Do the following: i)Explain why 3 x 4 x 7 x 9 x 11 + 2 x 3 is composite number. (ii) Find the zeroes of the polynomial x² – 3 and verify the relationship between zeroes and the co-efficients. (iii) Solve by substitution method 2x + 3y=9; 4x + 6y =18 (iv) Find the roots of 100x² – 20x + 1= 0 (v) How many terms of the AP: 24,21,18,...... must be taken so that their sum is 78
Answers
Answer:
let the number of terms to get sum 78 is n. Solving the quadratic equation, we get n=4 and n=13. So you can take either 4 terms or 13 terms to get the sum 78.
Step-by-step explanation:
1.
6th
Maths
Playing With Numbers
Prime Numbers and Composite Numbers
Explain why 7 x 11 x 13 + 1...
MATHS
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Asked on December 26, 2019 by
Protyush Jaggi
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
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ANSWER
Given 7×11×13+13
=13×(7×11+1)=3×78
This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.
similarly in
7×6×5×4×3 ×2×1+5
=5(7×6×4×3 ×2×1+1)=5×1009
This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.
2. answer in above photo !!
3. In substitution method, we solve one equation for one of the variables and substitute that value in other equation. after this step, there will be one equation only with one variable, which can be easily solved. so the answer is x = 4.5 and y = 0.
4. 2 photo is the answer !!
5. Given:24,21,18,... are in A.P
a=24,d=21−24=−3
Sum=
2
n
[2a+(n−1)d]
⇒78=
2
n
[2×24+(n−1)(−3)]
⇒156=n[48−3n+3]
⇒156=n[51−3n]
⇒3n
2
−51n+156=0
⇒3n
2
−12n−39n+156=0
⇒3n(n−4)−39(n−4)=0
⇒(n−4)(3n−39)=0
∴n=4,n=
3
39
=13
When n=4,s
4
=
2
4
[2×24+(4−1)(−3)]=2[48−9]=2×39=78
When n=13,s
13
=
2
13
[2×24+(13−1)(−3)]=
2
13
[48−36]=
2
13
×12=78
Hence number of terms n=4 or n=13
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