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2 years ago

Given the table of values below, which equation best represents the information?

Mathematics

2 answers:

Oliga [24]2 years ago

8 0

f(x) = 2x is the Answer!

Arisa [49]2 years ago

5 0

Answer:

Step-by-step explanation:

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Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H is a vector space. If

Verizon [17]

Answer:

Yes. It is a vector space over the field of rational numbers $\mathbb{Q}$

Step-by-step explanation:

An element $p$ of the set $H$ has the form

$p(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}$

where $a_{0},a_{1},a_{2},a_{3},a_{4}$ are rational coefficients.

The operations of addition and scalar multiplication are defined as follows:

$p(x)+q(x)=(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+x_{4}x^4)+(b_{0}+b_{1}x+b_{2}x^{2}+b_{3}x^{3}+b_{4}x^{4})=(a_{0}+b_{0})+(a_{1}+b_{1})x+(a_{2}+b_{2})x^{2}+(a_{3}+b_{3})x^{3}+(a_{4}+b_{4})x^{4}$

$\lambda p(x)=\lambda (a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4})=\lambda a_{0}+\lambda a_{1}x+\lambda a_{2}x^{2}+\lambda a_{3}x^{3}+\lambda a_{4}x^{4}$

The properties that $H$ , together the operations of vector addition and scalar multiplication, must satisfy are:

Conmutativity
Associativity of addition and scalar multiplication
Additive Identity
Additive inverse
Multiplicative Identity
Distributive properties.

This is not difficult with the definitions given. The most important part is to show that $H$ has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that $\mathbb{Q}$ is a field, then it is closed under sum and multiplication.

7 0

2 years ago

Perform the indicated operation. 17 + (-5) 12 -12 22 -22

almond37 [142]

Please correct me if I'm wrong!! :)

6 0

3 years ago

Read 2 more answers

Ededwfeq3efq3f444edrfervew 97

PilotLPTM [1.2K]

Answer:

What ????

Step-by-step explanation:

4 0

2 years ago

Describe how the graph of g(x) is related to the graph of f(x) = 1/x. g(x) = -1/x +5

umka21 [38]

Answer:

yea

Step-by-step explanation:

4 0

3 years ago

Solve 5(x+6)+x=x+45 what are the points?

FinnZ [79.3K]

Answer:

x=3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

5(x+6)+x=x+45

(5)(x)+(5)(6)+x=x+45(Distribute)

5x+30+x=x+45

(5x+x)+(30)=x+45(Combine Like Terms)

6x+30=x+45

Step 2: Subtract x from both sides.

6x+30−x=x+45−x

5x+30=45

Step 3: Subtract 30 from both sides.

5x+30−30=45−30

5x=15

Step 4: Divide both sides by 5.

5x /5 = 15 /5

x=3

5 0

3 years ago

Read 2 more answers