Answer:
The cook made 7 pints
Step-by-step explanation:
Just minus the half pints
Answer:
number of yellow marbles=62.
Step-by-step explanation:
It is given that in a bag there are yellow marbles and blue marbles and the total number of marbles=73.
Let the number of Blue marbles=x, then according to the question, number of yellow marbles will be =5x+7.
Now, Total number of marbles= number of yellow marbles+number of blue marbles.
⇒73=x+5x+7
⇒73-7=6x
⇒66=6x
⇒x=11
Therefore, numberof blue marbles=x=11 and
number of yellow marbles=5x+7=5(11)+7=55+7=62.
I think it is number 2, x^2-x+2
Step-by-step explanation:
all work is pictured/shown
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
