Answer:
Step-by-step explanation:
We'll take this step by step. The equation is
![8-3\sqrt[5]{x^3}=-7](https://tex.z-dn.net/?f=8-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-7)
Looks like a hard mess to solve but it's actually quite simple, just do one thing at a time. First thing is to subtract 8 from both sides:
![-3\sqrt[5]{x^3}=-15](https://tex.z-dn.net/?f=-3%5Csqrt%5B5%5D%7Bx%5E3%7D%3D-15)
The goal is to isolate the term with the x in it, so that means that the -3 has to go. Divide it away on both sides:
![\sqrt[5]{x^3}=5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E3%7D%3D5)
Let's rewrite that radical into exponential form:
![x^{\frac{3}{5}}=5](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B5%7D%7D%3D5)
If we are going to solve for x, we need to multiply both sides by the reciprocal of the power:
![(x^{\frac{3}{5}})^{\frac{5}{3}}=5^{\frac{5}{3}}](https://tex.z-dn.net/?f=%28x%5E%7B%5Cfrac%7B3%7D%7B5%7D%7D%29%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%3D5%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D)
On the left, multiplying the rational exponent by its reciprocal gets rid of the power completely. On the right, let's rewrite that back in radical form to solve it easier:
![x=\sqrt[3]{5^5}](https://tex.z-dn.net/?f=x%3D%5Csqrt%5B3%5D%7B5%5E5%7D)
Let's group that radicad into groups of 3's now to make the simplifying easier:
because the cubed root of 5 cubed is just 5, so we can pull it out, leaving us with:
which is the same as:
![x=5\sqrt[3]{25}](https://tex.z-dn.net/?f=x%3D5%5Csqrt%5B3%5D%7B25%7D)
Answer:
Tan T = 7/24
Step-by-step explanation:
Firstly, please check attachment to have a picture of the triangle we are solving.
Now, we are concerned with calculating the ratio that represents the tangent of angle T.
Mathematically, the tangent of an angle is the ratio of the length of the opposite to the length of the adjacent.
In this question, our opposite is 7 while the adjacent is 24.
Thus Tan T = 7/24
Answer:
Hence, the total cost of mailing 10 ounces is:
$ 2.52
Step-by-step explanation:
If postage costs $.54 for the first ounce and $.22 for the each additional ounce.
i.e. cost of first ounce=$ 0.54.
Now let x denote the number of ounces after the first ounce,
Hence, the cost of x ounces=$ (0.22×x)=$ 0.22 x
Hence, the cost of mailing (x+1) ounces is: $ (0.54+0.22 x)
Now, we have to find the cost of mailing a 10- ounce envelope.
i.e. after the first ounce we need 9 more ounces.
Hence, the total cost of mailing is calculated as:
![=$ (0.54+0.22\times 9)\\\\=$ (0.54+1.98)\\\\=$ 2.52\\](https://tex.z-dn.net/?f=%3D%24%20%280.54%2B0.22%5Ctimes%209%29%5C%5C%5C%5C%3D%24%20%280.54%2B1.98%29%5C%5C%5C%5C%3D%24%202.52%5C%5C)
Hence, cost of mailing 10 ounces is:
$ 2.52
The answer is a since 150/6 is 25
Answer:
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