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3 years ago

Equation for the line that passes through (4,7) and is perpendicular to the line Y= 2/3x-1

Mathematics

2 answers:

alexdok [17]3 years ago

8 0

Answer:

y = -3/2x + 13

Step-by-step explanation:

In order for a line to be perpendicular, it must have an opposite reciprocal slope to the given line. In this instance, the opposite reciprocal of 2/3 would be -3/2. Insert the information given into the point-slope formula.

$y-7=-\frac{3}{2}(x-4)\\\\y-7=-\frac{3}{2}x+6\\\\y=-\frac{3}{2}x+13$

hichkok12 [17]3 years ago

3 0

Answer: y=-3/2x+13

Step-by-step explanation:

(4,7) m=2/3

x,y m⊥=-3/2

7=-3/2(4)+b

7=-6+b

13=b

y=-3/2x+13

feel free to let me know if its wrong

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Find the distance from the point to the line. (-1,-2,1);x=4+4t, y=3+t, z=6-t .The distance is ____ Typn exact answer, using radi

lawyer [7]

Answer:

The distance is<u> 4.726 </u>

Step-by-step explanation:

we need to find the distance from the point to the line

Given:- point (-1,-2,1) and line ; x=4+4t, y=3+t, z=6-t .

used formula $d=\frac{|a\times b|}{|a|}$

Let point P be (-1,-2,1)

using value t=0 and t=1

The point Q (4 , 3, 6) and R ( 8, 4, 5)

Let a be the vector from Q to R : a = < 8 - 4, 4 - 3, 5 - 6 > = < 4, 1, -1 >

Let b be the vector from Q to P: b = < -1 - 4, -2 - 3, 1 - 6> = < -5, -5, -5 >

The cross product of a and b is:

$a \times b= \begin{vmatrix} i & j & k\\ 4 &1&-1\\-5 &-5&-5\\ \end{vmatrix}$

= -6i+15j-15k

The distance is : $d=\frac{\sqrt{(-6)^{2}+(15)^{2}+(-15)^{2}}}{\sqrt{(4)^{2}+(1)^{2}+(-1)^{2}}}$

$=\frac{\sqrt{36+225+225}}{\sqrt{16+1+1}}$

$d=\frac{\sqrt{486}}{\sqrt{18}}$

≈4.726

Therefore, the distance is<u> 4.726 </u>

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3 years ago

Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state wh

Damm [24]

Answer:

dependent

Step-by-step explanation:

The given system is :

15x-18=3y

5x=y+6

Rewrite the equations in standard form to get:

15x-3y=18

5x-y=6

Multiply the bottom equation by 3.

15x-3y=18

Sub both equations:

0-0=0

0=0

We got an identity

The system is dependent because there are infinitely many solutions

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4 years ago

Use the law of syllogism to complete the conclusion. statement 1: if p, then q. statement 2: if q, then r. conclusion: if p, the

aliina [53]

p→r

<h3>Law of syllogism</h3>

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost similar to the transitive property.

now if we want to define general case then we can say tha

a→b

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now according to statements given in the problem

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which completes the syllogism.

hence , p→r is the required answer.

learn more about syllogism here:

brainly.com/question/5142648

#SPJ4

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2 years ago