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AfilCa [17]
2 years ago
7

50 points! Tell whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter.

Mathematics
1 answer:
Nady [450]2 years ago
6 0

Answer:

  • (1,3) is inside the triangle

Step-by-step explanation:

Orthocenter is the intersection of altitudes.

We'll calculate the slopes of the two sides and their altitudes ad find the intersection.

<h3>Side QR</h3>
  • m = (3 - 5)/(4 - (-1)) = -2/5

<u>Perpendicular slope:</u>

  • -1/m = 5/2

<u>Perpendicular line passes through S(-1, -2):</u>

  • y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2
<h3>Side RS</h3>
  • m = (-2 - 3)/(-1 -4) = -5/-5 = 1

<u>Perpendicular slope:</u>

  • -1/m = -1/1 = -1

<u>Perpendicular line passes through Q(-1, 5):</u>

  • y - 5 = -(x - (-1)) ⇒ y = -x + 4

The intersection of the two lines is the orthocenter.

<u>Solve the system of equations to get the coordinates of the orthocenter:</u>

  • 5/2x + 1/2 = x + 4
  • 5x + 1 = -2x + 8
  • 7x = 7
  • x = 1

<u>Find y-coordinate:</u>

  • y = -1 + 4 = 3

The orthocenter is (1, 3)

If we plot the points, we'll see it is inside the triangle

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MissTica

Answer:

$0.75 per song

Step-by-step explanation:

Given that the relationship between variable s and c is a proportional relationship, and is represented by the equation, c = 0.75s.

Where,

c = total costs

s = number of songs

The constant of proportionality, k, = 0.75.

Thus, 0.75 represents the cost per sing downloaded.

The answer is:

✔️$0.75 per song

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TiliK225 [7]

Answer:

This is not the answer this is the trick to find it

Step-by-step explanation:

The points after reflection will follow points equal but different direction, to the path followed before the reflection. So, if the line would cover 3.5 on the x and 5 on the y; it will reflect symmetrically giving you the formula to get your answer.

7 0
2 years ago
In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand contain
aalyn [17]

Answer:

0.00597

Step-by-step explanation:

Given,

Total number of cards = 52,

In which flush cards = 20,

Also, the number of spade flush cards = 5,

Since,

\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}

Thus, the probability of a hand containing a spade flush, if each player has 5 cards

=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}

=\frac{^{20}C_5}{^{52}C_5}

=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}

=\frac{15504}{2598960}

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3 years ago
A small business makes 3-speed and 10-speed bicycles at two different factories. Factory A produces 16 3-speed and 20 10-speed b
GarryVolchara [31]

Answer:

Factory A should be operated 6.11 days

Factory B should be operated 6.88 days

The minimum cost for factory A is $6,110

The minimum cost for factory B is $5,504

Step-by-step explanation:

Factory A

Daily production: 16 3-speed and 20 10-speed bikes

Total daily production = 16+20 = 36 speed bikes

Order: 80 3-speed and 140 10-speed bikes

Total order = 80+140 = 220 speed bikes

Number of days = 220/36 = 6.11 days

Cost per day = $1,000

Minimum cost for 6.11 days = $1000 × 6.11 = $6,110

Factory B

Daily production: 12 3-speed and 20 10-speed bikes

Total daily production = 12+20 = 32 speed bikes

Total order = 220 speed bikes

Number of days = 220/36 = 6.88 days

Cost per day = $800

Cost for 6.88 days = $800 × 6.88 = $5,504

6 0
3 years ago
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