Answer:
9.1
Step-by-step explanation:
cus I seen it on usatesprep
Fist break up each number in the hundreds column add the tens and the ones then add the hundreds to the previous answer
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
The answer is 96, don't ask how, just know.
Answer:
175 dimes and 75 quarters
Step-by-step explanation:
Make a system of equations, where d is the number of dimes and q is the number of quarters:
d + q = 250
0.1d + 0.25q = 36.25
Solve by elimination by multiplying the top equation by -0.1:
-0.1d - 0.1q = -25
0.1d + 0.25q = 36.25
0.15q = 11.25
q = 75
Then, plug in 75 as q into one of the equations to solve for d:
d + q = 250
d + 75 = 250
d = 175
So, there are 175 dimes and 75 quarters
