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garik1379 [7]
3 years ago
15

How do you simplify 4/42

Mathematics
2 answers:
kolbaska11 [484]3 years ago
3 0

Answer:

4/42 = 2/21 when simplified down

Step-by-step explanation:

Cancel the common factor: 2

=2/21

jarptica [38.1K]3 years ago
3 0

Answer:

<h2>2/21</h2>

Step-by-step explanation:

\frac{4}{42}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{2}{21}\\\\\left(\mathrm{Decimal:\quad }\:0.09523 \right)

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Determine whether the set of all linear combinations of the following set of vector in R^3 is a line or a plane or all of R^3.a.
Temka [501]

Answer:

a. Line

b. Plane

c. All of R^3

Step-by-step explanation:

In order to answer this question, we need to study the linear independence between the vectors :

1 - A set of three linearly independent vectors in R^3 generates R^3.

2 - A set of two linearly independent vectors in R^3 generates a plane.

3 - A set of one vector in R^3 generates a line.

The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :

a. Let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}-2&5&-3\\6&-15&9\\-10&25&-15\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix  ⇒

\left[\begin{array}{ccc}-2&5&-3\\0&0&0\\0&0&0\end{array}\right]

We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).

We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).

At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.

b. Again, let's put the vectors into the rows of a matrix :

\left[\begin{array}{ccc}1&2&0\\1&1&1\\4&5&3\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&1\\0&1&-1\\0&0&0\end{array}\right]

We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).

c. Finally :

\left[\begin{array}{ccc}0&0&3\\0&1&2\\1&1&0\end{array}\right] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

\left[\begin{array}{ccc}1&1&0\\0&1&2\\0&0&3\end{array}\right]

The set is linearly independent so the set of all linear combination of the set c. is all of R^3.

4 0
3 years ago
Todd would like to purchase a bicycle that costs $246. This is $48 more than twice the cost of his last bicycle. How much did hi
Rasek [7]
246-48= 198

198/2= 99

Todd's last bike cost $99.
4 0
3 years ago
You deposit $500 in a savings account that earns 2.5% interest compounded yearly. Find the balance in the account after 1 year.
Viktor [21]

Answer:

$512.5

Step-by-step explanation:

Given data

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R=2.5%

T= 1 year

The compound interest formula is

A=P(1+r)^t

substitute

A=500(1+0.025)^1

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A=500*1.025

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It's 6/12 then 1/2. Good luck
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