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BlackZzzverrR [31]
3 years ago
14

What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where

$a$ and $b$ are integers?
Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

Answer:

k=-16,k=-8,k=8,k=16

Step-by-step explanation:

We are given quadratic equations as

x^2+kx+15

and it can be factored as

=(x+a)(x+b)

now, we can multiply factor term

(x+a)(x+b)=x^2+(a+b)x+ab

now, we can compare

x^2+(a+b)x+ab=x^2+kx+15

so, we get

k=a+b

ab=15

we are given that

'a' and 'b' are integers

so, we can find all possible factors

15=(-1\times -15),(1\times 15)

15=(-3\times -5),(3\times 5)

so, we can find k

At (-1\times -15):

k=a+b

we can plug values

k=-1-15

k=-16

At (1\times 15):

k=a+b

we can plug values

k=1+15

k=16

At (-3\times -5):

k=a+b

we can plug values

k=-3-5

k=-8

At (3\times 5):

k=a+b

we can plug values

k=3+5

k=8

So, values of k are

k=-16,k=-8,k=8,k=16

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Tasya [4]

Answer:

0.25 = 25% probability that it will rain today and ruin your picnic

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Cloudy skies

Event B: Rain

20% of all days start with clouds in the air

This means that P(A) = 0.2

50% of rainy days start with rain clouds in the air

50% of 10%. So

P(A \cap B) = 0.5*0.1 = 0.05

What is the probability that it will rain today and ruin your picnic

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05}{0.2} = 0.25

0.25 = 25% probability that it will rain today and ruin your picnic

3 0
2 years ago
2x-32=12<br> means they spent how much
Hoochie [10]

Answer:

22

Step-by-step explanation:

6 0
2 years ago
A vertical right circular cylindrical tank has height h=8 feet high and diameter d=6 feet. It is full of kerosene weighing 50 po
Mariana [72]

Answer:

The work done to  pump all of the kerosene from the tank to an outlet is W=45238.9\: J  

Step-by-step explanation:

The work is defined by:

W=\int dFdx (1)    

The force here will be the product between the volume and the kerosene weighing, so we have :

dF=\pi R^{2}dy*50

This force will be in-lbs.

Where R is the radius (3 feet)                    

Then using (1), we have:

W=\int \pi R^{2}dy*50(8-y)  

Here 8-y is a distance at some point of the tank. Now, to get the work done from the base to the top of the tank we will need to take integral from 0 to 8 feet.

W=\int_{0}^{8} \pi 3^{2}dy*50(8-y)

W=450\pi \int_{0}^{8}dy(8-y)

W=450\pi(\int_{0}^{8} 8dy-\int_{0}^{8} ydy)

W=450\pi(8y|_{0}^{8} -\frac{y^{2}}{2}|_{0}^{8})  

W=450\pi(8*8 -\frac{8^{2}}{2})

W=450\pi(64 -\frac{64}{2})

Therefore, the work done to  pump all of the kerosene from the tank to an outlet is W=45238.9\: J  

I hope it helps you!  

6 0
3 years ago
2+2(560)+5638+163936
dmitriy555 [2]

170696 is the answer fellow user

8 0
3 years ago
Read 2 more answers
Select from the following choices those graphs that represent only a dilation applied to this polygon with a scale factor great
romanna [79]

Answer:

B and C

Step-by-step explanation:

Required

Select graphs that are dilated by a scale factor greater than 1

For graph A:

Graph A is smaller than the original graph. This indicates dilation with a scale factor less than 1

For graph B:

Graph B is bigger than the original graph and is dilated over (0,0). This indicates dilation with a scale factor greater than 1

For graph C:

Graph C is bigger than the original graph; however, it is not dilated over (0,0). This indicates dilation with a scale factor greater than 1

For graph D:

Graph D is bigger than the original graph; however, it is not only dilated but also flipped over (i.e. rotated).

<em>Hence, b and c is true</em>

5 0
3 years ago
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