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2 years ago

Write the equation of a polynomial of degree 3, with zeros 1, 2 and -1 where f(0)=2

Mathematics

1 answer:

ser-zykov [4K]2 years ago

4 0

Answer:

f(x) = x^3 - 2x^2 - x + 2

Step-by-step explanation:

since the zeroes are 1,-1, and 2. we can write the function like

f(x) = (x-1)(x+1)(x-2)

f(x) = (x^2-1)(x-2)

f(x) = x^3 -2x^2 -x +2

and it is true that f(0)=2

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Sharon, Mark, Beverly and Bruce each work as a doctor, lawyer, teacher or farmer. From the clues below, decide who is the doctor

pychu [463]

Answer:

C. Beverly

Step-by-step explanation:

5 0

3 years ago

Simplify by using the distributive property 5 ( 2x - 5 )

drek231 [11]

Hello!

The problem has asked that we simplify the given expression using the Distributive Property. The Distributive Property states the following:

a(b + c) = ab + ac
a(b – c) = ab – ac

In this case, we’ll use the second of the two formulas listed above. Let’s begin by inserting any known values given in the original problem:

a(b – c) = ab – ac
5(2x – 5) = 5(2x) – 5(5)

Now simplify the right side of the equation:

5(2x) – 5(5) = 10x – 25

We have now proven that 5(2x – 5) is equal to 10x – 25. Therefore, the correct answer is C.

I hope this helps!

3 0

3 years ago

Read 2 more answers

Find the vector equation of the line through the points (1, 2, −1) and (2, 4, 5). Is the point (−5, −10, −37) on this line?

pav-90 [236]

Answer:

(1+t, 2+2t, -1+6t); C is on this line.

Step-by-step explanation:

Let's find the vector equation of the line.

Given information:

Point A is (1, 2, -1)

Point B is (2, 4, 5)

Point C is (-5, -10, -37)

The difference between the two first given points (A, B) is:

B-A=(2, 4, 5)-(1, 2, -1)=(2-1, 4-2, 5-(-1))=(1, 2, 6) which is called the direction vector, so the equation is:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)=(1+t, 2+2t, -1+6t)

Now let's find if point C is on the line:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)-(1, 2, -1)=t*(1, 2, 6)

(-5-1, -10-2, -37+1)=t*(1, 2, 6)

(-6, -12, -36)=t*(1, 2, 6) from where we can obtain:

1*t=-6 --> t=-6

2*t=-12 --> t=-6

6*t=-36 --> t=-6

In conclusion, because from all the equations we obtained t=-6, then point C is on this line.

7 0

2 years ago

A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a diam

Inga [223]

Answer:

$a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}$

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

Let A denotes the event that the card is a diamond and B denotes the card is red.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}$

Let A denotes the event that the card is red and B denotes the card is diamond.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}$

Let A denotes the event that the card is nine and B denotes the card is red.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}$

Let A denotes the event that the card is a king and B denotes the card is a face card.

$P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}$

7 0

2 years ago

Find X. Enter a number for your answer. Do not type the symbol for degree or the<br> word "degrees"

Lena [83]

Use angle sum property (the 3 angles in a triangle sum up to 180°).

2x + x + 54 = 180

3x + 54 = 180

3x = 180 - 54

3x = 126

x = 126/3

x = 42

_____

Hope it helps ⚜

6 0

1 year ago

Read 2 more answers