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Anuta_ua [19.1K]
1 year ago
6

What is the distance between the following points?

Mathematics
1 answer:
PilotLPTM [1.2K]1 year ago
5 0
Answer :

right : 9,7
left :-2,7
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Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)
Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17. The polynomial is in standards when has the form p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}, where n is the order of the polynomial. The example has the following information:

n = 3, a_{0} = 17, a_{1} = -6, a_{2} = 2, a_{3} = 5.

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials p_{1} and p_{2} such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i} and p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}, where m \geq n

p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be p_{1} a polynomial such that:

p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}

And \alpha an scalar. If the polynomial is multiplied by the scalar number, then:

\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}

Lastly, the following expression is constructed by distributive property:

\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}

Hence, polynomials are closed with respect to multiplication.

4 0
3 years ago
What is a counterexample for "subtraction of whole numbers is commutative" ??
devlian [24]
The commutatice property for addition says a+b=b+a
If it was for subtraction, then it would be a-b=b-a
Take a=7 and b=5
7-5 is not equal to 5-7
2 is not equal to -2
So subtraction is not commutative for whole numbers.

Hope this helps :)
6 0
3 years ago
Simplify by combining like terms:<br> 3x - 10 + 2 + 6x
olya-2409 [2.1K]

Answer:

9x-8 is the simplified form

7 0
3 years ago
Subtract (3 + 2i) from (–9 – 8i).<br><br> –17 – 5i<br><br> –6 – 6i<br><br> –12 – 10i<br><br> 12 + 10
kupik [55]

Answer:

-12 - 10i

Step-by-step explanation:

We are subtracting 3 + 2i from -9 - 8i.  Rewrite the left side as -3 - 2i and then ADD this result to -9 - 8i:

-9 - 8i

-3 -2i

-----------

-12 - 10i

8 0
2 years ago
Read 2 more answers
A. What would be the cost of the Standard Daily Rate plus Mileage plan?
Jobisdone [24]

Answer:

Part a) \$190

Part b) \$315

Part c) Standard Daily Rate plus Mileage plan

Step-by-step explanation:

Part a) What would be the cost of the Standard Daily Rate plus Mileage plan?

Let

y ----> the total cost

x ----> the number of kilometers

we have that

For a Luxury car

y=70+0.30x

For x=400 km

substitute

y=70+0.30(400)

y=\$190

Part b) What would be the cost of the Unlimited Mileage plan?

we know that

The Unlimited Mileage plan for a Luxury car is $105 per day (see the table)

The trip are three days

so

To find the total cost multiply $105 by 3

3(\$105)=\$315

Part c) Which is the better plan?

Compare

\$190 < \$315

therefore

For this trip the better plan is the Standard Daily Rate plus Mileage plan

7 0
3 years ago
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