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Dennis_Churaev [7]
3 years ago
15

Water coming out from a fountain is modeled by the function f(x) = -x2 + 5x + 4 where f(x) represents the height, in feet, of th

e 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?
Mathematics
1 answer:
slava [35]3 years ago
6 0
F ( x ) = - x² + 5 x + 4
between x = 3 and x = 5:
f ( 3 ) = - 3² + 5 · 3 + 4 = - 9 + 15 + 4 = 10
f ( 5 ) = - 5² + 5 · 5 + 4 = - 25 + 25 + 4 = 4
Average rate of change:
( 4 - 10 ) / ( 5 - 3 ) = - 6 : 2 = - 3 feet / sec 
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Answer:

q=-3 2/5

Step-by-step explanation:

First multiply -13 with (q+4)

-13q-52=7q+16

Now you have to change the order before = the numbers with q and after = the numbers without anything

-13q-7q=52+16

Remember that when you change positions the symbol too

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-20q=68

Now u have to divide as i do

q=68/-20

you can simplify it

q=3 8/-20

Now divide by the greater divisor in this case is 4

q=3 2/-5

And organize it

q=-3 2/5

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Hopefully it helps.

5 0
3 years ago
Can you answer these 3 questions for me plz
finlep [7]
A.
1hr \: 15min = 75min

c = 0.22t = 0.22 \times 75 = 16.5

cost is $16.50

B.

26.40 = 0.22 \times t

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t = \frac{26.40}{0.22} = 120min

C. This is the same as part B, only the rate changed

t = \frac{26.40}{0.25} = 105.6min

they ask for the greatest number of minutes, so we round down (take the floor of the value).

the answer is 105 minutes.
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3 years ago
Which congruence theorems can be used to prove △EFG ≅ △JHG? Check all that apply.
sasho [114]

Answer:

ASA  and AAS

Step-by-step explanation:

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ.  This makes EJ a transversal.  This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent.  We also know that ∠EGF and ∠HGJ are vertical angles and are congruent.  This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent.  Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

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