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3 years ago

Find the orthocenter of a triangle ABC with vertices at A(2, 2), B(0, -4), and C(6, -2).

Mathematics

1 answer:

bulgar [2K]3 years ago

4 0

Hello,

H=(3,-1)

(AB)≡y-2=(x-2)*(-4-2)/(0-2)==>y=3x-4
(BC)≡y+4=(x-0)*(-2+4)/(6-0)==>y=x/3-4
(AA')≡y-2=(x-2)*(-3)==>y=-3x+8
(CC')≡y+2=(x-6)*(-1/3)==>y=-x/3

(AA') ∩ (CC'):
x+3y=0 (1)
3x+y=8 (2)
==>-3*(1)+(2): -y8=8==>y=-1 and x=3

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Maya drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Maya drove

Roman55 [17]

Answer:

480 miles.

Step-by-step explanation:

Let x represent the distance between Maria's house and mountains ans r represent Maria's rate for going trip.

We have been given that there was heavy traffic on the way there, and the trip took 12 hours.

$\text{Distance}=\text{Rate}\times \text{Time}$

$x=12r$

We are also told that hen Maya drove home, there was no traffic and the trip only took 8 hours. Maria's average rate was 20 miles per hour faster on the trip home.

So Maria's speed while returning back would be $r+20$ .

$x=8(r+20)$

Upon equating both distances, we will get:

$12r=8(r+20)$

$12r=8r+160$

$12r-8r=8r-8r+160$

$4r=160$

$r=\frac{160}{4}$

$r=40$

Upon substituting $r=40$ in equation $x=12r$ , we will get:

$x=12r\\\\x=12(40)\\\\x=480$

Therefore, Maya live 480 miles away from the mountains.

7 0

3 years ago

What would go in the blank?

luda_lava [24]

Answer:44

Step-by-step explanation:

Because all angles are the same on a triangle

8 0

3 years ago

Read 2 more answers

Describe how to subtract two numbers written in scientific notation with the same power of 10

OverLord2011 [107]

Answer:

All you need to do is subtract the coefficient.

Step-by-step explanation:

For example a minus b is c. So this is simply going to be c times d to the e you can do that if these two are the same.

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2 years ago

What is the definition of perfect cube and can you give an example

PilotLPTM [1.2K]

A perfect cube is a natural number in the form
${a}^{3} = a \times a \times a$
therefore
${1}^{3} = 1 \\ {2}^{3} = 8 \\ {3}^{3} = 27 \\ {4}^{3} = 64 \\ {5}^{3 } = 125 \\ . \\ . \\ .\\ .$
and also you can define it as any natural number who's third root is also a natural number for examble
$\sqrt[3]{1000} = 10$
so you can say that the tenth perfect cube is 1000

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3 years ago

Derek collects quarters that have the names of the 50 U.S. states on them. He has collected 12

Lelechka [254]

Time taken to collect 12 different state quarters is 2.5 months.

Now , we need to find time taken to collect all 50 state quarters.

Let , time required is x.

So,

$\dfrac{x}{50}=\dfrac{2.5}{12}\\\\x=\dfrac{2.5}{12}\times 50\\\\x=10.4$

Therefore, time required is 10.7 months.

Hence, this is the required solution.

3 0

3 years ago