Answer:
Option D
Step-by-step explanation:
Given expression has been given as,
![\sqrt[5]{224x^{11}y^8}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B224x%5E%7B11%7Dy%5E8%7D)
![\sqrt[5]{224x^{11}y^8}=\sqrt[5]{2\times 2\times 2\times 2\times 2\times 7(x^{11})(y^8)}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B224x%5E%7B11%7Dy%5E8%7D%3D%5Csqrt%5B5%5D%7B2%5Ctimes%202%5Ctimes%202%5Ctimes%202%5Ctimes%202%5Ctimes%207%28x%5E%7B11%7D%29%28y%5E8%29%7D)
![=\sqrt[5]{(2^5)\times (7)(x^{10}\times x)(y^5\times y^3)}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B5%5D%7B%282%5E5%29%5Ctimes%20%287%29%28x%5E%7B10%7D%5Ctimes%20x%29%28y%5E5%5Ctimes%20y%5E3%29%7D)


![=2x^2y\sqrt[5]{7xy^3}](https://tex.z-dn.net/?f=%3D2x%5E2y%5Csqrt%5B5%5D%7B7xy%5E3%7D)
Option D will be the answer.
Pls. see attachment.
We need to solve for the angles of the smaller triangle in
order to solve for the angle of the larger triangle which would help us solve
the missing measurement of a side.
Given:
51 degrees.
Cut the triangle into two equal sides and it forms a right
triangle. All interior angles of a triangle sums up to 180 degrees.
180 – 51 – 90 = 39 degrees
39 degrees * 2 = 78 degrees.
Angle Q is 78 degrees.
In the bigger triangle, 4.3 is the hypotenuse. We need to
solve for the measurement of the long leg which is the opposite of the 78
degree angle.
We will use the formula:
Sine theta = opposite / hypotenuse
Sin(78 deg) = opposite / 4.3
Sin(78 deg) * 4.3 = opposite
4.21 = opposite. This is also the height of the triangle.
Area of a triangle = ½ * base * height
A = ½ * 3units * 4.21units
A = 6.315 square units.
Answer:
y=4, x=8
Step-by-step explanation:
system:
x+y = 12, x=2y
convert to 1 variable, simplify:
2y+y=12
3y=12
y=4
x=2y=4*2=8
Let us start dividing 30 by small prime numbers in increasing order .
the smallest prime number we use is 2
Let's divide 30 by 2 quotient is 15
so we get : 30 = 2* 15
15 is not a prime number , it can be factorized further .
now we start dividing 15
2 can not divide 15 so we move to next prime number that is 3
can 3 divide 15? yes .
we get a quotient 5
so 30 is now : 2* 15 = 2* 3*5
now we have to work on 5 but 5 is a prime number so we stop here .
the prime factorization of 30 is : 2* 3* 5
Answer : 2 *3*5