Joanie ran in 6 races last month. Each race was 360 feet long. What was the total distance that Joanie ran in the races?

The measurements given can form a triangle, and to solve it, we would use the Law of Sines. After confirming the possibility of a triangle, we solve for the unknown angle C using the known values and compute the remaining angle and side.

To determine if a triangle is formed by the given measurements and solve it using the Law of Sines, we need to check if the given angle and sides satisfy the triangle inequality. The measurements given are angle B = 137°, side c = 6, and side b = 11. A triangle is possible if the sum of the two smallest sides is greater than the length of the longest side. Here the angle is very large, suggesting that the opposite side (b) must be the longest; however, since side b is indeed longer than side c, this condition is satisfied, so a triangle can be formed.

To solve the triangle using the Law of Sines, we set up the following ratio:

    b/sin(B) = c/sin(C)

After substituting the known values into the equation, we get:

    11/sin(137°) = 6/sin(C)

Now, we solve for sin(C) to find the angle C, and subsequently use the sum of angles in a triangle (180°) to find the remaining angle A. Once angle A is known, we can use the Law of Sines again to find the remaining side a. If at any point we find that the calculation results in an invalid sine value (greater than 1 or less than -1), we must then state that no real solution exists.

It is important to note that if we find angle C to be obtuse (greater than 90°), the triangle will not have a unique solution because it would contradict our initial assumption that angle B, being the largest given angle, is opposite the longest side.

Answer:  The correct option is (B) 81°.

Step-by-step explanation:  We are given to find the measure of the missing angle of the quadrilateral shown in the figure.

The measures of three angles of the quadrilateral are 65°, 78° and 136°.

To find the value of x, the measure of the fourth angle.

We know that

the sum of the measures of four angles of a quadrilateral is 360°. so, we must have

[tex]65^\circ+78^\circ+136^\circ+x=360^\circ\\\\\Rightarrow 279^\circ+x=360^\circ\\\\\Rightarrow x=360^\circ-279^\circ\\\\\Rightarrow x=81^\circ.[/tex]

Thus, the measure of the missing angle is 81°.

Option (B) is CORRECT.

Answer:

312

Step-by-step explanation:

The other answer has a great explanation. I am just confirming this answer to be correct! :)

Answer:

The activities can a person participate in to be considered "actively looking" for a job are:

1. He should be active on social media.

2. Updated resume on social median platform like LinkedIn , Indeed, et cetera.

3. Highlight the companies whose vacancy is there in the newspaper and should actively participate in the walking interviews.

To actively look for a job, participate in activities like job searching, networking, resume customization, and submitting applications.

Prepare for interviews, enhance skills, and stay updated with job alerts, social media, and professional organizations.

Engage in informational interviews, volunteer, and consider career workshops for effective job hunting.

To be considered "actively looking" for a job, a person can engage in various activities, including:

Networking: Attend job fairs, industry events, and join professional organizations to expand your network.

Connect with current and former colleagues on LinkedIn.

Online Job Searches: Regularly search job boards, company websites, and online job portals for relevant job openings.

Customizing Resumes and Cover Letters: Tailor your resume and cover letter to match specific job applications, highlighting relevant skills and experience.

Submitting Applications: Actively submit job applications for positions that match your qualifications and career goals.

Interview Preparation: Prepare for interviews by researching companies, practicing common interview questions, and refining your interview skills.

Updating LinkedIn Profile: Maintain an up-to-date LinkedIn profile with a professional photo, relevant skills, and endorsements.

Utilizing Recruitment Agencies: Register with recruitment agencies or headhunters who specialize in your industry.

Skill Enhancement: Enhance your qualifications by taking relevant courses, certifications, or attending workshops.

Volunteer or Intern: Consider unpaid opportunities, internships, or volunteer work to gain experience or maintain skills.

Join Job Search Workshops: Attend workshops or webinars that offer job search strategies, interview tips, and resume building guidance.

Set Up Job Alerts: Subscribe to email notifications or job alert services on job websites to receive updates on new postings.

Informational Interviews: Connect with professionals in your desired field for informational interviews to learn more about potential job opportunities.

Utilize Social Media: Follow companies of interest on social media platforms for job postings and engage in professional discussions.

Job Search Apps: Use mobile apps designed for job seekers to search and apply for jobs on the go.

Utilize Career Centers: If you're a student or alumni, use your school's career center resources for job search assistance.

Attend Job Seeker Support Groups: Join local job seeker support groups or online forums for job search advice and emotional support.

Cold Outreach: Reach out directly to companies of interest, even if they don't have posted job openings, to express your interest and inquire about potential opportunities.

Being actively engaged in multiple aspects of job searching demonstrates commitment and increases your chances of finding a suitable position.

Remember to track your job search activities for reference and follow up on applications and networking connections.

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The expression is 26x36 to the 7th power if the number of 8-character passwords.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

The number of 8-character passwords that can be formed using letters and digits if the password must begin with a letter.

From the condition given:

= 26 x (36)⁶

Thus, the expression is 26x36 to the 7th power if the number of 8-character passwords.

a. 21x36 to the 7th power

b.26x36 to the 7th power

c.26 to the 5th power x 10 to the 3rd

d.36 to the 8th power

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Answer:

x=7

Step-by-step explanation:

3*7*7 = 147

147-16 = 131

so x=7

note x could be -7 also

To convert log4 14 to a logarithm of base 3, you can use the change of base formula. The required conversion would be log3 14 divided by log3 4.

To write log4 14 as a logarithm of base 3, we would use the change of base formula. The change of base formula is logba = logca / logcb, where logba is the logarithm we want to convert, c is the new base, a is the number, and b is the original base. So, in this case, we want to write log4 14 as a logarithm of base 3, so using the formula, it would be (log3 14) / (log3 4).

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The range of the function f(x) = |x - 1| - 2 is all real numbers greater than or equal to -2.

The function f(x) = |x - 1| - 2 represents the absolute value of x minus 1, subtracted by 2.

The range of the function can be determined by finding the minimum and maximum values it can take.

Since the absolute value of a number is always greater than or equal to zero, the lowest value that f(x) can take is when |x - 1| = 0, which happens when x = 1.

Therefore, the minimum value of f(x) is -2.

As x increases or decreases from 1, the value of f(x) increases.

So, there is no upper bound for the range of f(x).

Therefore, the range of the function is all real numbers greater than or equal to -2.

To find the new width of a photograph after reducing its length to 8 inches, while maintaining the original aspect ratio, set up a proportion based on the original dimensions and solve for the new width, which results in 4.8 inches.

The question involves a proportional reduction of a photograph's dimensions. To determine the new width, we need to maintain the same ratio between the width and the length as in the original photograph. Initially, the photograph measures 12 inches wide by 20 inches long. If reduced so that the length is 8 inches, the width will also reduce in the same ratio.

Let's denote the new width as w. The original ratio is 12/20, which should be equal to the new ratio w/8.

Now, creating a proportion, we have:

12/20 = w/8

By cross-multiplying, we get:

20 × w = 12 × 8

w = (12 × 8) / 20

w = 96 / 20

w = 4.8

Therefore, the new width of the photograph is 4.8 inches.

Final answer:

The zeros of the polynomial function f(x) are (12) and (4).

Explanation:

The zeros of the polynomial function f(x) = [tex]x^2[/tex] - 16x + 48 can be found by factoring the quadratic equation or using the quadratic formula. To factor, we look for two numbers that multiply to give the constant term (48) and add to give the coefficient of the middle term (-16). After finding such numbers, the polynomial can be factored into two binomials.

In this case, the two numbers are -12 and -4 because (-12) * (-4) = 48 and (-12) + (-4) = -16. Therefore, the factored form of the polynomial is (x - 12)(x - 4).

To find the zeros, we set each factor equal to zero:

x - 12 = 0 ⇒ x = 12

x - 4 = 0 ⇒ x = 4

Hence, the zeros of the polynomial function f(x) are (12) and (4).