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3 years ago

Find a quadratic polynomial the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.

Mathematics

1 answer:

Olenka [21]3 years ago

7 0

Step-by-step explanation:

We khow the sum and the product of the zeroes of this quadratic polynomial

Here is a trick :

when we khow the sum S and the product P ofvtwo numbers we can find them by solving :

x²-Sx+p=0

here S= -8 and P=12

so:

x²+8x+12=0

Let Δ be the discrminant of this equation: a= 1 , b= 8 and c=12

Δ= 8²-4*12 =16

the zeros are:

(-8-4)/2= -6

(-8+4)/2 = -2

verify:

-6+(-2)= -8

-2*(-6)= 12

now the polynomial quadratic is:

(x+6)(x+2)

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Find the area under the standard normal distribution curve for the following intervals. a. Between z = 0 and z = 2.0 b. To the r

vesna_86 [32]

Answer:

a) $P(0$

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

$P(0$

b) $P(Z>1.5) =1-P(Z$

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

$P(Z>1.5) =1-P(Z$

c) $P(z$

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

$P(z$

d) $P(-2.78$

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

$P(-2.78$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Part a

We want this probability:

$P(0$

And we can use the following excel code to find the probability:

"=NORM.DIST(2,0,1,TRUE)-NORM.DIST(0,0,1,TRUE)"

$P(0$

Part b

For this case we want this probability:

$P(Z>1.5)$

And we can use the complement rule and we have:

$P(Z>1.5) =1-P(Z$

And we can use the following code and we got:

"=1-NORM.DIST(1.5,0,1,TRUE)"

$P(Z>1.5) =1-P(Z$

Part c

We want this probability:

$P(z$

And we can use the following code and we got:

"=NORM.DIST(-1.75,0,1,TRUE)"

$P(z$

Part d

We want this probability:

$P(-2.78$

And we can use the following excel code to find the probability:

"=NORM.DIST(1.66,0,1,TRUE)-NORM.DIST(-2.78,0,1,TRUE)"

$P(-2.78$

5 0

4 years ago

How many miles are in 19.08 kilometers?

Vedmedyk [2.9K]

Answer:

11.86 miles

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

Please answer 9 or 11 or both pleasseeee

boyakko [2]

Answer:

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3 years ago

Solve this simultaneous e<br> x + y = 26<br> 3x + y = 56

trapecia [35]

Answer:

x= 15 and y= 11

Step-by-step explanation:

The goal here is to solve

x + y =26 and

3x + y =56 for the variables x and y.

First, let's work on your first equation, x + y =26

After this initial survey of the equations, the system of equations we'll set out to solve is:

x+y = 26 and 3x+y = 56

Let's start by solving x+y = 26 for the variable x.

Move the y to the right hand side by subtracting y from both sides, like this:

From the left hand side:

y - y = 0

The answer is x

From the right hand side:

The answer is 26-y

Now, the equation reads:

x = 26-y

To isolate the x, we have to divide both sides of the equation by the other variables

around the x on the left side of the equation.

and this is the final solution to your equation.

Next, let's solve 3x+y = 56 for the variable y.

Move the 3x to the right hand side by subtracting 3x from both sides, like this:

From the left hand side:

3x - 3x = 0

The answer is y

From the right hand side:

The answer is 56-3x

Now, the equation reads:

y = 56-3x

To isolate the y, we have to divide both sides of the equation by the other variables

around the y on the left side of the equation.

and this is the final solution to your equation.

Now, plug the earlier result, x=26-y, in for x everywhere it occurs in

y=56-3x.

This gives y=56-3(26-y). Now all we have to do is solve this for y,to have our first solution.

26-y evaluates to 26-y

Multiply 3 by 26-y

we multiply 3 by each term in 26-y term by term.

This is the distributive property of multiplication.

Multiply 3 and 26

3 × 26 = 78

Multiply 3 and -y

Multiply 1 and y

The y just gets copied along.

3 × -y = -3y

3*(26-y) evaluates to 78-3y

56 - 78 = -22

The answer is -22+3y

56-3*(26-y) evaluates to -22+3y

Move the 3y to the left hand side by subtracting 3y from both sides, like this:

From the left hand side:

y - 3y = -2y

The answer is -2y

From the right hand side:

3y - 3y = 0

The answer is -22

Now, the equation reads:

-2y = -22

To isolate the y, we have to divide both sides of the equation by the other variables

around the y on the left side of the equation.

The last step is to divide both sides of the equation by -2 like this:

To divide y by 1

The y just gets copied along in the numerator.

The answer is y

-2y ÷ -2 = y

-22 ÷ -2 = 11

The solution to your equation is:

y = 11

Lastly, to find the solution for x, we plug this answer for y into the earlier result that

x=26-y.

This gives x=26-(11). Now, simplify this.

26-(11) evaluates to 15

x= 15

So, the solutions to your equations are:

x= 15 and y= 11

3 0

3 years ago

Read 2 more answers

Determine the intercepts of the line. X entercept (. , ) Y intercept (. , )

dedylja [7]

Answer:

x - intercept = (-7.5, 0)

y-intercept =(0, 5.5)

Step-by-step explanation:

Line is intersecting x and y axes at points (- 7.5, 0) and (0, 5.5) respectively.

Therefore, x - intercept = (- 7.5, 0) and y-intercept =(0, 5.5).

4 0

3 years ago