Answer: f(2)=7
Step-by-step explanation:
F(2)= 4x2^2-5x2+1
4x4-10+1
6+1=7
Step 1. Solve both inequalities for

:




Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines

and

:

(1)

(2)
Replace (1) in (2):

Solve for

:


(3)
Replace (3) in (1):



We can conclude that the point (-2,3) is in the solution of the system if <span>
inequalities</span>
; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.
Answer:
144.2 cm
Step-by-step explanation:
Length of the iron rod is 7.4cm
Radius is 3.1m
Therefore the surface area can be calculated as follows
= 2πrl
= 2×3.142×3.1×7.4
= 144.2 I'm
Hence the surface area is 144.2cm
Answer:
b.
Step-by-step explanation:
We have to look at sign changes in f(x) to determine the possible positive real roots.

There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.
Now we have to look at sign changes in f(-x) to determine the possible negative real roots.

There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:
1 positive
3 or 1 negative
We need to pair them up now with all the possible combinations.
If we have 1 positive and 1 negative, we have to have 2 imaginary
If we have 1 positive and 3 negative, we have to have 0 imaginary
Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.