Answer:
B
Step-by-step explanation:
Using the expansion
tan(x - y) =
, then
tan(x -
)
= 
note that tan( -
) = - tan(
) = - 
= 
=
→ B
Answer:
The solutions of the equation are t = 4(√5 + 1) or 4(√5 - 1).
Step-by-step explanation:
We have to solve the given quadratic equation of single variable t.
The equation is 16 = 2t + 0.25t²
⇒ 0.25t² + 2t - 16 = 0
⇒ 25t² + 200t - 1600 = 0 {Multiplying both sides with 100}
⇒ 25t² + 200t + 400 - 400 - 1600 = 0
⇒ (5t + 20)² - 2000 = 0
⇒ (5t + 20)² - (20√5)² = 0
⇒ (5t + 20 + 20√5)(5t + 20 - 20√5) = 0
So, (5t + 20 + 20√5) = 0 or, (5t + 20 - 20√5) = 0
⇒ (t + 4 + 4√5) = 0 or, (t + 4 - 4√5) = 0
⇒ t = - 4(1 + √5) or, t = 4(√5 - 1) (Answer)
You just need to equate the expressions to find the values for a,b and c. First, let's settle that 2^5/4=8, and 8 is 2^3. Also, an important tool here is the indicie rule:

1st expression: 2^5/4=8
2nd expression: It tells us that 2^5/2^a=2^3 (I know that this equals to 8 as all the expressions are equal therefore is the same as our first expression). Using the indicie law, this means that a=2
3rd expression: 2^b must equal to 8 as well, so b=3
4th expression: c=8 as all of the other expressions we have figured out equal to 8
So a=2, b=3 and c=8
I got 8 but then I did it on my calculator and it said 12 so its 12
Alright this equation has two big steps. First we need to find the price after it was marked up, then we need to take that number and find the discounted price.
To find the cost after a percent of it was added, we just need to multiply the two together and add.
=
$
23.50
+
(
$
23.50
⋅
(
63
%
100
)
)
(we divide by 100 to get the number out of a percent)
=
$
23.50
+
(
$
23.50
⋅
0.63
)
=
$
23.50
+
$
14.81
=
$
38.31
Ok now that we have the number after the price increase, we now need to find the final answer after a discount of
50
%
(do the exact same idea as above but switch the sign)
=
$
38.31
−
(
$
38.31
⋅
(
50
%
100
)
)
=
$
38.31
−
(
$
38.31
⋅
0.5
)
=
$
38.31
−
$
19.16
=
$
19.15