Answer:
257 is prime.
Step-by-step explanation:
To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.
In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)
- 257 is odd, so it is not divisible by 2.
- The sum of its digits is 14, therefore, it is not divisible by 3.
- 257 ends in 7, therefore it's not divisible by 5.
- 257/ 7 = 36.71 so it's not divisible by 7.
- 257/ 11 = 23.36 so it's not divisible by 11
- Finally 257 / 13= 19.76 so it's not divisible by 13.
Therefore, 257 is prime.
Answer: (x - 2)² + (y - 14)² = 1
Step-by-step explanation:
<u>Concept:</u>
Here, we need to know the idea of the circle formula.
Circle formula: (x - h)² + (y - k)² = r²
Center = (h, k)
Radius = r
If you are still confused, please refer to the attachment below for a graphical explanation.
<u>Solve:</u>
Center = (2, 14)
Radius = 1
<em>Given formula</em>
(x - h)² + (y - k)² = r²
<em>Substitute the value into the formula</em>
(x - 2)² + (y - 14)² = (1)²
<em>Simplify</em>
(x - 2)² + (y - 14)² = 1
Hope this helps!! :)
Please let me know if you have any questions
Answer:
m∠ABC = 119° and DC = 105 feet
Step-by-step explanation:
For better understanding of the solution see the attached figure of the trapezium ABCD :
m∠BCD = 61°
By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°
⇒ m∠ABC = 180° - 61°
⇒ m∠ABC = 119°
Now, to find length of DC,
Draw a perpendicular BE on CD ⇒ CD = DE + EC
AB = DE
⇒ DE = 80 feet
In ΔBEC, By using Pythagoras theorem
EC² = BC² - BE²
⇒ EC² = 65² - 60²
⇒ EC = 25 feet
Hence, DC = 80 + 25
= 105 feet
To find the dividend per share, we divide the total dividend amount by the total shares.
Dividend per share = 40,000 / 60,000
Dividend per share = $0.67
Your share = 100 x 0.67
Your share = $66.67
Three-forty one over one thousand XD