answer:To find the distance from the right focus of the hyperbola frac{{x}^{2}}{4}-frac{{y}^{2}}{5}=1 to the line x+2y-8=0, we follow these steps: 1. **Identify the right focus of the hyperbola**: The standard form of a hyperbola is frac{{x}^{2}}{a^{2}}-frac{{y}^{2}}{b^{2}}=1 for a horizontal hyperbola, where the foci are located at (pm c,0), with c=sqrt{a^{2}+b^{2}}. For our hyperbola, a^{2}=4 and b^{2}=5, so c=sqrt{4+5}=sqrt{9}=3. Thus, the right focus is at (3,0). 2. **Calculate the distance from the focus to the line**: The distance d from a point (x_0,y_0) to a line Ax+By+C=0 is given by d=frac{|Ax_0+By_0+C|}{sqrt{A^{2}+B^{2}}}. Substituting the focus (3,0) and the line x+2y-8=0 (where A=1, B=2, and C=-8) into this formula, we get: [ d = frac{|1cdot3+2cdot0-8|}{sqrt{1^{2}+2^{2}}} = frac{|3-8|}{sqrt{1+4}} = frac{|-5|}{sqrt{5}} = frac{5}{sqrt{5}} = sqrt{5} ] Therefore, the distance from the right focus of the hyperbola to the line is boxed{sqrt{5}}.

answer:1. There are 26 choices for the first letter. 2. There are 26 choices for the second letter, 26 choices for the third letter, and 26 choices for the fourth letter (the middle three letters). 3. The fifth letter must be the same as the first letter, so there's only 1 choice for it once the first letter is chosen. Thus, the number of possible combinations of such five-letter words is calculated by: [ 26 times 26 times 26 times 26 times 1 = 26^4 ] Calculating the power: [ 26^4 = 456976 ] Therefore, the total number of five-letter words that begin and end with the same letter is boxed{456976}.

answer:Given the problem, the focus is to identify whether the received SMS about the bank card being locked is genuine or fraudulent, and to outline the steps to verify its authenticity. 1. **Understand the Definition of Fraudulence**: Fraudulence refers to the act of getting valuable property from a person by means of deceit or breach of trust, whereby the victim voluntarily hands over their assets to the perpetrator. This understanding is crucial in identifying fraudulent activities. 2. **Immediate Reaction and Common Fraudulent Outcomes**: - **Immediate Loss of Funds**: If you respond to such messages by calling the provided number, there is a risk of funds being directly withdrawn from your bank account during the call. - **Phishing for Card Details**: Scammers might pose as bank officials to acquire sensitive information such as the card number, expiration date, and CVV code. This often leads to unauthorized transactions. 3. **Verification Steps**: - **Do Not Respond Hastily**: Resist the urge to quickly reply or call the number provided in the SMS. - **Verify the Source**: - Compare the received message with previous legitimate messages received from your bank. - Note that Sberbank, for example, only uses the short number 900 for sending SMS notifications, not any other long numbers. Scammers often mimic real contacts by slightly altering the number. 4. **Check the Sender’s Number**: Be cautious about the sender’s number. Fraudulent messages often come from numbers similar to official ones but include slight variations. For banks like Sberbank, the legitimate sender number is 900. Any deviations should be treated with suspicion. 5. **Reaching Out to the Bank**: - **Use Official Contact Information**: Call the customer service number listed on the back of your bank card. This ensures you are reaching out to a legitimate representative. - **Inquire with a Bank Representative**: Provide details of the SMS to the bank official and confirm whether it was legitimately sent by the bank. 6. **Notify the Bank of Suspicious Activity**: Inform the bank about the fraudulent attempt. Some banks have started programs to reward individuals who report fraud attempts, contributing to the database of known scams. # Conclusion: In summary, the steps to handle a suspicious SMS about a bank card being blocked include: 1. Not reacting hastily. 2. Verifying the sender's number against known legitimate numbers. 3. Calling the official customer service number found on the bank card. 4. Consulting with a bank representative to confirm the legitimacy of the message. 5. Reporting the fraudulent attempt to the bank. Adopting these measures helps protect against potential fraud and ensures that responses are made only to legitimate communications. boxed{}

answer:The standard equation for a circle with center at the point (a, b) and radius r is (x-a)^{2}+(y-b)^{2}=r^{2}. Given the center coordinates (-3, 4) and radius r = sqrt{3}, we can substitute these values into the standard form of the circle's equation: begin{align*} (x - (-3))^{2} + (y - 4)^{2} & = (sqrt{3})^{2} (x + 3)^{2} + (y - 4)^{2} & = 3 end{align*} Thus, the correct standard equation of the given circle is boxed{(x+3)^{2}+(y-4)^{2}=3}, which corresponds to option C.