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nirvana33 [79]
3 years ago
12

4x-7;×=7 math problem

Mathematics
1 answer:
DENIUS [597]3 years ago
4 0
??????????what????????????
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Calculate pt3 such that a line from pt1 to pt3 is perpendicular to the line from pt1 to pt2, and the distance between pt1 and pt
Leni [432]
Let the point_1 = p₁ = (1,4)
and      point_2 = p₂ = (-2,1)
and      Point_3 = p₃ = (x,y)

The line from point_1 to point_2 is L₁ and has slope = m₁
The line from point_1 to point_3 is L₂ and has slope = m₂
m₁ = Δy/Δx = (1-4)/(-2-1) = 1
m₂ = Δy/Δx = (y-4)/(x-1)
L₁⊥L₂ ⇒⇒⇒⇒ m₁ * m₂ = -1
∴ (y-4)/(x-1) = -1 ⇒⇒⇒ (y-4)= -(x-1)
(y-4) = (1-x) ⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒⇒ equation (1)

The distance from point_1 to point_2 is d₁
The distance from point_1 to point_3 is d₂
d = \sqrt{Δx^2+Δy^2}
d₁ = \sqrt{(-2-1)^2+(1-4)^2}
d₂ = \sqrt{(x-1)^2+(y-4)^2}
d₁ = d₂
∴ \sqrt{(-2-1)^2+(1-4)^2} = \sqrt{(x-1)^2+(y-4)^2} ⇒⇒ eliminating the root
∴(-2-1)²+(1-4)² = (x-1)²+(y-4)²
 (x-1)²+(y-4)² = 18
from equatoin (1)  y-4 = 1-x
∴(x-1)²+(1-x)² = 18            ⇒⇒⇒⇒⇒ note: (1-x)² = (x-1)²
2 (x-1)² = 18
(x-1)² = 9
x-1 = \pm \sqrt{9} = \pm 3
∴ x = 4 or x = -2
∴ y = 1 or y = 7

Point_3 = (4,1)  or  (-2,7)












8 0
3 years ago
6/6 as a sum of fractions three different ways
Kryger [21]
You can do 12/12 8/8 10/10 3/3 and 2/2 all equal to 6/6 all in different ways.
4 0
3 years ago
Read 2 more answers
Select the correct answer.
Lostsunrise [7]

Answer:

d

Step-by-step explanation:

3 0
2 years ago
Three universities receive endowments totaling 110 million dollars. Northern U receives twice as much as wester U. Eastern Us en
puteri [66]

Answer:

Western U gets 20 million

Norther U gets 40 million

Eastern U gets 50 million

Step-by-step explanation:

We need to find the amount each university gets.

Let

Northern U get n

Western U get w

Eastern U get e

We can write equations from the given word problem:

n + w + e = 110

and

n = 2w

e = n + w - 10

Putting 2nd in 3rd, we get:

e = 2w + w - 10

e = 3w - 10

Now putting this and 2nd in first, we solve for w:

n + w + e = 110

2w + w + 3w - 10 = 110

6w = 120

w = 20

AND n = 2 (20) = 40

AND e = 3(20) - 10 = 50

So,

Western U gets 20 million

Norther U gets 40 million

Eastern U gets 50 million

5 0
3 years ago
$7.50 meal; 6.5% tax whats the total price?
ICE Princess25 [194]
7.987, rounded $7.99
5 0
3 years ago
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