All categories

3 years ago

Given: ZDEF is a right angle. Using a paragraph proof, prove 41 is acute.

Mathematics

1 answer:

Slav-nsk [51]3 years ago

4 0

Let G be some point on the diagonal line away from point E.

Angle DEG represents angle 1.

We're given that angle DEF is a right angle which means it's 90 degrees. Angle DEG is some angle smaller than 90 degrees. By definition, that must mean angle 1 is acute. Any acute angle is smaller than 90 degrees. There's not much else to say other than this is just a definition problem.

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

Extra side notes:

If angle 1 was a right angle, then that would mean angle GEF would have to be 0 degrees; however the diagram shows this isn't the case.

If angle 1 was obtuse, then there's no way we'd be able to fit it into angle DEF. In other words, there's no way to have an angle larger than 90 fit in a 90 degree angle.

You might be interested in

Which of the following represents the measure of all angles coterminal with 418° angle?

Elena L [17]

418° is the same angle as 360° + 58° .

And then, if you add any whole number of 360s onto it,
you get the same angle again.

So it's 58+360n with n=any whole number
(n=0 doesn't work, so it's not 'integer'. '0' is an integer.)

5 0

3 years ago

Read 2 more answers

29. repetition of digits is permitted and the letters must be 2 DIFFERENT vowels (a, e, i, o, u).

vova2212 [387]

Answer:

c) 20,000

Step-by-step explanation:

Number of digits = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 = 10,

Number of vowel letters = a, e, i, o, u = 5

Repetition of digits is permitted but repetition of vowel letters is not permitted

Let the password be presented in dash form as shown below:

____ ____ ____ ____ ____ =

D D D V V

where:

D = possible number of digits to fill the spot

V = possible number of vowels to fill the spot

Since repetition of digits is permitted, each spot marked as D can be filled with any one of 10 digits from 0 - 9

The first spot marked V has 5 possible options (a, e, i, o, u) & the second spot marked V only has 4 possible options (since repetition of vowels is not permitted).

We then place the number of possibilities in each spot and multiply them to determine the number of passwords possible

10 * 10 * 10 * 5 * 4 = 20,000

Therefore, the number of possible passwords is 20,000

5 0

3 years ago

F(h) = 45+ 20 h +0.5 g(h) = 45 + 33(0.5) (h+0.5)

larisa [96]

Steps:

Question 1:

Step 1: Multiply both sides by h+0.5.

Step 2: Factor out variable f.

Step 3: Divide both sides by h^2+0.5h.

Question 2

Let's solve for g.

Step 1: Divide both sides by h.

Answers:

1: f=45h+42.5/h²+0.5h

2: g=16.5h+53.25/h

Please mark Brainliest

Hope this helps.

8 0

3 years ago

List the prime numbers up to 40

maria [59]

Answer:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

8 0

3 years ago

Read 2 more answers

Find the mean, median, and mode of 12, 9, 17, 15, 10

igor_vitrenko [27]

Answer:

Mean: 12.6

Median: 12

Mode: 9, 10, 12, 15, 17

Step-by-step explanation:

Mean: To find the mean you have to add up all your terms and divide your result by the number of terms you have. ((12+9+17+15+10) / 5)

Median: To find the median you have to organize your terms from least to greatest and then find your center term. (12)

Mode: Normally to find your mode would be to organize your terms from least to greatest and see which of your terms occurs the most. In this case all terms occur only once, making all your terms the mode.

7 0

3 years ago