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3 years ago

Factorise the following

Mathematics

1 answer:

Valentin [98]3 years ago

4 0

Answer:

Step-by-step explanation:

First take out a factor of 2:

2(1 - 25x^2)

Then factor the difference of squares:

2(1 -5x)(1+5x)

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Determine if the set of polynomials {x^2 –2x+1, 2x² + 3x -4,-x2+x+5) is a linearly independent set in P2. Is it a basis for P? W

WITCHER [35]

Answer with Step-by-step explanation:

We are given that a set of polynomials ${x^2-2x+1,2x^2+3x-4,-x^2+x+5}$

We have to find that given set is a linearly independent set in $P_2$

and given set is a basis for $P_2$ or not.

Matrix of given set of polynomials

A= $\left[\begin{array}{ccc}1&-2&1\\2&3&-4\\-1&1&5\end{array}\right]$

Linearly Independent set :If any row or any column is not a linear combination of other rows or columns then the set is linearly independent set.

Any row or column is not a linear combination of other rows or columns.Therefore, given set is a linearly independent set .

We know that

$P_2=x^2$

Element of $P_2$ is of the form

$ax^2+bx+c$

Every element of $p_2$ is a linear combination of given set of polynomials.

Hence, given set is linearly independent in $p_2$ .

If any set is basis for any vector space then it satisfied the following two conditions

1.Given set is linearly independent.

2.Every element of given vector space spanned by the given set.

Given set of polynomials are linearly independent and spanned every element of $P_2$ .

Therefore, given set is as basis for $p_2$ because the set is linearly independent and spanned $P_2$ .

7 0

3 years ago

What is the term for the number 9 based on its position in the number 10.0976?

Nat2105 [25]

Usually decimal numbers have in tenths(0) and hundreths (9). So 9 is in the hundreths place.

7 0

3 years ago

What is the exact volume of the cone?

victus00 [196]

Answer: [D]: " 196π in.³ " .
_____________________________________________________
Explanation:
_____________________________________________________
Given: radius, "r", equal 7 in.
Given: height, "h", equals 4 in.

Volume: V = Base area * h ;

The base area of a cone is a circle: A = π * r² = π* (7²) = 49π .

(NOTE: Since all answer choices given are in terms of "π" ; we will leave the units in terms of "π").

V = (Based area) * h = (49π in.) * (4 in.) = (49*4)π in.³
= 196π in.³ ; which is: Answer choice: [D] .
__________________________________________________________

8 0

4 years ago

Read 2 more answers

The distance a car travels can be found using the formula d=r t where d is distance, r is the rate of speed, and t is time. How

netineya [11]

Answer:

35 miles

Step-by-step explanation:

70miles per hour x1/2 hour =35distance the car travels

7 0

3 years ago

Under his cell phone plan, Ethan pays a flat cost of $59 per month and $5 per gigabyte. He wants to keep his bill under $70 per

svetlana [45]

Answer:

59/350

Step-by-step explanation:

Under his cell phone plan, Ethan pays a flat cost of $59 per month and $5 per gigabyte. He wants to keep his bill under $70 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Ethan can use while staying within his budget.

so say that you have 59$ as a flat cost do when you have a problem like this its kinda easy but what you are going to do is take 59 and divide 5 and see what you get you are going to get 11.8 then divide 11.8 into 70 and see what you get then lets see you would get a number that is a fraction answer sis at top.

Glad i could help you have a nice day!!!

4 0

3 years ago

Read 2 more answers