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Use the following four coordinates to determine which one has a distance of 5 units from point A (2, 6). (5 points) (5, 2) (2, 5) (6, 7) (7, 5)

Answers

Answer 1
Answer:

A right triangle with legs measuring 3 units and 4 units has a hypotenuse measuring 5 units.

You need to find a point which has a difference in x and y of 3 and 4 or 4 and 3 from the point A(2, 6).

Look at (5, 2) and compare with A(2, 6).

Difference in x: 5 - 2 = 3

Difference in y: 6 - 2 = 4

Since the differences in x and y are 3 and 4, the hypotenuse will measure 5.

Answer: (5, 2)

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21) Which is the correct reasoning to use when simplifying this expression?−200 ÷ −25A) The quotient of two even integers is always positive. B) The product of two even integers is always positive. C) The quotient of two negative integers is always negative. D) The quotient of two negative integers is always positive.
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There are 80 participants in a competition. The average score of each participant is 58.5. The average score of the male participants is 64 and the average score of the female participants is 56. How many male participants are there in the competition?

Answers

Answer:

  • 25

Step-by-step explanation:

Given

  • Total number of participants= 80
  • Male = x
  • Female = 80 - x
  • Average = 58.5
  • Average for male = 64
  • Average for female = 56

Equation to reflect the sum:

  • 64x + 56(80 - x) = 80*58.5
  • 64x - 56x = 80*(68.5 - 56)
  • 8x = 80*2.5
  • x = 25

The answer is 25 male participants

What is the slope of the line described by the equation below?y= 10x + 2
A. -10
B. 10
C. 2
O D. -2

Answers

Answer:

B because when you compare y= mx+ c where M is the slope or gradient

Which expression is equivalent to the given expression?12(x – 17)

A.
12x – 29

B.
12 + 12 • 17

C.
12x – 12 • 17

D.
12x – 17

Answers

12(x-17)

the answer would be C
12x-12*17

Which of the following is equivalent to 18 minus StartRoot negative 25 EndRoot?

Answers

Answer:

18-5i

Step-by-step explanation:

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

18-√(-25)   Original Question

18-(√(25) * √(-1) )   Split

18-5*(√(-1) )   Solve for square root

12-√(-1)   Subtract

You can substitute √(-1) for i

12-i   Substitute

The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 491. Find the first term of the progression and the common difference
2. Find the value of n

Answers

Answer:

For 1: The first term is 10 and the common difference is (3)/(2)

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

a_n=a_1+(n-1)d

where,

a_1 is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

S_n=(n)/(2)[2a_1+(n-1)d]

where,

S_n is the sum of nth terms

  • For (1):

The 11th term of the progression:

25=a_1+10d               .......(1)

Sum of first 4 numbers:

49=(4)/(2)[2a_1+3d              ......(2)

Forming equations:

98=8a_1+12d

25=a_1+10d                  ( × 8)

The equations become:

98=8a_1+12d

200=8a_1+80d

Solving above equations, we get:

102=68d\n\nd=(102)/(68)=(3)/(2)

Putting value in equation (1):

25=a_1+10(3)/(2)\n\na_1=[25-15]=10

Hence, the first term is 10 and the common difference is (3)/(2)

  • For 2:

The nth term is given as:

49=10+(n-1)(3)/(2)

Solving the above equation:

39=(n-1)(3)/(2)\n\nn-1=26\n\nn=27

Hence, the value of n is 27

Final answer:

The value of n when the nth term of the progression is 49 is 22.

Explanation:

The 11th term of the progression (a11) is 25.

The sum of the first 4 terms (S4) is 49.

The nth term (an) is 49.

Let's find the answers to your questions:

Find the first term of the progression (a1) and the common difference (d):

We know that the nth term of an AP can be expressed as:

an = a1 + (n - 1)d

Substituting the values:

a11 = a1 + (11 - 1)d

25 = a1 + 10d

Now, we need to find a1 and d. We'll also use the information that the sum of the first 4 terms (S4) is 49. In an AP, the sum of the first n terms (Sn) can be expressed as:

Sn = (n/2)[2a1 + (n - 1)d]

For S4:

49 = (4/2)[2a1 + (4 - 1)d]

49 = 2[2a1 + 3d]

Now, we have two equations:

25 = a1 + 10d

49 = 2[2a1 + 3d]

Let's solve this system of equations to find a1 and d.

1. First, rearrange the first equation to isolate a1:

a1 = 25 - 10d

Now, substitute this expression for a1 into the second equation:

49 = 2[2(25 - 10d) + 3d]

Simplify and solve for d:

49 = 2[50 - 20d + 3d]

49 = 2[50 - 17d]

49 = 100 - 34d

34d = 100 - 49

34d = 51

d = 51/34

d = 3/2

2. Now that we have the common difference (d), we can find a1 using the first equation:

a1 = 25 - 10d

a1 = 25 - 10(3/2)

a1 = 25 - 15/2

a1 = (50 - 15)/2

a1 = 35/2

a1 = 17.5

So, the first term of the progression (a1) is 17.5, and the common difference (d) is 3/2.

Find the value of n when the nth term of the progression is 49:

We know that an = 49, and we can use the formula for an in an AP:

an = a1 + (n - 1)d

Substitute the values:

49 = 17.5 + (n - 1)(3/2)

49 - 17.5 = (n - 1)(3/2)

31.5 = (n - 1)(3/2)

To isolate n, multiply both sides by (2/3):

(n - 1)(3/2) = 31.5 * (2/3)

(n - 1) = 21

Now, add 1 to both sides to find n:

n = 21 + 1

n = 22

So, the value of n when the nth term of the progression is 49 is 22.

Learn more about Arithmetic Progression here:

brainly.com/question/35697112

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Approximately how many times greater is 6 x 10^-6 than 2 x 10^-8

Answers

Answer:

300

Step-by-step explanation:

(6*10^-6)/(2*10^-8\n) = 3(6/2)*10^(-6-(-8)=2) = 300
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