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UkoKoshka [18]
2 years ago
10

Riangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

Mathematics
1 answer:
DochEvi [55]2 years ago
7 0

Answer:

Step-by-step explanation:

1. Part A: We know parts of our triangle since the cosine of X is given.  XY = 2.5 and XZ = 5.59 and since it is a scale factor of 2, ABC is most likely similar to XYZ by angle measures and the special relationship is, that they are all equal, because with a scale factor of two, all the ratios in triangle ABC will simplify to the ratios of triangle XYZ. 

Part B: Because triangle XYZ was dilated with a scale factor of 2 to create triangle ABC, just multiply the sides by 2 to get the sides AC and CB, which is AB = 2 times XY and CB = 2 times XZ. 

2. We can first find the hypothenuse by adding squaring 8 and 6 to have 100. Then square root it to have 10 as our hypothenuse

Now we can use sin x = 6/10 and cos y = 6/10

3. Since this is using the angle of elevation, we can say that the length of side AB is perpendicular from the perspective of angle of elevation, and the hypotenuse's length is known, so in this case, we can use a sine or cosecant ratio. 

Sin(40 Degrees) = AB/100

AB = 100 x sin(40 Degrees) ft

AB ~ 64.28 ft which can be rounded to 64 ft

The triangle I drew was a right triangle with points A, B, and C. 40 is on point C while 100 ft was on the hypotenuse. The kite was near A and the ground was between segment B and C.

4. Since the angle and Adjacent line is given and it is asking us to find H which is the opposite, we well try and be using Tangent = opposite/adjacent 

500 ft Multiply by tan39 = 405 (Estimated after rounding to nearest hundreth 404.892).

To be honest, I didn't know so much about these questions but this might give a better understanding and if I'm wrong then I apologize.

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There are 15 candidates for 4 job positions.
Veronika [31]

Answer:

32760 ways

Step-by-step explanation:

Given

Number of Candidates = 15

Job Positions = 4

Required:

Number of outcomes

This question represent selection; i.e. selecting candidates for job positions;

This question can be solved in any of the following two ways

Method 1.

The first candidate can be chosen from any of the 15 candidates

The second candidate can be chosen from any of the remaining 14 candidates

The third candidate can be chosen from any of the remaining 13 candidates

The fourth candidate can be chosen from any of the remaining 12 candidates

Total Possible Selection = 15 * 14 * 13 * 12

<em>Total Possible Selection = 32760 ways</em>

<em></em>

Method 2:

This can be solved using permutation method which goes thus;

nPr = \frac{n!}{(n-r)!}

Where n = 15 and r = 4

So;

nPr = \frac{n!}{(n-r)!} becomes

15P4 = \frac{15!}{(15-4)!}

15P4 = \frac{15!}{11!}

15P4 = \frac{15*14*13*12*11!}{11!}

15P4 = 15*14*13*12

15C4 = 32760

<em>Hence, there are 32760 ways</em>

8 0
3 years ago
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Pepsi [2]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
Write an expression for this phrase.<br> 2. A third of a number n
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A third of a number n 

= \frac{1}{3} * n =  \frac{1}{3} n =  \frac{n}{3}
5 0
3 years ago
Silas had 3 times as much money as Raja. Silas spent $84 of his money to buy a birthday gift for his grandma while Raja was awar
Tamiku [17]

Answer:

Total amount Silas and Raja has at first = $252

Step-by-step explanation:

Let,

Amount Silas had = x

Amount Raja had = y

According to given statement;

x = 3y       Eqn 1

x-84 = y+42     Eqn 2

Putting value of x from Eqn 1 in Eqn 2

3y - 84 = y+42

3y-y = 42+84

2y = 126

Dividing both sides by 2

\frac{2y}{2}=\frac{126}{2}\\y=63

Putting y = 63 in Eqn 1

x = 63(3)

x = 189

Total amount they had = 189 + 63 = $252

Hence,

Total amount Silas and Raja has at first = $252

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