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Identity:
An identity is an equality which is true for all values of a variable in the equality.
(a + b)³ = a³+ b³+ 3ab(a + b)
In an identity the right hand side expression is called expanded form of the left hand side expression.
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Solution:
(i) (2x + 1)³
Using identity
(a + b)³ = a³+ b³+ 3ab(a + b)
(2x + 1)³
= (2x)³ + 1³ + (3×2x×1)(2x + 1)
= 8x³+ 1 + 6x(2x + 1)
= 8x³ + 1 + 12x² + 6x
(ii) (2a – 3b)³
Using identity,
(a – b)³ = a³–b³ – 3ab(a – b)
(2a – 3b)³ = (2a)³– (3b)³ – (3×2a×3b)(2a – 3b)
=8a³–27b³–18ab(2a –3b)
= 8a³–27b³–36a²b + 54ab²
(iii) [3x/2 + 1]³
Using identity,
(a + b)³ = a³+ b³+ 3ab(a + b)
[3x/2 +1]³
=(3x/2)³+1³+ (3×(3x/2)×1)(3x/2+ 1)
=27x³/8+1+9/2x×(3x/2+1)
= 27x³/8 + 1 + 27/4 x² + 9/2x
= (27/8)x³ + (27/4) x² + 9/2 x + 1
(iv) [x–2/3 y]³
Using identity,
(a - b)³=a³-b³-3ab(a-b)
(X+ 2/3y)³
= (x)³–(2/3 y)³– (3×x×2/3 y)(x – 2/3 y)
= x³– 8y³/27–2xy(x – 2/3 y)
= x³– (8/27)y³–2x²y+ 4/3xy²
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Hope this will help you....
Step-by-step explanation:
Answer: 11/15 hours
Step-by-step explanation:
Find LCD (lowest common denominator)
1/3=5/15
2/5=6/15
6/15+5/15=11/15 hours or 44 minutes
Answer:
x=1
Step-by-step explanation:
Answer:
<h2>
x∈{-1, 8}</h2>
Step-by-step explanation:
![\log_2x +\log_2(x-7) = 3\\\\\log_2[x\cdot(x-7)]= 3\log_22\\\\\log_2(x^2-7x)= \log_22^3\\\\x^2-7x=2^3\\\\x^2-7x-8=0\quad\implies \quad a=1\,,\ \ b=-7\,,\ \ c=-8 \\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot(-8)}}{2\cdot1}= \dfrac{7\pm\sqrt{49+32}}{2} =\dfrac{7\pm\sqrt{81}}{2}\\\\x=\dfrac{7+9}2=8\qquad\vee\qquad x=\dfrac{7-9}2=-1](https://tex.z-dn.net/?f=%5Clog_2x%20%2B%5Clog_2%28x-7%29%20%3D%203%5C%5C%5C%5C%5Clog_2%5Bx%5Ccdot%28x-7%29%5D%3D%203%5Clog_22%5C%5C%5C%5C%5Clog_2%28x%5E2-7x%29%3D%20%5Clog_22%5E3%5C%5C%5C%5Cx%5E2-7x%3D2%5E3%5C%5C%5C%5Cx%5E2-7x-8%3D0%5Cquad%5Cimplies%20%5Cquad%20a%3D1%5C%2C%2C%5C%20%5C%20b%3D-7%5C%2C%2C%5C%20%5C%20c%3D-8%20%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-7%29%5Cpm%5Csqrt%7B%28-7%29%5E2-4%5Ccdot1%5Ccdot%28-8%29%7D%7D%7B2%5Ccdot1%7D%3D%20%5Cdfrac%7B7%5Cpm%5Csqrt%7B49%2B32%7D%7D%7B2%7D%20%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B81%7D%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B7%2B9%7D2%3D8%5Cqquad%5Cvee%5Cqquad%20x%3D%5Cdfrac%7B7-9%7D2%3D-1)
Answer:
Step-by-step explanation:
<u>Key skills needed: Probability, Possible Outcomes</u>
1) We are given a spinner --> With numbers: 1,2,3,4,5,6,7, and 8
That means there are 8 numbers on the spinner.
2) The problem asks what is the probability that the spinner will not land on 5 or the 8.
To calculate this --> 
3) The accepted outcomes are when the spinner lands on --> 1,2,3,4,6,7
That is 6 accepted outcomes.
4) The total outcomes is 8 (since there are numbers the spinner can land on).
5) Therefore, the answer would be 
can be simplified into as both the numerator (6) and the denominator (8) share a factor of 2.
6) With this --> is the answer.
