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lorasvet [3.4K]

2 years ago

10

Equation

0%3D%20%20-%201" id="TexFormula1" title="(z + \frac{6}{7} ) + \frac{2}{14} = - 1" alt="(z + \frac{6}{7} ) + \frac{2}{14} = - 1" align="absmiddle" class="latex-formula">

1 answer:

ddd [48]2 years ago

5 0

Given:

The equation is

$\left(z+\dfrac{6}{7}\right)+\dfrac{2}{14}=-1$

To find:

The solution of the given equation.

Solution:

We have,

$\left(z+\dfrac{6}{7}\right)+\dfrac{2}{14}=-1$

It can be written as

$\left(z+\dfrac{6}{7}\right)+\dfrac{1}{7}=-1$

$\left(z+\dfrac{6}{7}\right)=-1-\dfrac{1}{7}$

Multiply both sides by 7.

$7z+6=-7-1$

$7z+6=-8$

$7z=-8-6$

$7z=-14$

Divide both sides by 7.

$z=\dfrac{-14}{7}$

$z=-2$

Therefore, the value of z is -2.

You might be interested in

Evaluate rs + 14s when r = 6 and s = 8

Ivahew [28]

Answer:

160

Step-by-step explanation:

Plug in 6 for r, and 8 for s in the expression:

(r)(s) + (14)(s) = (6)(8) + (14)(8)

Remember to follow PEMDAS. First, multiply, then add:

(6 * 8) + (14 * 8)

48 + 112

112 + 48 = 160

160 is your answer.

~

3 0

3 years ago

Determine whether the given vectors are orthogonal, parallel or neither. (a) u=[-3,9,6], v=[4,-12,-8,], (b) u=[1,-1,2] v=[2,-1,1

nevsk [136]

Answer:

a) $u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

b) $u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

c) $u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

Step-by-step explanation:

For each case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

Part a

u=[-3,9,6], v=[4,-12,-8,]

The dot product on this case is:

$u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

Part b

u=[1,-1,2] v=[2,-1,1]

The dot product on this case is:

$u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

Since the angle between the two vectors is not 0 or 180 degrees we can conclude that are either.

Part c

u=[a,b,c] v=[-b,a,0]

The dot product on this case is:

$u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

5 0

3 years ago

Read 2 more answers

What is the measure of c?<br> a = 15<br> j = 24<br> k = 32

inessss [21]

Answer:

The answer to your question is c = 20

Step-by-step explanation:

Data

a = 15

j = 24

k = 32

c = ?

Process

Use proportions to solve this problem. Compare the small triangle and the large triangle.

1.- Proportion of the small triangle

c/15

2.- Proportion of the large triangle

k/j

3.- Equal but terms and solve for c

c/15 = k/j

-Substitution

c / 15 = 32/24

c = 32(15)/24

-Result

c = 20

4 0

3 years ago

What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?

svet-max [94.6K]

Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

8 0

3 years ago

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Solve this:<br><br> -4<3x-4<_ 11<br><br> A. 5 B. 0 C. 0

statuscvo [17]

Your answer most likely will be A

4 0

3 years ago