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MissTica
3 years ago
14

Find (f-g)(x) for the following functions. f(x) = 12x + 20 g(x) = –11x2 + 10x + 33

Mathematics
2 answers:
IRINA_888 [86]3 years ago
3 0

Answer:

11x2 + 2x-13

Step-by-step explanation:

We must build the new function f-g, which turns to be a sum between polynomials.

f(x)-g(x)= 12x+20 + 11x2- 10x-33

f(x)-g(x)= 12x+20 + 11x2- 10x-33

f(x)-g(x)= 11x2 + 2x-13

ad-work [718]3 years ago
3 0

Answer:

11x2 + 2x - 13

Step-by-step explanation:

Let's notice that (f-g)(x) is equal to f(x)-g(x) because f(x) and g(x) are polynomial functions. Therefore, we just have to do a sum of polynomials.

Let's remember that, when adding or subtracting polynomials, we have to add or subtract the coefficients of like terms (this means, the ones that have the same exponent for the x) .

(f-g)(x) = f(x)-g(x) = 12x + 20 - (–11x2 + 10x + 33)

Don't forget to put the g(x) between parenthesis because the minus sign affects all the terms and changes their signs.

12x + 20 + 11x2 - 10x - 33 =  

11x2 + (12x - 10x) + (20 - 33) =

11x2 + 2x - 13

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What expression best estimates -18 1/4 ÷ 2 2/3<br>a. 18÷3<br>b. -18÷3<br>c. -18÷(-3)<br>d. 18÷(-3)​
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HELP ASAP!!!<br> Find the value of 'A' in the set of complementary angles.
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7 0
3 years ago
10. The probability of buying pizza for dinner is 34% and the probability of buying
kipiarov [429]

Answer:

The probability of eating pizza given that a new car is bought is 0.952

Step-by-step explanation:

This kind of problem can be solved using Baye’s theorem of conditional probability.

Let A be the event of eating pizza( same as buying pizza)

while B is the event of buying a new car

P(A) = 34% = 0.34

P(B) = 15% = 15/100 = 0.15

P(B|A) = 42% = 0.42

P(B|A) = P(BnA)/P(A)

0.42 = P(BnA)/0.34

P(B n A) = 0.34 * 0.42 = 0.1428

Now, we want to calculate P(A|B)

Mathematically;

P(A|B = P(A n B)/P(B)

Kindly know that P(A n B) = P(B n A) = 0.1428

So P(A|B) = 0.1428/0.15

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4 0
3 years ago
Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
irga5000 [103]

Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

8 0
3 years ago
Read 2 more answers
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