B because absolute value means the distance of a point on a number line from 0. So the absolute value of -6 is 6 and you add that to 4
Answer:
√95 cm
Step-by-step explanation:
To solve, you need to use the pythagorean theorem, or a^2 + b^2 = c^2
The hypotenuse is the c and let one leg be b. You can write:
a^2 + 7^2 = 12^2
a^2 + 49 = 144
Now, you need to solve for a:
a^2 = 144 - 49
a^2 = 95
a = √95 cm, or about 9.75cm
Answer:
Third option.
Step-by-step explanation:
You need to cube both sides of the equation. Remember the Power of a power property:
![(a^m)^n=a^{mn](https://tex.z-dn.net/?f=%28a%5Em%29%5En%3Da%5E%7Bmn)
![\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%3D3x%5E2y%28%5Csqrt%5B3%5D%7B6y%5Ed%7D%29%5C%5C%5C%5C%28%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%29%5E3%3D%283x%5E2y%28%5Csqrt%5B3%5D%7B6y%5Ed%7D%29%29%5E3%5C%5C%5C%5C162x%5Ecy%5E5%3D27x%5E6y%5E36y%5Ed)
According to the Product of powers property:
![(a^m)(a^n)=a^{(m+n)](https://tex.z-dn.net/?f=%28a%5Em%29%28a%5En%29%3Da%5E%7B%28m%2Bn%29)
Then. simplifying you get:
![162x^cy^5=162x^6y^{(3+d)}](https://tex.z-dn.net/?f=162x%5Ecy%5E5%3D162x%5E6y%5E%7B%283%2Bd%29%7D)
Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:
![c=6](https://tex.z-dn.net/?f=c%3D6)
You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:
![3+d=5\\d=5-3\\d=2](https://tex.z-dn.net/?f=3%2Bd%3D5%5C%5Cd%3D5-3%5C%5Cd%3D2)