Which space figure has six faces that are all regular quadrilaterals

makvit [3.9K]

The steps are to first distribute the 1/3 into (x-9) and then to move the +6 on the left over to the right:

First distribute:
y + 6 = 1/3(x-9) becomes y + 6 = 1/3x-3

Now subtract 6 from both sides:
y = 1/3 x - 3 - 6

y = 1/3 x - 9

7 0

3 years ago

Which expression is equivalent to x^-5/3<br><br> Answer choices:

Alex17521 [72]

Answer:

1/3x5 the Answer is b

Step-by-step explanation:

6 0

3 years ago

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

3 years ago

PLZ HELP!!!! WILL GIVE BRAINLIEST!!! @YOLOSWAGGS51 I REALLY NEED YOUR HELP!!!!

jek_recluse [69]

[2(x+10)] =
well we have to add first
x=1 + 10= 11 since there is parenthesis around the "11" it is times 11 x 2 = 22

we will just have to times this and put a - in front of the 90 (3x - 30) = -90

Hope I could help out.

8 0

3 years ago

Task I

Sever21 [200]

Answer:

The total money invested in the field will be $\$1,623.80$