Answer:
15
Step-by-step explanation:
using the rule of exponents
= 
= 
= 
= 15
Answer: C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)
Step-by-step explanation:
The data set is:
(9, 22)
(10,32)
(11, 41)
(12, 30).
In the usual notation, the number at the left is the input (belons to the domain) and the number in the right is the output (belongs to the range).
Then the domain would be:
{9, 10, 11, 12}
and the range:
{22, 32, 41, 30}
The correct option is C
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
Answer:
x=-7
Step-by-step explanation:
-30=5(x+1)
6-1(x+1)
x=-1-6
=-7
Answer:
300 percent change
Step-by-step explanation:
300 is 400 percent of 75.(75x4 is 300.) Therefore, the percent change is
400 - 100 = 300.
