Which equation represents the vertex form of the equation y=x^2-20x+104?
which equation represents the vertex form of the equation y=x^2-20x+104? - 1

Answers

Answer 1
Answer:

From the graph above, the vertex of the graph (h,k) is (10,4).

The general equation in its vertex form is,

y=(x-h)^2+k

Therefore,

y=(x-10)^2+4

Hence, option D is the correct answer.


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Which of the following statements is not​ true? A. If the probability of an event occurring is​ 1.5, then it is certain that event will occur. B. If the probability of an event occurring is​ 0, then it is impossible for that event to occur.

What is the length of AB?

15
9
4.5
18

Answers

Answer:

18

Step-by-step explanation:

Let X be the midpoint of the chord AB

Distance between X and the centre:

15-3 = 12

XB² = 15² - 12²

XB² = 81

XB = 9

AB = 2XB = 18

Answer:

4.5

Step-by-step explanation:

Line segment of length k is divided into 3 equal parts. What is distance between midpoints of first and third segments?A) 2k/3 B) k C) k/6 D) 2k

Answers

The distance between the midpoints of the first segment and the third segment is 2k/3. Hence, option A is the right choice.

What is the mid-point of a line segment?

The mid-point of a line segment is the point from which the distance to both ends of the line segment is equal.

How to solve the question?

In the question, we are given a line segment of length k units, which is divided into 3 equal parts.

We are asked to find the distance between the midpoints of the first and third segments.

Firstly, we divide the line segment at points k/3 and 2k/3, to get three equal parts of lengths k/3 each.

Now, the mid-point of the first segment = (0 + k/3)/2 = k/6.

The mid-point of the third segment = (2k/3 + k)/2 = 5k/6

Therefore, the distance between the midpoints of the first segment and the third segment is (5k/6 - k/6) = 4k/6 = 2k/3. Hence, option A is the right choice.

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Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

ans is A


There are 420 students . The ratio from girls to boys is 4- 3 . How many more girls?

Answers

There are 60 more girls

Final answer:

There are 420 students divided into 7 parts due to the ratio of girls to boys being 4:3. With one part totaling 60 students, there are 240 girls and 180 boys. Thus, there are 60 more girls than boys.

Explanation:

To solve this problem, you need to understand the concept of ratios. In this case, the ratio of girls to boys is 4:3. This means that for every 4 girls, there are 3 boys. If we add the two parts of the ratio together, we get 7 parts. This means that the total number of students, which is 420, is to be divided into 7 parts.

So, one part of this ratio is equal to 420 divided by 7, which equals 60 students. Since the ratio claims there are 4 parts of girls and 3 parts of boys, to find out the numbers of girls and boys, we multiply each part of the ratio by 60. Hence, the total number of girls is 4 multiplied by 60, which equals 240 and the number of boys is 3 multiplied by 60, which equals 180.

Therefore, the difference in number between girls and boys is 240 minus 180, which equals 60. So there are 60 more girls than boys.

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Which of the following is false regarding number sets

Answers

Answer:

D

Step-by-step explanation:

just took a random guess

The value of the Euler \phi function (\phi is the Greek letter phi) at the positive integer n is defined to be the number of positive integers less than or equal to n that are relativel prime to n, For example for n=14, we have {1, 3, 5, 9, 11, 13} are the positive integers less than or equal to 14 which are relatively prime to 14. Thus \phi (14) = 6.Find the following:\phi(9) = __________.\phi(15) = __________.\phi(75) =__________.

Answers

Answer:

\bf \phi (9)=5

\bf \phi (15)=8

\bf \phi (75)=40

Step-by-step explanation:

Positive integers relative primes to 9 which are less or equal than 9

{1,2,4,5,7}

so

\bf \phi (9)=5

Positive integers relative primes to 15 which are less or equal than 15

{1,2,4,7,8,11,13,14}

and

\bf \phi (15)=8

Positive integers relative primes to 75 which are less or equal than 75

{1,2,4,7,8,11,13,14,16,17,19,22,23,26,28,29,31,32,34,37,38,41,43,44,46,47,49,52,53,56,58,59,61,62,64,67,68,71,73,74}

and

\bf \phi (75)=40

Greatest comment factor of 14^3 and 13^4

Answers

Answer:

14^3 = 2,744. Common factors are 1,2,4,7,8,14,28,49,56...

13^4 = 2,197. Common factors are 1, 13, 169, and 2197.