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SashulF [63]
2 years ago
9

Water coming out of a fountain is modeled by the function f(x) = −x^2 + 5x + 4 where f(x) represents the height, in feet, of the

water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 3 to x = 5 represent?
A. The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.
B. The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds.
C. The water travels an average distance of 3 feet from 3 seconds to 5 seconds.
D. The water travels an average distance of 5 feet from 3 seconds to 5 seconds.
Mathematics
2 answers:
Anastaziya [24]2 years ago
6 0
Calculating x=3 and x=5, we get f(x)=10 and 4 respectively by plugging the numbers into the equation. Finding the difference and dividing by 2 (since there are 2 seconds between 3 and 5), we get 3, so the answer is either A or C. Since it doesn't only fall 3 feet, we need to specify that it is 3 feet per second, A is right!
Tanzania [10]2 years ago
4 0

Answer:

The correct option is A) The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

Step-by-step explanation:

Consider the provided function.

f(x)=-x^2+5x+4 where f(x) represents the height, in feet.

Substitute the value of x = 3 in the provided equation.

f(3) = -x^2 +5x +4

f(3) = -(3)^2 +5(3)+4

f(3) = -9+15+4

f(3) = 10

Now, substitute the value of x = 5 in the provided equation.

f(5) = -x^2 +5x +4

f(5) = -5^2 +5(5) +4

f(5) = -25+25 +4

f(5) = 4

Now, to find the average rate of change of f(x) from x = 3 to x = 5.

Calculate the difference of f(5) and f(3) and divide it by 2, because the difference between 3 and 5 is 2.

\frac{f(3)-f(5) }{2}

\frac{10-4}{2}

\frac{6}{2}=3

The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

Thus, the correct option is A) The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

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Answer:

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Step-by-step explanation:

Let the required number be x.

Therefore, according to the given condition:

{x}^{2}  - 28 = 3x \\  {x}^{2}  - 3x - 28 = 0 \\  {x}^{2}  - 7x + 4x - 28 = 0 \\ x(x - 7) + 4(x - 7) = 0 \\ (x - 7)(x + 4) = 0 \\ x - 7 = 0 \: or \: x + 4 = 0 \\ x = 7 \: or \: x =  - 4 \\

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3 years ago
Which types of dilation are the given scale factors?
Drupady [299]

Answer:

Tbh Im new to this.

Step-by-step explanation:

i think -5/4 is con

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3 0
2 years ago
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Jet001 [13]

Answer:

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(b)0.8

(c)First Term

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(e)$819.20

Step-by-step explanation:

The exponential function for modelling growth or decay is given as:

A(t)=A_o(1\pm r)^t,

Where:

Plus indicates growth and minus indicates decay.

A_o$ is the Initial Value\\r is the growth/decay rate\\t is the time period

For a powerful computer that was purchased for $2000, but loses 20% of its value each year.

(a)Since it loses value, it is a decay.

(b)Multiplier

Its value decays by 20%.

Therefore, our multiplier(1-r) =(1-20&)=1-0.2

Multiplier =0.8

(c)$2000 is our First term (or Initial Value A_o)

(d)The function for this problem is therefore:

f(t)=f_o(1- r)^t\\f(t)=2000(1- 0.2)^t\\\\f(t)=2000(0.8)^t

(e)Since we require the worth of the computer after 4 years,

t=4 years

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6 0
3 years ago
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zloy xaker [14]
I think the answer is false✨
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