The solution (B) x=79.
Rewriting the equation to find the solution -
(x+2)³/₄=27
Raising both sides of the equation with exponent ⁴/₃
((x+2)³/₄)⁴/₃ = 27⁴/₃
Cancelling the exponents on Left Hand Side of the equation. Writing the value on Right Hand Side of the equation in exponent form
x + 2 = (3³)⁴/₃
Cancelling 3 on Right Hand Side of the equation
x + 2 = 3⁴
Solving Right Hand Side of the equation
x + 2 = 81
Shifting 2 to Right Hand Side of the equation
x = 81 - 2
Performing subtraction on Right Hand Side of the equation
x = 79
Hence, the solution is (B) x=79.
Learn more about calculations on solution of x -
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Can you explain it or maybe take a picture?
m
=
−
2
, (
3,
5
)
Find the value of b
using the formula for the equation of a line.
b
=
11
Now that the values of
m (slope) and b
(y-intercept) are known, substitute them into
y
=
m
x
+
b to find the equation of the line. y
=
−
2
x
+
11
The sum of all the even integers between 99 and 301 is 20200
To find the sum of even integers between 99 and 301, we will use the arithmetic progressions(AP). The even numbers can be considered as an AP with common difference 2.
In this case, the first even integer will be 100 and the last even integer will be 300.
nth term of the AP = first term + (n-1) x common difference
⇒ 300 = 100 + (n-1) x 2
Therefore, n = (200 + 2 )/2 = 101
That is, there are 101 even integers between 99 and 301.
Sum of the 'n' terms in an AP = n/2 ( first term + last term)
= 101/2 (300+100)
= 20200
Thus sum of all the even integers between 99 and 301 = 20200
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