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Leokris [45]
2 years ago
11

Determine if the following relations are functions. If they are functions, also state the domain and range.

Mathematics
2 answers:
Nezavi [6.7K]2 years ago
7 0
No they are not functions
Zigmanuir [339]2 years ago
6 0

Answer:

No it is not a function because the 10 in the input is repeated twice (the arrow is connected to 2 numbers)

D= {7, 9, 10}

R= {7, 9, 8, 10}

The pairs are (7, 7), (9, 9), (10, 8), (10, 10)

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100 POINTS + BRAINLIST
mojhsa [17]

Problem 1

Since point P is the tangent point, this means angle OPT is a right angle

angle OPT = 90 degrees

Let's use the Pythagorean theorem to find the missing side 'a'

a^2 + b^2 = c^2

a^2 + 7^2 = 12^2

a^2 + 49 = 144

a^2 = 144 - 49

a^2 = 95

a = sqrt(95)

a = 9.7467943

a = 9.7

----------------

Let's use the sine and arcsine rule to find angle y

sin(angle) = opposite/hypotenuse

sin(y) = 7/12

y = arcsin( 7/12 )

y = 35.6853347

y = 35.7

The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or \sin^{-1}

====================================================

Problem 2

Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.

We use the converse of the Pythagorean theorem to check.

Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.

In this case we have

  • a = 7
  • b = 13
  • c = 16

Which leads to

a^2 + b^2 = c^2

7^2 + 13^2 = 16^2

49 + 169 = 256

218 = 256

We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.

We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.

Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.

You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.

7 0
2 years ago
Read 2 more answers
Please help me out if you can
Arlecino [84]

Answer:

(a, 0)

Step-by-step explanation:

Point S has the same x-coordinate as does Point R:  a.

Point S has the y-coordinate 0, as Point S lies on the x-axis.

Correct final answer:  (a, 0) represents Point S.

6 0
3 years ago
Can someone please help
Sliva [168]

Answer:

i got no clue

Step-by-step explanation:

ignc

4 0
3 years ago
Find the slope of the line?<br> the slope is____
chubhunter [2.5K]

Answer:

Slope is m= -1

Step-by-step explanation:

Use the slope formula to find the slope m .

y=mx+b

3 0
3 years ago
The lowest number is 11 the range is 13 and the median is 17 what are the 3 numbers
11Alexandr11 [23.1K]

Answer:

11, 17, and 28.

Step-by-step explanation:

x, y, z\\

Lowest number is x

Median is y

Highest number is z

x=11\\y=17\\\\z-x=17\\z-11=17\\z-11+11=17+11\\z=28\\\\x=11\\y=17\\z=28\\\\11, 17, 28

3 0
3 years ago
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