Answer:
$50.09
Step-by-step explanation:
48 increase 4.35% =
48 × (1 + 4.35%) = 48 × (1 + 0.0435) = 50.088
![{5}^{3} \: \times \: {5}^{ - 5}](https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B3%7D%20%20%5C%3A%20%20%5Ctimes%20%20%5C%3A%20%20%7B5%7D%5E%7B%20-%205%7D%20)
- We first compute the product.
![{5}^{ - 2}](https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B%20-%202%7D%20)
- We can transform the product into positive if we use this formula:
![\boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%7Ba%7D%5E%7B%20-%20n%7D%20%20%5C%3A%20%20%3D%20%20%5C%3A%20%20%5Cfrac%7B1%7D%7B%20%7Ba%7D%5E%7Bn%7D%20%7D%20%7D)
<h3>We apply it:</h3>
![{5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}](https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B%20-%202%7D%20%20%5C%3A%20%20%3D%20%20%5C%3A%20%20%20%5Cboxed%7B%20%5Cbold%7B%5Cfrac%7B1%7D%7B%20%7B5%7D%5E%7B2%7D%20%7D%20%7D%7D)
<h2>Answer: </h2>
![\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}](https://tex.z-dn.net/?f=%5Ctext%7BOption%20C.%7D%20%5C%3A%20%20%5Cboxed%7B%20%20%5Cbold%7B%5Cfrac%7B1%7D%7B%20%7B5%7D%5E%7B2%7D%20%7D%20%7D%7D)
<h3><em><u>MissSpanish</u></em></h3>
Answer:
okkkkkk are you ok like actually
Answer:
![\dfrac{9}{13}-\dfrac{19}{13}i](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B13%7D-%5Cdfrac%7B19%7D%7B13%7Di)
Step-by-step explanation:
Remember ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
You are given the fraction ![\dfrac{3+5i}{-2+3i}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%2B5i%7D%7B-2%2B3i%7D)
First, multiply the numerator and the denominator by -2-3i:
![\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%2B5i%7D%7B-2%2B3i%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B%28-2%2B3i%29%28-2-3i%29%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B%28-2%29%5E2-%283i%29%5E2%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B4-9i%5E2%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B4%2B9%7D)
This gives you 13 in denominator, now multiply two complex numbers in numerator:
![(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i](https://tex.z-dn.net/?f=%283%2B5i%29%28-2-3i%29%3D-6-9i-10i-15i%5E2%3D-6-19i%2B15%3D9-19i)
Thus, the initial fraction is
![\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i](https://tex.z-dn.net/?f=%5Cdfrac%7B9-19i%7D%7B13%7D%3D%5Cdfrac%7B9%7D%7B13%7D-%5Cdfrac%7B19%7D%7B13%7Di)