Answer:
Step-by-step explanation:
Alright, lets get started.
Della bought a tree seeding that was
feet tall means
feet.
First year it grew
feet means it grew
feet.
It means after 1 year, the height of tree will be = ![\frac{9}{4}+\frac{7}{6}=\frac{41}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B4%7D%2B%5Cfrac%7B7%7D%7B6%7D%3D%5Cfrac%7B41%7D%7B12%7D)
After 2 years, the height of tree is = 5 feet
So, it grew in second year = ![5-\frac{41}{12}](https://tex.z-dn.net/?f=5-%5Cfrac%7B41%7D%7B12%7D)
So, it grew in second year = ![\frac{60-41}{12}=\frac{19}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B60-41%7D%7B12%7D%3D%5Cfrac%7B19%7D%7B12%7D)
So, it grew in second year=
feet. : Answer
Hope it will help :)
Answer:
is the correct answer.
Step-by-step explanation:
Given:
![$\frac{5}{2+\sqrt{6}}$](https://tex.z-dn.net/?f=%24%5Cfrac%7B5%7D%7B2%2B%5Csqrt%7B6%7D%7D%24)
To find:
if given term is written as following:
![$\frac{A\sqrt{B}+C}{D}$](https://tex.z-dn.net/?f=%24%5Cfrac%7BA%5Csqrt%7BB%7D%2BC%7D%7BD%7D%24)
<u>Solution:</u>
We can see that the resulting expression does not contain anything under
(square root) so we need to rationalize the denominator to remove the square root from denominator.
The rule to rationalize is:
Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.
Applying this rule to rationalize the given expression:
![\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B2%2B%5Csqrt%7B6%7D%7D%20%5Ctimes%20%5Cdfrac%7B2-%5Csqrt6%7D%7B2-%5Csqrt6%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B5%20%5Ctimes%20%282-%5Csqrt6%29%7D%7B%282%2B%5Csqrt%7B6%7D%29%20%5Ctimes%20%282-%5Csqrt6%29%7D%20%5C%5C%5CRightarrow%20%5Cdfrac%7B10-5%5Csqrt6%7D%7B2%5E2-%28%5Csqrt6%29%5E2%7D%5C%20%5C%20%5C%20%5C%20%5C%20%20%20%28%5Cbecause%20%5Cbold%7B%28a%2Bb%29%28a-b%29%3Da%5E2-b%5E2%7D%29%5C%5C%5CRightarrow%20%5Cdfrac%7B10-5%5Csqrt6%7D%7B4-6%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B10-5%5Csqrt6%7D%7B-2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B-5%5Csqrt6%2B10%7D%7B-2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B5%5Csqrt6-10%7D%7B2%7D)
Comparing the above expression with:
![$\frac{A\sqrt{B}+C}{D}$](https://tex.z-dn.net/?f=%24%5Cfrac%7BA%5Csqrt%7BB%7D%2BC%7D%7BD%7D%24)
A = 5, B = 6 (Not divisible by square of any prime)
C = -10
D = 2 (positive)
GCD of A, C and D is 1.
So, ![A +B+C+D = 5+6-10+2 = \bold3](https://tex.z-dn.net/?f=A%20%2BB%2BC%2BD%20%3D%205%2B6-10%2B2%20%3D%20%5Cbold3)
Answer:
25*pi or
78.5 square units.
Step-by-step explanation:
If there was no shaded area, the area of the circle would be pi * r^2
r = 10
Area = pi * 10^2
Area = 100 * pi
Since there is a shaded area, the shaded part looks to be 1/4 of the whole. There's no indication of what it actually is, but 1/4 should be close enough.
Area_shade = 1/4 (100*pi)
Area_shade = 25 * pi
That's one answer.
Another is 25 * 3.14 = 78.5 square units
Answer:
Therefore values of a and b are
![a=3\ and\ b = 2](https://tex.z-dn.net/?f=a%3D3%5C%20and%5C%20b%20%3D%202)
Step-by-step explanation:
Rewrite
in the form
where a and b are integers,
To Find:
a = ?
b = ?
Solution:
..............Given
Which can be written as
![(\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%20coefficient%5C%20of%5C%20x%29%5E%7B2%7D%3D%28%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-6%29%5E%7B2%7D%3D9)
Adding half coefficient of X square on both the side we get
...................( 1 )
By identity we have (A - B)² =A² - 2AB + B²
Therefore,
![x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D-6x%2B9%3Dx%5E%7B2%7D-2%5Ctimes%203%5Ctimes%20x%2B3%5E%7B2%7D%3D%28x-3%29%5E%7B2%7D)
Substituting in equation 1 we get
![(x-3)^{2}=2](https://tex.z-dn.net/?f=%28x-3%29%5E%7B2%7D%3D2)
Which is in the form of
![(x-a)^{2}=b](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%3Db)
On comparing we get
a = 3 and b = 2
Therefore values of a and b are
![a=3\ and\ b = 2](https://tex.z-dn.net/?f=a%3D3%5C%20and%5C%20b%20%3D%202)
The LCM is (x+4)(x-3)(x+5)