Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if 
here;
Thus;
∴
Hence, we can conclude that r(t) and s(t) are parallel.
Answer:
Given: In parallelogram ABCD, AC=BD
To prove : Parallelogram ABCD is rectangle.
Proof : in △ACB and △BDA
AC=BD ∣ Given
AB=BA ∣ Common
BC=AD ∣ Opposite sides of the parallelogram ABCD
△ACB ≅△BDA∣SSS Rule
∴∠ABC=∠BAD...(1) CPCT
Again AD ∥ ∣ Opposite sides of parallelogram ABCD
AD ∥BC and the traversal AB intersects them.
∴∠BAD+∠ABC=180∘ ...(2) _ Sum of consecutive interior angles on the same side of the transversal is
180∘
From (1) and (2) ,
∠BAD=∠ABC=90∘
∴∠A=90∘ and ∠C=90∘
Parallelogram ABCD is a rectangle.
<h2>
Answer with explanation:</h2>
In statistics, The Type II error occurs when the null hypothesis is false, but fails to be rejected.
Given : Suppose the null hypothesis, 
, is: Darrell has enough money in his bank account to purchase a new television.
Then , Type II error in this scenario will be when the null hypothesis is false, but fails to be rejected.
i.e. Darrell has not enough money in his bank account to purchase a new television but fails to be rejected.
Find the slope of the line connecting (1990,435000) and (2005,482300):
482300-435000 47300
m = ----------------------- = ---------------- = 3153/yr (approx)
2005 - 1990 15 yr
Use the point-slope formula to find the equation of this str. line:
y-435000 = (3153/yr)(x-1990)
The year 2020 is 30 years after 1990. Thus, the expected pop in 2020 is
given by y-435000 = 3153(30) = 94590, so that y = 529590.
Answer:
x=28
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x+5+x−5=56
x+5+x+−5=56
(x+x)+(5+−5)=56(Combine Like Terms)
2x=56
2x=56
Step 2: Divide both sides by 2.
2x/2=56/2
x=28
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