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
First you need to pick a number for y. Lets say you pick 0
Then you need to +3 to each side
Then you can say 3=x+2 or -3=x+2.
To find x you need to subtract 2.
You answer would be (1,3) and (-5.-3)
Answer:
The enlargement will be 25 times and the enlargement area will be 
.
Step-by-step explanation:
It is given that each grid unit is equal to 3 inches. SO we have to use this scale.
The total height of the scale drawing is 21 inch and the enlargement has a height given as 105 inches. Therefore it has scale factor of 5. It means that each dimension is enlarged by 5 times the dimension in the scale drawing. So the enlargement of the logo will be 25 times and the enlargement area will be 2250 square inches.
X
X+2
X+4
Those are 3 consecutive odd integers
f(x) = 7x² - 3x + 1
g(x) = 3x - 2
1. g(0) This means that x is 0, so you can plug in 0 for x in the equation:
g(x) = 3x - 2
g(0) = 3(0) - 2
g(0) = -2
2. g(1) x is 1
g(x) = 3x - 2
g(1) = 3(1) - 2
g(1) = 3 - 2
g(1) = 1
3. f(1) x is 1
f(x) = 7x²- 3x + 1
f(1) = 7(1)² - 3(1) + 1
f(1) = 7 - 3 + 1
f(1) = 5
4. f(x) = 7x²- 3x + 1
f(-2) = 7(-2)²- 3(-2) + 1
f(-2) = 7(4) + 6 + 1
f(-2) = 28 + 7
f(-2) = 35
