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Firlakuza [10]
3 years ago
14

Function f(x) = ax^{2}+bx+c, where a, b, and c are some constants. Define functions g and h as follows:

Mathematics
1 answer:
zimovet [89]3 years ago
4 0
G(x) = f(x+1) - f(x)
=[ a(x+1)^2+b(x+1)+c ] - [ax^2+bx+c]
=[ a(x^2+2x+1) +bx + b + c ] - [ax^2 + bx + c]
=[ ax^2 + 2ax + a + bx + b + c ] - [ax^2 + bx + c]
= ax^2 + 2ax + a + bx + b + c - ax^2 - bx - c
= 2ax + a + b
Therefore g(x) = 2ax + a + b
h(x) = g(x+1) - g(x)
=2a (x+1) + a + b - [2ax+a+b]
=2ax + 1 + a +b - 2ax - a - b
Therefore h(x) = 1


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Answer:

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Step-by-step explanation:

3 0
2 years ago
The cover of a soccer ball consists of interlocking regular pentagons and regular hexagons. Why can't they be interlocked in thi
FinnZ [79.3K]

Answer: Because of gaps between the vertex of Pentagons and hexagon.

Step-by-step explanation:

The Pentagon has 5 sides and 5 vertex angles. While hexagon has 6 sides and six vertex angles

The sum of the angle of polygon is equal to ( n - 2 )180

Sum of the angle of a Pentagon will be: (5 - 2)×180 = 540

Each vertex angle of a Pentagon = 540/5 = 108

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Each vertex angle of a hexagon =

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5 0
3 years ago
Find the mean of 58, 43, 33, 69, 41, and 74.
andrew11 [14]
The mean is the average of a given data set and can be obtained by taking the sum of all numbers and dividing that by the amount of numbers in the data set.

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5 0
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The table shows the values of a function f(x). What is the average rate of change of f(x) from 1 to 4?
Sav [38]

Answer:

-80

Step-by-step explanation:

The average rate of change is

a.r.c = f(4) - f(1)

        --------------

             4-1

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a.r.c = 244  - 484

        --------------

             3

        = -240/3

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6 0
3 years ago
Read 2 more answers
Which of the equation of the line with slope 3 that contains point (-1,5)
SpyIntel [72]

The point-slope form:

y-y_1=m(x-x_1)

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y-5=3(x-(-1))

\boxed{y-5=3(x+1)}      <em>use distributive property</em>

y-5=3x+3           <em>add 5 to both sides</em>

\boxed{y=3x+8} - slope-intercept form

3 0
3 years ago
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