Step-by-step explanation:
what is that X, and X²???
Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Given the percentage taken off and the reduced price, the original price of the item is $142.
<h3>What was the original price of the item?</h3>
Given the data in the question;
- Percentage off the item = 20%
- Reduced price of the item = $113.60
- Original price of the item = ?
The original price of the item is at 100%, if the 20% is taken off. The price is now at 80%.
Hence 80% of the original price will give the reduced price.
Let the original price be represented by x
80% × x = $113.60
We solve for x
80/100 × x = $113.60
80x/100 = $113.60
Cross multiply
80x = $11360
x = $11360/80
x = $142
Given the percentage taken off and the reduced price, the original price of the item is $142.
Learn more about Percentages here: brainly.com/question/24159063
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Answer:
x < - 7
Step-by-step explanation:
Given
- 3x + 4 > 25 ( subtract 4 from both sides )
- 3x > 21
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.
x < - 7
Answer:
Point D
Step-by-step explanation:
It goes from Point C to move forward one, and then it says that it's four points from B.