ d

154= $\pi$ d

154=22/7·d

154×7/22=d

7x7=d

49=d

So our diameter is 49m.

THANK YOU

If my answer was REALLY helpfull to you then hit that like and don't forget to make me Brainlist ok PLZZ

Discussion

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