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Naya [18.7K]
3 years ago
8

Activity 1: Put me in the Box!

Mathematics
1 answer:
Contact [7]3 years ago
6 0

Step-by-step explanation:

To find - Determine the hypothesis and the conclusion of the given

               statement  the hypothesis in Box A and the conclusion in Box B.

             1. Vertical angles are congruent

             2. Bats are mammals that can fly.

             3. You are a good citizen when you obey rules and regulations.

             4. A number is divisible by 10 if its last digit is a 0.

             5. 3x + 6 = 21, because x = 5​

Proof -

Firstly we will write the conditional statements , so that we can easily find the hypothesis and the conclusion of the given statement.

1.)

Given statement - Vertical angles are congruent

Conditional statement - If two angles are vertical , then they are congruent.

Hypothesis - Two angles are vertical

Conclusions - They are congruent.

2.)

Given statement - Bats are mammals that can fly

Conditional statement - If bats are mammals , then they can fly.

Hypothesis - Bats are mammals

Conclusions - They can fly.

3.)

Given statement - You are a good citizen when you obey rules and regulations.

Conditional statement - If you are a good citizen , then you obey rules and regulations.

Hypothesis - You are a good citizen

Conclusions - You obey rules and regulations.

4.)

Given statement - A number is divisible by 10 if its last digit is a 0.

Conditional statement - If a number is divisible by 10, then its last digit is a 0.

Hypothesis - A number is divisible by 10

Conclusions - Its last digit is 0.

5.)

Given statement - 3x + 6 = 21, because x = 5​

Conditional statement - If 3x + 6 = 21, then x = 5

Hypothesis - 3x + 6 = 21

Conclusions - x = 5

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cupoosta [38]

Answer:

The cost is a fixed $2, plus $3.25 for any additional hour.

Then if you rent it for x hours, the cost is:

c(x) = $2 + $3.25*x

Is this situation continuous or discrete?

Yes, it is discrete, because x is "the number of hours"

so if you rent it for 1.30 hours, they will say "ok, this is equivalent to two hours".

This means that while the values of x are continuous, the possible costs are:

{$2, $2 + $3.25, $2 + 2*$3.25, ....}

Which is a discrete set.

Then the sign for 1 to 5 hours will be:

1 hour ---------- $2 + $3.25 = $5.25

2 hours -------- $2 + 2*$3.25 = $8.50

3 hours--------- $2 + 3*$3.25 = $11.75

4 hours--------- $2 + 4*$3.25 =  $15

5 hours -------- $2 + 5*$3.25 = $18.25

In the other park the cost is only $4 for each hour (no fixed cost) then the total cost for x hours is:

c(x) = $4*x

Now, which option is better?

If we look at the costs for different numbers of hours for this other equation, we have:

1 hour ----- $4

2 hours ---- 2*$4 = $8

3 hours ----- 3*$4 = $12

4 hours ------ 4*$4 = $16

Then: if you want to skate 2 hours or less, Skate City is cheaper, if you want to skate more than that, kate Days is cheaper.

This happens because the first one has a smaller slope, meaning that is larger at first, but as x grows the price does not grow as much as in Skate City

7 0
3 years ago
Which of the following transformations has the same result as a rotation of 90 degrees clockwise?
krek1111 [17]
The best and most correct answer among the choices provided by your question is the second choice or letter B.

Reflection of a horizontal line <span>has the same result as a rotation of 90 degrees clockwise.</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
3 0
3 years ago
Read 2 more answers
What is the sequence of 5,11,18,26...
antoniya [11.8K]
11-5=6
18-11-7
26-18=8
........... so on and so forth.
I think you get the point.
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The midpoint of AB is at (3,7) and A is at (0,-5). Where is B located?
Veronika [31]
I attached your answer below...

4 0
3 years ago
1. A plane is flying at an altitude of 13000 feet. The angle of depression from the plane to a control tower is 20 degrees. The
Mariulka [41]

Answer:

see explanation

Step-by-step explanation:

There is a right triangle formed between the height above the tower to the plane, the horizontal and the line from the tower to the plane.

The height above the tower to the plane = 13000 - 150 = 12850 ft

The angle between the plane and the tower is 20° , angle of depression.

Using the tangent ratio in the right triangle formed, with the adjacent side being the horizontal ( hor ) distance, then

tan20° = \frac{opposite}{adjacent} = \frac{12850}{hor} ( multiply both sides by hor)

hor × tan20° = 12850 ( divide both sides by tan20° )

hor = \frac{12850}{tan20} ≈ 35305 ft ( to the nearest foot )

(2)

Arianna is 60 + 5 = 65 ft above the ground ( to her eye level )

Using the right triangle formed with legs 65 and 37  and angle of depression x, then

tanx° = \frac{opposite}{adjacent} = \frac{37}{65} , thus

x = tan^{-1} (\frac{37}{65} ) ≈ 30° ( to the nearest degree )

4 0
3 years ago
Read 2 more answers
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