Using translation concepts, it is found that the transformations to create function d are given as follows:
- Horizontal shift right 1 unit.
- Vertical shift up 5 units.
- Frequency multiplied by 2.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent cosine function is given by:
f(x) = cos(x).
The translated function is given by:
d(x) = cos(2x - 1) + 5.
Which means that:
- 1 was subtracted in the domain, hence the was a horizontal shift right 1 unit.
- 5 was added in the range, hence there was a vertical shift up 5 units.
- There was a multiplication by 2 in the domain, hence the frequency is multiplied by 2.
More can be learned about translation concepts at brainly.com/question/4521517
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The best step to do next is to add 80 to both sides of equation:
5 ( x² + 8 x ) + 80 = 14 + 80
and since 80 = 5 · 16
5 ( x² + 8 x + 16 ) = 94 Answer : B )
After that we will continue like this:
5 ( x + 4 )² = 94
( x + 4 )² = 18.8 ... etc
Step-by-step explanation:
explained in the photo
Answer:
The answer is $19.44
Step-by-step explanation:
First you have to find 25% of $28.80 (which is 7.20). Then, you subtract the $7.20 from your 28.80. You do that because you are getting a 25% discount. Then, you find 10% of $21.60 (your answer for the 25% discount) and you subtract 10% of $21.60. After that, you get your total of $19.44.
I hope you find this helpful.
Answer:
4 sqrt(2) - sqrt(70)
Step-by-step explanation:
Simplify the following:
(4 sqrt(14) + 4 sqrt(10)) (3 sqrt(7) - 4 sqrt(5))
Factor 4 out of 4 sqrt(14) + 4 sqrt(10) giving 4 (sqrt(14) + sqrt(10)):
4 (sqrt(14) + sqrt(10)) (3 sqrt(7) - 4 sqrt(5))
(sqrt(10) + sqrt(14)) (3 sqrt(7) - 4 sqrt(5)) = sqrt(10) (-4 sqrt(5)) + sqrt(10)×3 sqrt(7) + sqrt(14) (-4 sqrt(5)) + sqrt(14)×3 sqrt(7) = -20 sqrt(2) + 3 sqrt(70) - 4 sqrt(70) + 21 sqrt(2) = sqrt(2) - sqrt(70):
Answer: 4 sqrt(2) - sqrt(70)
