Multiply (2 – 7i)(

Explain the cyclin-dependent regulation cell cycle

insens350 [35]

Cyclins drive the events of the cell cycle by partnering with a family of enzymes called the cyclin-dependent kinases (Cdks). A lone Cdk is inactive, but the binding of a cyclin activates it, making it a functional enzyme and allowing it to modify target proteins.

hope this helps!

7 0

3 years ago

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The length of ZX is 2 units. What is the perimeter of triangle XYZ?

dezoksy [38]

Keywords

triangle,perimeter,distance, length, side, points

we know that

The perimeter of a triangle is the sum of the three length side

To find the length side calculate the distance between two points

The formula to calculate the distance between to points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Step 1

Find the distance ZY

$Z(1,0)\\Y(3,1)$

substitute the values

$d=\sqrt{(1-0)^{2}+(3-1)^{2}}$

$dZY=\sqrt{5}\ units$

Step 2

Find the distance XY

$X(-1,4)\\Y(3,1)$

substitute the values

$d=\sqrt{(1-4)^{2}+(3+1)^{2}}$

$dXY=\sqrt{25}=5\ units$

Step 3

Find the perimeter of the triangle

$P=ZX+ZY+XY$

we have

$dZX=2\sqrt{5}\ units$

$dZY=\sqrt{5}\ units$

$dXY=5\ units$

Substitute

$P=(2\sqrt{5}+\sqrt{5}+5)\ units$

therefore

the answer is

$P=(3\sqrt{5}+5)\ units$

4 0

3 years ago

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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?

skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0

3 years ago

Help me out with this question..this is a practice question not a graded one

galina1969 [7]

We shall begin by drawing up a table of the data set;

The Probability of selecting someone in the 22 - 29 age bracket is derived as

P[22 - 29] = No of req outcomes/No of possible outcomes

P[22 - 29] = 258/360

P[22 - 29] = 0.7166

The probability of selecting someone who refused to respond is derived as

P[Dont respond] = 42/360

P[Dont respond] = 0.1166

Note however that these are dependent events. That means the outcome of one event directly affects that of the other event. In this experiment, you are required to select one person from the entire sample size. Hence the probability of P[22 - 29] OR P[Dont respond] is derived by adding both probabilities and this results in;

The probability of getting someone who falls within the 22 - 29 age bracket or someone who refuses to repond is described as non mutually exclusive events. Mutually exclusive events are those that cannot possibly occur in one experiment. For example you cannot get a King of Hearts OR an Ace of Hearts in one draw from a standard deck of 52 cards. However when you can get either one or the other in one single experiment, then this is refered to as non mutualy exclusive events. So the probability of drawing from a standard deck of 52 cards, a King OR an Ace is an example of non mutually exclusive events because you can get either one or the other with just a single draw of a card. In this experiment, you need to select just one person and the probability of the person being either within the age of 22 - 29 OR being a non-respondent is a non mutually exclusive event. You can select someone randomly and he'll be within 22 - 29 years of age, and its more than likely that that person did not respond to your survey. Fact is,out of those who were 22 - 29, some responded, and some did not. So they all stand a chance of being selected, regardless of how slim their chances were.

Hence, the results should be

P[22 - 29 or Dont respond] = P[22 - 29] + P[Dont respond] - P[(22 - 29) * (Dont respond)]

P[22 - 29 or Dont respond] = ([0.7166] + [0.1166]) - [0.7166 * 0.1166]

P[22 - 29 or Dont respond] = (0.8332) - 0.08355

P[22 - 29 or dont respond] = 0.74965

The results show that the probability of choosing someone who is within the 22 - 29 age bracket or someone who did not respond is 0.74965 which as a percentage is 74.965% (approximately 75%)

3 0

2 years ago

a company donates 935 pencils to a school. the pencils are divided evenly among 9 classrooms. the rest of the pencils are given

wariber [46]

The problem deals with a division and the rest of it, that is dividing the total amount of pencils into 9 classrooms and the rest, lets express it as fraction:
935/9 = 103 + 8/9
that is, if we multiply 103*9 we get 927 and are 8 pencils left over, therefore, 8 pencils are donated to the library and each classroom gets 103 pencils, in total 935 pencils are donated.

8 0

4 years ago

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Multiply (2 – 7i)(–1 + 4i).