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xenn [34]
3 years ago
15

x and x+1 are the two continuous natural numbers, then (i) Write the next two natural numbers. (ii) Find the product of first an

d the fourth number. (iii) Find the product of second and the third number. (iv) Find the relation between these products.
Mathematics
2 answers:
Gala2k [10]3 years ago
7 0

Answer:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) x( x+4)=a

    (x+1)(x+3)= a+3  

Step-by-step explanation:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;

x(x+4)=a

(x+1)(x+3)= a+3

Alinara [238K]3 years ago
3 0

Step-by-step explanation:

x is followed by x+1 so each time we add one

our sequence goes like this:

  • x
  • x+1
  • x+1+1⇒ x+2
  • x+2+1⇒x+3

the first number is x and the fourth one is x+3

  • x*(x+3)
  • x²+3x

the second number is x+1 and the third one is x+2

  • (x+1)(x+2)
  • x²+2x+x+2
  • x²+3x+2

the first product is x²+3x and the second one is x²+3x+2

Let P be x²+3x and P' be x²+3x+2

  • P'-P = 2
  • P' = P+2
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3 0
3 years ago
Use the principle of inclusion and exclusion to find the number of positive integers less than 1,000,000 that are not divisable
wel
This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.

∴N(c₁) = \frac{999,999}{6} = 166666
N(c₂) = \frac{999,999}{4} = 250000
∴N(c₁c₂) = \frac{999,999}{24} = 41667
∴ Number of positive integers that are not divisible by 4 or 6,

N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
8 0
3 years ago
If angle 0 is in quadrant I, what is the value of
Brilliant_brown [7]

Answer:

the \: answer \: is \: c \:  =  -  \frac{ \sqrt{14} }{5}

Step-by-step explanation:

\sin^{2}0 + ( \frac{ \sqrt{11} }{5} ) ^{2}  = 1( \sin^{2}0 +  \cos^{2} 0 = 1)

{ \sin }^{2}0 +  \frac{11}{25} = 1   \\  { \sin }^{2}0 =  \frac{14}{25}

\sin0_{1} =  -  \frac{ \sqrt{14}}{5} while \sin0_{2} =  \frac{ \sqrt{14} }{5}

  • Therfore theta is QI
  • Therfore sin theta >0
  • therefore \:  \sin0 =  \frac{ \sqrt{14} }{5}
4 0
1 year ago
Solve this equation -9-6+12h+40=22<br><br> A. h=24<br> B. h= -4/7<br> D. h= -4
BartSMP [9]
-9-6+12h+40=22
12h+25=22
12h=-23
h=-23/12
8 0
3 years ago
Read 2 more answers
Joe is finding the length of a rectangular prism. The volume of the prism is 204 ft3. The width is 3.5 ft, and the height is 5 f
zmey [24]

Answer:

B. He added 3.5 and 5 when he should have multiplied them.

Step-by-step explanation:

Let's observe Joe's steps:

- V = lwh

- 204 = 3.5 * (5) * l

Here, * means to multiply, so we're supposed to multiply 3.5 to 5, which would give you the answer 17.5. Unfortunately, look what Joe got: he obtained the value of 8.5, and if we observe, 3.5 + 5 = 8.5.

That's how we know that Joe added instead of multiplied, as he should have done. Thus, the answer is B.

8 0
3 years ago
Read 2 more answers
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