Csc x · sec x - tan x =
= 1 / sin x · 1 / cos x - sin x / cos x =
= 1 / sinx cos x - sin² x / sin x cos x =
= ( 1 - sin² x ) / (sin x cos x) =
= cos² x / ( sin x cos x ) =
= cos x / sin x = cot x
Answer:
Yes The triangles are similar by SAS Similarity Theorem
Step-by-step explanation:
we know that
<u>Side-Angle-Side Similarity,</u> states that If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar
In this problem
Angle L is congruent with Angle Z
so
Verify if the included sides are proportional
so

substitute the values

-----> is true
therefore
The triangles are similar by SAS
The difference between consecutive integers is 1.
Let x = smaller integer.
Then x + 1 is the next greater consecutive integer.
x(x + 1) = 132
x^2 + x - 132 = 0
(x + 12)(x - 11) = 0
x + 12 = 0 or x + 11 = 0
x = -12 or x = -11
Since x is the smaller of the two integers, the answers are:
-12, -11
11, 12
There are two pairs of such integers.
Answer:
the amount borrowed is ≅ $527
Step-by-step explanation:
Given that;
simple interest rate r = 180% p.a
Let the amount borrowed (principal) be $x.
time t = 4 weeks = 28 days
= 28/365 year
= 0.0767 year
we all know that :


Simple interest = 0.13806x
Total amount to be paid after 4 weeks= Interest+Principal
= x + 0.13806x
= 1.13806x
Thus;
1.13806x = $600
x = $600/ 1.13806
x = $527.21
Hence; the amount borrowed is ≅ $527
Answer:
<h2>N = 2,200</h2>
'Percent (%)' means 'out of one hundred':
0.83% = 0.83 'out of one hundred',
p% is read p 'percent',
0.83% = 0.83/100 = 0.83 ÷ 100
Calculate percentage:
'Percentage' is obtained by multiplying 2,200 by 0.83%
0.83% × 2,200 =
(0.83 ÷ 100) × 2,200 =
(0.83 × 2,200) ÷ 100 =
1,826 ÷ 100 =
18.26
Step-by-step explanation:
Hope it is helpful....