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2 years ago

What is the solution of the system of equations? {7/2x−1/2y=9/23x−y=5 Enter your answer in the boxes. ( _ , _ )

Mathematics

2 answers:

In-s [12.5K]2 years ago

6 0

I think the answer is (1,-2)

dimulka [17.4K]2 years ago

5 0

Answer:

(1, -2)

Step-by-step explanation:

I hope that helps :/

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Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.

alina1380 [7]

Answer:

$v_1=(\frac{1}{10},-\frac{3}{10})$

$v_2=(-\frac{1}{10},\frac{3}{10})$

Step-by-step explanation:

First we define two generic vectors in our $\mathbb{R}^2$ space:

$v_1 = (x_1,y_1)$
$v_2 = (x_2,y_2)$

By definition we know that Euclidean norm on an 2-dimensional Euclidean space $\mathbb{R}^2$ is:

$\left \| v \right \|= \sqrt{x^2+y^2}$

Also we know that the inner product in $\mathbb{R}^2$ space is defined as:

$v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2$

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

$\left \| v_1 \right \|= \sqrt{x^2+y^2}=1$

and

$\left \| v_2 \right \|= \sqrt{x^2+y^2}=1$

As second condition we have that:

$v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0$

$v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0$

Which is the same:

$y_1=-3x_1\\y_2=-3x_2$

Replacing the second condition on the first condition we have:

$\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}$

Since $x_1^2= \frac{1}{10}$ we have two posible solutions, $x_1=\frac{1}{10}$ or $x_1=-\frac{1}{10}$ . If we choose $x_1=\frac{1}{10}$ , we can choose next the other solution for $x_2$ .

Remembering,

$y_1=-3x_1\\y_2=-3x_2$

The two vectors we are looking for are:

$v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})$

5 0

2 years ago

(answer choices are in the pictures.) <br><br> Which arc measures 180°?

nydimaria [60]

I believe it is DC

180 degrees is about halfway, so DC definitely captures that.

5 0

3 years ago

Write the word sentence as an inequality.

igomit [66]

Answer:

-23 divided by -7

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

please help me if you can if your going to say I'm cheating i don't care cause i know I'm not thanks!!

Dovator [93]

Big fat badussy balls

4 0

2 years ago

Graph the line. y = -5x + 1

gizmo_the_mogwai [7]

Answer:

See below.

Step-by-step explanation:

To graph y = -5x + 1 we must move 1 unit up and 5 units down plus a unit to the right

Since the slope is negative, therefore, we move down 5 units

Since the y-intercept is positive 1 then we move 1 unit up

Important Note: Start by the y-intercept first, then the slope

6 0

3 years ago