It will be a 6 because the 8.5 is actually 8.50. So when subtracting mentally 8.50 - 4.64 you know 0 - 4 cannot be subtracted. Barrow a 1 from the 5 and now it'll be like 10 - 4. Which 10 - 4 = 6
8.50
- 4.64
= 3.86
Answer: 1. x = -2(y - 4)² + 1
2. x = -y² + 5
3. y = -5(x + 1)² + 2
<u>Step-by-step explanation:</u>
Notes: The vertex formula of a parabola is x = a(y - k)² + h or y = a(x - h)² + k
- (h, k) is the vertex
- p is the distance from the vertex to the focus
1)
Now input a = -2 and (h, k) = (1, 4) into the equation x = a(y - k)² + h
x = -2(y - 4)² + 1
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2)
Now input a = -1 and (h, k) = (5, 0) into the equation x = a(y - k)² + h
x = -1(y - 0)² + 5 → x = -y² + 5
***********************************************************************************
3)
Now input a = -5 and (h, k) = (-1, 2) into the equation y = a(x - h)² + k
y = -5(x + 1)² + 2
Answer:
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
Solving (b):
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
Solving (c):
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
Solving (d):
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
The answer is 5
Explanation:
We need to use the Pythagorean,
a^2 + b^2 = c^2
Where c is the hypotenuse
We can fill in spots now 12^2 + b^2 = 13^2
And then we solve 144 + b^2 = 169
Next we get b^2 alone
169-144=25
So we get b^2=25
For the final step you have to find the square root of 25 to get b alone which is 5
<h3>
Answer: 7, 4, 1, -2, -5</h3>
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Explanation:
The notation a(1) = 7 means that the first term is 7
The second term would be a(2) and so on.
To get a(2), we plug in n = 2 to find that...
a(n) = a(n-1) - 3
a(2) = a(2-1) - 3
a(2) = a(1) - 3
a(2) = 7 - 3
a(2) = 4
The second term is 4. We find this by subtracting 3 from the first term.
To get the third term, we repeat the same set of steps but now use n = 3
a(n) = a(n-1) - 3
a(3) = a(3-1) - 3
a(3) = a(2) - 3
a(3) = 4 - 3
a(3) = 1
This process is repeated as much as you want to generate as many terms as you want.
In short, you subtract 3 from each term to get the next term. This implies that we have an arithmetic sequence with starting term 7 and common difference -3.
So that's how we end up with the first five terms: 7, 4, 1, -2, -5