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Stolb23 [73]
2 years ago
7

Given the function f(x) = x² + 8x + 12, determine the average rate of change of

Mathematics
1 answer:
Kitty [74]2 years ago
3 0

The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,

\dfrac{f(b)-f(a)}{b-a}

Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is

\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}

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2. Every December, Tagaytay City Science National High School is sponsoring a
kirza4 [7]

Answer:

a: 162

b: 142

Step-by-step explanation:

a: december 1=2

a: december 2=6

a: december 3 = 6 x 3 = 18

a: december 4 = 18 x 3 =54

a: december 5 = 54 x 3 =162

~ triples the number of newspapers means "x3" ~

so on the last day, 162 newspapers

B: sum up all the newspapers:

2 + 6 + 18 + 54 + 162

= 8 + 18 + 54 + 162

= 26 + 54 + 162

= 80 + 162

= 242 all in total newspapers

3 0
2 years ago
URGENT this is a question on my precalculus test I need help on. Thank you so much
sp2606 [1]

Answer:

a. 5i + 13j

b. 8i

c. 10i + 6j

Step-by-step explanation:

a. 2i + 6j + 3i + 7j = 5i + 13j

b. 3i + 7j + 5i - 7j = 8i

c. 2i + 6j + 3i + 7j + 5i - 7j = 10i + 6j

5 0
3 years ago
The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on We
Alekssandra [29.7K]
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
------------------------------------
2*(1) - (2)
------------------------------------
4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
------------------------------------
       9B+6C = 1,140 --- (4)
------------------------------------
3(2) -4(3)
-----------------------------------
12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
-----------------------------------
         -15B-6C = -1,620 --- (5)
------------------------------------
(4) + (5)
------------------------------------
9B+6C = 1140
-15B-6C = -1620 +
-------------------------------------
-6B = -480 => 6B = 480 => B = 480/6 = 80
-------------------------------------------------------
Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
------------------------------------------------------------------------------
Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
----------------------------------------------------------------------------------------------
The rates are:
A = $100
B = $80
C = $70
--------------------------------
On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
6 0
3 years ago
Read 2 more answers
Carl, Gilda, Conroy, and Kyla are the four candidates in a school election. Carl received 1/5 of the votes, Gilda received 5% of
Juliette [100K]
Firstly, we can convert all of the fractions into percentages. To do this, we need to make the denominator of the fraction 100, and whatever we do to the denominator we must also do to the numerator.

5 x 20 = 100
1 x 20 = 20.

So Carl recieves 20/100 or 20% of the votes.

4 x 25 = 100
1 x 15 = 25

So Conroy receives 25/100 or 25% of the votes.

If we add these together and Gilda's 5%, we get 50%. Since there are 100% votes overall, we need to do 100 - 50 = 50.
 
Kyla receives 50% of the votes.
8 0
3 years ago
Read 2 more answers
What is the volume of a sphere if it has a radius of 2 feet? (Use 3.14 for π .) 33.49 ft 3 100.48 ft 3 75.36 ft 3 25.12 ft 3
cricket20 [7]
I think the answer is the first one
5 0
3 years ago
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