Plz help. Which problem is a linear equation?

If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$

5 0

3 years ago

Read 2 more answers

rectangle ABCD is graphed in the cordinate plane. The following are the verticies of the rectangle; A(-6,-4),B(-4,-4),C(-4,-2),

Sholpan [36]

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

$\textrm{Perimeter of Rectangle}=2(Length+Width)$

Length = AB

Width = BC

Now By Distance Formula we have'

$l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting the values we get

$l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}$

$l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit$

Similarly

$l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}$

$l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit$

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values in Perimeter we get

$\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit$

Therefore Perimeter of Rectangle ABCD is 4 units

8 0

3 years ago

35 out of 50 students in a class wear glasses. What percentage of students in the class wear glasses?

Mashutka [201]

Answer:

70%

Step-by-step explanation:

Percentage is out of 100

35/50 change denominator

multiply both numerator and denominator by 2

70/100= 70%

8 0

2 years ago

Idek how to explain this but please help me

Leno4ka [110]

Answer:

Put 4 in the place of x then you'll get

$\frac{10}{22}$

3 0

3 years ago

Read 2 more answers

The set of points in space that are a given distance from a given point is called a(n) __________.

Marrrta [24]

The answer would be B. Edge

The set of points in space that are a given distance from a given point is called an <u>Edge.</u>

D would be incorrect since it doesn’t have any edges and is like a circle but is 3D. A cylinder is also incorrect since it has curves from top to bottom. C is also incorrect since it only shows one side, which is called the face. That leaves you with edge which would be the correct answer.

Hope this helps! :3

8 0

3 years ago