Answer:
g (x) = 2 ^ (x + 2)
Step-by-step explanation:
For this case the transformation of f (x) is given by
g (x) = 2 ^ (x + 2)
To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)
For (-2,1)
g (-2) = 2 ^ ( -2 + 2)
g(-2)=1
For (-1,2)
g (-1) = 2 ^ ( -1+ 2)
g(-1)=2
For (0,4)
g (0) = 2 ^ ( 0+ 2)
g(0)=4
<h3>
Answer: D) 18</h3>
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Work Shown:
Here are the variables we're working with
- a = first term
- b = last term (aka nth term)
- n = number of terms
- S = sum of the first n terms
In this case, we know that
- a = unknown (what we want to solve for)
- b = -12
- n = 14
- S = 42
We can use this formula to help find the answer
S = (n/2)*(a+b)
This formula only works for arithmetic sequences
So,
S = (n/2)*(a+b)
42 = (14/2)*(a+(-12))
42 = 7(a-12)
42/7 = a-12
6 = a-12
6+12 = a
18 = a
a = 18 is the first term of this arithmetic sequence
That's why the answer is choice D.
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Side note: your book or your teacher may use the notation but I figured it would be easier to use 'a' and b in place of and respectively.
Answer:
A. c = 18d + 11
Step-by-step explanation:
From the given table, we have two points : (1,29) and (2,47).
Now let us use slope formula to find the slope :
slope =18
Now we use point slope form to get the final equation.
Using point (1,29) and slope 18,
So final equation becomes c=18d +11
The answer is the Third solution.
example:
C = (18 × 2) + 11
C = 36 + 11
C = 47
Answer:
y=3x-2
Step-by-step explanation:
The ordered pairs (0, -2), (1, 1), (2, 4), (3, 7) and (4, 10) represent a linear function, because 1-(-2)=4-1=7-4=10-7=3.
The equation for the unknown linear function is y=ax+b.
Then
1. -2=a·0+b, b=-2;
2. 1=a·1+b, a=1-b=1-(-2)=3.
Therefore, the equation is y=3x-2.
Answer:
Step-by-step explanation:
Factorise the denominator of the second fraction
y² - 1 = (y - 1)(y + 1) ← difference of squares
To obtain a common denominator
multiply numerator/ denominator of first fraction by (y + 1)
= - ← subtract numerators leaving the common denominator
=
=
= ← cancel common factor (y - 1) on numerator/denominator
=