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lyudmila [28]
2 years ago
9

Given f(x)=3x^2+kx+9, and the remainder when f(x) is divided by x-3 is 6, then what is the value of k?

Mathematics
1 answer:
elena55 [62]2 years ago
3 0

Answer:

k = - 10

Step-by-step explanation:

6=9+3(k+9)

3(k+9)=-3

k+9= -1

k= -10

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The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power
Mumz [18]

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years  

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = P(\bar F S) ∪ P( \bar S F) ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)

=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36

4 0
3 years ago
Simplify (a+b) ²-2ab​
Scrat [10]

Answer:

a² + b²

Step-by-step explanation:

(a + b)² - 2ab ← expand parenthesis using FOIL

= a² + 2ab + b² - 2ab ← collect like terms

= a² + b²

6 0
3 years ago
In right triangle CAB, find the hypotenuse, CB<br> A 4 root 13<br> B 20<br> C 4 root 5<br> D 208
svetoff [14.1K]

Answer:

<h3>A4root13 или С 4root5</h3>

Step-by-step explanation:

4 0
3 years ago
If snickers are sold in pack of 6 and kit Kats are sold in packs of 15 how many packs do you need to buy to have a equal amount
iragen [17]

Answer: 5 packs of Snickers and 2 packs of Kit Kats.


Step-by-step explanation: How? Okay so snickers come in packs of 6 to find the number that will be equal to Kit Kats you must figure out factors. 30 has a factor of 6 and 15. 5 packs of snickers will get you 30 total snickers. 2 packs of Kit Kats will get you a total of 30 Kit Kats. I hope this helped! (:


3 0
3 years ago
Evaluate 3C1.<br><br> a)3<br> b)1<br> c)2<br> d)6
murzikaleks [220]

Answer: Option a) 3

Step-by-step explanation:

The formula for calculating combinations is as follows

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Where "n" is the amount of items in a set and you can choose "r" from them

3C1 reads as: The combination of 1 in 3. You have a set of 3 elements and choose 1 of them.

n = 3\\\\r = 1

So :

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5 0
3 years ago
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