Answer:
Kindly check attached picture
Step-by-step explanation:
The total Number of people = 40
Number wearing hat only = number wearing Number wearing hat - (sunscreen and hat)
28 - 20 = 8
Number wearing sunscreen only :
40 - (8 + 20 + 3)
40 - 31
= 9
Kindly find completed venn diagram below.
It’d be (7,2)! Since you add 2+5 and 2+0.
Given:
The function is
![f(x)=2x^3+ax^2-37x-60](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E3%2Bax%5E2-37x-60)
The binomial
is a factor of f(x).
To find:
The value of
.
Solution:
If
is a factor of f(x), then
.
It is given that,
is a factor of f(x), then
.
We have,
![f(x)=2x^3+ax^2-37x-60](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E3%2Bax%5E2-37x-60)
Substituting x=4, we get
![f(4)=2(4)^3+a(4)^2-37(4)-60](https://tex.z-dn.net/?f=f%284%29%3D2%284%29%5E3%2Ba%284%29%5E2-37%284%29-60)
![f(4)=2(64)+a(16)-148-60](https://tex.z-dn.net/?f=f%284%29%3D2%2864%29%2Ba%2816%29-148-60)
![f(4)=128+16a-208](https://tex.z-dn.net/?f=f%284%29%3D128%2B16a-208)
![f(4)=16a-80](https://tex.z-dn.net/?f=f%284%29%3D16a-80)
Now,
![f(4)=0](https://tex.z-dn.net/?f=f%284%29%3D0)
![16a-80=0](https://tex.z-dn.net/?f=16a-80%3D0)
![16a=80](https://tex.z-dn.net/?f=16a%3D80)
![a=\dfrac{80}{16}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B80%7D%7B16%7D)
![a=5](https://tex.z-dn.net/?f=a%3D5)
Therefore, the value of a is 5.
Answer:
g(x) is a factor of P(x).
Step-by-step explanation:
By the factor theorem, If g(a) = 0 and P(a) = 0, then g(x) is a factor of P(x).
Here
P(x) = 2x^3-11x^2-4x+1
g(x) = 2x + 1, g(-1/2) = 0
check
P(-1/2)
= 2(-1/2)^3-11(-1/2)^2-4(-1/2)x+1
=-1/4 - 11/4 + 2 + 1
= 0
Therefore g(x) is a factor of P(x).
As a matter of fact,
P(x) = ( 2x + 1 )( x^2 - 6x + 1 )