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GalinKa [24]
3 years ago
5

Find the zeros of the polynomial function and state the multiplicity of each.

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
7 0

Answer:

a) 8, multiplicity 2; 8, multiplicity 3

Step-by-step explanation:

Remember that a is a zero of the polynomial f(x) if f(a)=0 and has multiplicity n if the termn (x-a) is n times in the factorization of f(x).

We have that

f(x)=3(x + 8)^2(x - 8)^3

Observe that

1. f(-8)=3(-8 + 8)^2(-8 - 8)^3=3*0*(-16)^3=0

and (x+8) appear two times in the factorization of f(x). Then -8 is a zero of f(x) with multiplicity 2.

2. f(8)=3(8 + 8)^2(8 - 8)^3=3*16^2*0^3=0

and and (x - 8) appear three times in the factorization of f(x). Then 8 is a zero of f(x) with multiplicity 3.

Since f(x) has degree 5 and the sum of the multiplicities is 5 then f(x) hasn't more zeros.

You might be interested in
(a/5) - (b/3) = (a/2) - (b/6), solve for a
Gnom [1K]

Answer:

a =  -  \frac{10}{17} b

Step-by-step explanation:

(a/5) - (b/3) = (a/2) - (b/6)

+(B/3) + (b/3)

NOTE: use property of equality to isolate <em>b</em> from <em>a</em>

(a/5) = (b/3) + (a/2) - (b/6)

-(a/2) - (a/2)

NOTE: continue to use property of equality to isolate <em>a</em><em> </em>from <em>b</em>

(a/5) - (a/2) = (b/3) - (b/6)

60((a/5) - (a/2)) = ((b/3) - (b/6))60

NOTE: 60 is a common multiple of 5, 2, 3, and 6

12a - 30a = 20b - 10b

NOTE: combine alike terms

-17a = 10b

-17a/-17 = 10b/-17

NOTE: decide by -16 to find what a is equal to

a =  -  \frac{10}{17} b

Final answer

5 0
3 years ago
HELP PLEASEEEE!!!!!!!!
nikdorinn [45]
Chin is correct because 5 x $.65 is $3.25., and he multiplied by US/GB

Nadene is incorrect because she took GB/US x 5
3 0
3 years ago
28 is increased by 150%. what's the final number
sp2606 [1]

Answer:

70

Step-by-step explanation:

20x(1+150%)

28x(1+1.5)

28x2.5

70

5 0
2 years ago
A parking lot charges $3 to park a car for the first hour and $2 per hour after that. If you use more than one parking space, th
fenix001 [56]
Consider the charge for parking one car for t hours.

If t is more than 1, then the function is y=3+2(t-1), because 3 $ are payed for the first hour, then for t-1 of the left hours, we pay 2 $.

If t is one, then the rule y=3+2(t-1) still calculates the charge of 3 $, because substituting t with one in the formula yields 3.


75% is 75/100 or 0.75. 

For whatever number of hours t, the charge for the first car is 3+2(t-1) $, and whatever that expression is, the price for the second car and third car will be 

0.75 times 3+2(t-1). Thus, the charge for the 3 cars is given by:

3+2(t-1)+0.75[3+2(t-1)]+0.75[3+2(t-1)]=3+2(t-1)+<span>0.75 × 2[3 + 2(t − 1)].


Thus, the function which total parking charge of parking 3 cars for t hours is:

</span><span>f(t) = (3 + 2(t − 1)) + 0.75 × 2(3 + 2(t − 1)) 


Answer: C</span>
4 0
3 years ago
It takes about 20 minutes to grade a student’s paper. How long, in hours, does it take to grade papers for a class of 30 people?
insens350 [35]

Answer:

The answer is 600 minutes (10 hours)

Step-by-step explanation:

20 minutes = 1 student.

30 students x 20 = 600 minutes

600mins / 60 (because an hour has 60 mins) = 10 hours.

5 0
3 years ago
Read 2 more answers
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