(-y + 5a - 4) + (3y - a - 5) is simplified to 2y + 4a - 11
Answer:
![3863.35 = 3500(1 + \frac{0.05}{2} )^{(2 \times 2)}](https://tex.z-dn.net/?f=3863.35%20%3D%203500%281%20%2B%20%20%5Cfrac%7B0.05%7D%7B2%7D%20%29%5E%7B%282%20%5Ctimes%202%29%7D%20)
Step-by-step explanation:
The formula for this equation is
![a = p(1 + \frac{r}{n} )^{(n \times t)}](https://tex.z-dn.net/?f=a%20%3D%20p%281%20%2B%20%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7B%28n%20%5Ctimes%20t%29%7D%20)
a is the final result
p is the starting amount (deposited)
r is the interest rate
n is the number of times it's compounded
t is the time
because it says compound annually and it's after 2 years both t and n equal 2. I rounded a for you, but if you don't need it rounded here it is: 3863.345117
Please double check me I may be wrong, this is my second time doing these type of questions
Answer:
5C 6D
Step-by-step explanation:
5, a^2 = b^2 + c^2
6,
A is wrong because two distinct lines intersect at 1 point only or 0 (they will never intersect when they are parallel)
B & C are wrong because lines contain infinite point
E is wrong because 2 parallel lines will never intersect, as the result, their common points = 0
Answer:
![c =\frac{8}{3}](https://tex.z-dn.net/?f=c%20%3D%5Cfrac%7B8%7D%7B3%7D)
Step-by-step explanation:
Given
![c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B4%20%2B%20%5Csqrt%207%7D%7B4%20-%20%5Csqrt%207%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B4%20-%20%5Csqrt%207%7D%7B4%20%2B%20%5Csqrt%207%7D%7D)
Required
Shorten
We have:
![c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B4%20%2B%20%5Csqrt%207%7D%7B4%20-%20%5Csqrt%207%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B4%20-%20%5Csqrt%207%7D%7B4%20%2B%20%5Csqrt%207%7D%7D)
Rationalize
![c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B4%20%2B%20%5Csqrt%207%7D%7B4%20-%20%5Csqrt%207%7D%20%2A%20%5Cfrac%7B4%20%2B%20%5Csqrt%207%7D%7B4%20%2B%20%5Csqrt%207%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B4%20-%20%5Csqrt%207%7D%7B4%20%2B%20%5Csqrt%207%7D%2A%5Cfrac%7B4%20-%20%5Csqrt%207%7D%7B4%20-%20%5Csqrt%207%7D%7D)
Expand
![c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B%284%20%2B%20%5Csqrt%207%29%5E2%7D%7B4%5E2%20-%20%28%5Csqrt%207%29%5E2%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B%284%20-%20%5Csqrt%207%29%5E2%7D%7B4%5E2%20-%20%28%5Csqrt%207%29%5E2%7D)
![c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B%284%20%2B%20%5Csqrt%207%29%5E2%7D%7B16%20-%207%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B%284%20-%20%5Csqrt%207%29%5E2%7D%7B16%20-%207%7D)
![c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B%5Cfrac%7B%284%20%2B%20%5Csqrt%207%29%5E2%7D%7B9%7D%7D%20%2B%20%20%5Csqrt%7B%5Cfrac%7B%284%20-%20%5Csqrt%207%29%5E2%7D%7B9%7D)
Take positive square roots
Take LCM
![c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}](https://tex.z-dn.net/?f=c%20%3D%5Cfrac%7B4%20%2B%20%5Csqrt%207%20%2B%204%20-%20%5Csqrt%207%7D%7B3%7D)
Collect like terms
![c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}](https://tex.z-dn.net/?f=c%20%3D%5Cfrac%7B4%20%20%2B%204%2B%20%5Csqrt%207%20-%20%5Csqrt%207%7D%7B3%7D)
![c =\frac{8}{3}](https://tex.z-dn.net/?f=c%20%3D%5Cfrac%7B8%7D%7B3%7D)
Answer:
79
Step-by-step explanation:
78
---------
7 | 62 03
49
----------
148 | 13 03
11 84
-----------
19
-----------
78^2 = 6084.
We observe that 78^2 < 6203.
79^2 = 6241.
We observe that 79^2 > 6203.
Hence the number to be added to 6203 is 6241 - 6203 = 38.
6203 + 38 = 3241
= 79 * 79
= 79.
Therefore 38 should be added to 6203 to obtain a perfect square.