Answer:
x=y-44 and x+y=410
Step-by-step explanation:
So, you want to use the equations x=y-44 and x+y=410 when x is Ann's score and y is Ruth's score. This is because x (Ann's score) is Ruth's score (y) but 44 less, so you subtract y-44 to get x. Then x+y would also have to equal 410 so that's the other equation. Graphing the 2 equations gets you to the point (183,227) in which Ann's score is 183 points and Ruth's score is 227 points.
Answer:
(4, 5 )
Step-by-step explanation:
Given the 2 equations
y = x + 1 → (1)
x + 2y = 14 → (2)
Substitute y = x + 1 into (2)
x + 2(x + 1) = 14 ← distribute and simplify left side
x + 2x + 2 = 14
3x + 2 = 14 ( subtract 2 from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Substitute x = 4 into (1) for corresponding value of y
y = 4 + 1 = 5
Solution is (4, 5 )
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: R= 1
Explanation: no matter how you do it you still get 1 bc its x divided by y which is 1
