Rewrite in standard form and use the form to find the vertex.
(1, 5)
(x - 1)^2 + 5
Answer:
55
Step-by-step explanation:
The absolute value of -30 is 30 and the absolute value of 25 is 25.
So you will end up with 30 + 25 which is 55.
Answer:
2/14, 4/28, 5/35, 7/70 or just 2/14
Step-by-step explanation:
Multiply both the numerator and denominator of 1/7 by 2, to get 2/14, or 2:14
And multiply the numerator and denominator of 1/7 by 3, to get 3/21, or 3:21. So 2:14 and 3:21 are two ratios that are equal to 1:7.
The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)
The distance between both lighthouses is 5783.96 m
I've added an attachment that represents the scenario.
From the attachment, we have:
![\mathbf{\angle A = 180^o - 120^o\ 43'}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20A%20%3D%20180%5Eo%20-%20120%5Eo%5C%2043%27%7D)
Convert to degrees
![\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20A%20%3D%20180%5Eo%20-%20%28120%5Eo%20%2B%5Cfrac%7B43%7D%7B60%7D%5Eo%29%7D)
![\mathbf{\angle A = 180^o - (120^o +0.717^o)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20A%20%3D%20180%5Eo%20-%20%28120%5Eo%20%2B0.717%5Eo%29%7D)
![\mathbf{\angle A = 180^o - (120.717^o)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20A%20%3D%20180%5Eo%20-%20%28120.717%5Eo%29%7D)
![\mathbf{\angle A = 59.283^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20A%20%3D%2059.283%5Eo%7D)
![\mathbf{\angle B = 39^o43'}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20B%20%3D%2039%5Eo43%27%7D)
Convert to degrees
![\mathbf{\angle B = 39^o + \frac{43}{60}^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20B%20%3D%2039%5Eo%20%2B%20%5Cfrac%7B43%7D%7B60%7D%5Eo%7D)
![\mathbf{\angle B = 39^o + 0.717^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20B%20%3D%2039%5Eo%20%2B%200.717%5Eo%7D)
![\mathbf{\angle B = 39.717^o}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20B%20%3D%2039.717%5Eo%7D)
So, the measure of angle S is:
---- Sum of angles in a triangle
![\mathbf{\angle S = 180 - 59.283 - 39.717}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20S%20%3D%20180%20-%2059.283%20-%2039.717%7D)
![\mathbf{\angle S = 81}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20S%20%3D%2081%7D)
The required distance is distance AB
This is calculated using the following sine formula:
![\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7BAB%7D%7B%5Csin%28S%29%7D%20%3D%20%5Cfrac%7BAS%7D%7B%5Csin%28B%29%7D%20%7D)
Where:
![\mathbf{AS = 3742}](https://tex.z-dn.net/?f=%5Cmathbf%7BAS%20%3D%203742%7D)
So, we have:
![\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7BAB%7D%7B%5Csin%2881%29%7D%20%3D%20%5Cfrac%7B3742%7D%7B%5Csin%2839.717%29%7D%7D)
Make AB the subject
![\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}](https://tex.z-dn.net/?f=%5Cmathbf%7BAB%3D%20%5Cfrac%7B3742%7D%7B%5Csin%2839.717%29%7D%20%5Ctimes%20%5Csin%2881%29%7D)
![\mathbf{AB= 5783.96}](https://tex.z-dn.net/?f=%5Cmathbf%7BAB%3D%205783.96%7D)
Hence, the distance between both lighthouses is 5783.96 m
Read more about bearing and distance at:
brainly.com/question/19017345