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Darina [25.2K]
3 years ago
12

Which real number property is illustrated here? *

Mathematics
1 answer:
liubo4ka [24]3 years ago
8 0

Answer:

Commutative property of multiplication

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Given the function f(x) = 5^x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average r
Masteriza [31]
Part A)

f(x) = 5^x
f(0) = 5^0
f(0) = 1
----------
f(x) = 5^x
f(1) = 5^1
f(1) = 5
----------
f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
----------
f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125

-------------------

Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4

Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100

================================================

Part B)

From part A) above, we found,

Rate of change for section A = 4
Rate of change for section B = 100

Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)

Answer for part B: 25

================================================

Extra:  Explain why one rate of change is greater than the other.

The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed. 

6 0
3 years ago
Question 1 [5 points]
RideAnS [48]
If I’m not wrong, it should be 1000-5+9.10% and add it to the tune and divide with the 9.90% and -3 and then you can get your answer
6 0
3 years ago
The sum of the first 10 terms of an arithmetic sequence is 235 and the
Degger [83]

Answer:

             \bold{a_1 = -42.65}\\\\\bold{d=14.7}

Step-by-step explanation:

The sum of the first 10 terms of an arithmetic sequence is:

S_{10}=a_1+a_2+...+a_{10}=\dfrac{a_1+a_{10}}{2}\cdot10=\dfrac{2a_1+(10-1)d}{2}\cdot10

\dfrac{2a_1+(10-1)d}{2}\cdot10=235\\\\(2a_1+9d)\cdot5=235\\\\2a_2+9d=47

the  sum of the second 10 terms is:  a₁₁ + a₁₂+...+ a₂₀

And the sum of the first 20 terms of an arithmetic sequence is:

S_{20}=a_1+a_2+...+a_{10}+a_{11}+...+a_{20}=\dfrac{2a_1+(20-1)d}{2}\cdot10

so the  sum of the second 10 terms is:

a_{11}+a_{12}+...+a_{20}=S_{20}-S_{10}

Therefore we have:

\dfrac{2a_1+(20-1)d}{2}\cdot10-\dfrac{2a_1+(10-1)d}{2}\cdot10=735\\\\(2a_1+19d)\cdot5-(2a_1+9d)\cdot5=735\\\\2a_1+19d-(2a_1+9d)=147\\\\10d=147\\\\d=14.7

and:  

2a_1+9\cdot14.7=47\\\\2a_1+132.3=47\\\\2a_1=-85.3\\\\a_1=-42,65

3 0
3 years ago
Which equation represents the line that passes through (-5,-2) and has a slope of 3
MrRa [10]

You already know the slope is 3 and you have the point, so you would plug it into y = mx + b

-2 = y

3 = m

-5 = x

Plug in:

-2 = 3(-5) + b

Solve:

-2 = -15 + b

-2 (+15) = -15 + b (+15)

13 = b

Now you have b, so you can form the equation where the slope is 3x and the y-intercept is 13.

Final answer: y = 3x + 13


8 0
3 years ago
The height of a rocket at different times after it was fired is shown in the table.
bearhunter [10]
I'll round off the first equation to 3 decimal points
1 - y=-4.848 x^{2}+19.985x+50.011
2 - 70.391 units
3 - 7.582 sec
6 0
3 years ago
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