Left Hand Side :
sin
x
+
cos
x
cot
x
We know that
cot
x
=
cos
x
sin
x
Therefore
sin
x
+
cos
x
cot
x
=
sin
x
+
cos
x
⋅
(
cos
x
sin
x
)
=
sin
x
+
cos
2
x
sin
x
=
sin
2
x
+
cos
2
x
sin
x
(We know the Trigonometric Identity
sin
2
x
+
cos
2
x
=
1
)
=
1
sin
x
=
csc
x
(Because Cosecant is the reciprocal of Sine)
Hence Proved.
Answer:
11449/160000
Step-by-step explanation:
The probability of selecting a single adult that thinks most celebrities are good role models is 214/800 = 107/400
The probability that both do is
(107/400)^2 =. 11449/160000
We have to identify the given object.
A. Cube: The given object is not a cube because cube is a box-shaped solid object that has six identical square faces. But here, the given figure does not have the identical faces.
B. Polygon: The given object is not a polygon because a polygon is any 2-dimensional shape formed with line segments. But here, the given figure is not 2-dimensional.
C. Polyhedron: The given object is a polyhedron because a polyhedron is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. Therefore, it is a polyhedron.
D. Prism: The given object is a prism because a prism is a polyhedron consisting of two parallel, congruent faces called bases. This is called a rectangular prism because a Prism with rectangular bases is a Rectangular Prism.
E. Pyramid: The given object is not a pyramid because a pyramid is a 3-dimensional shape whose base is a polygon. Each corner of a polygon is attached to a singular apex, which gives the pyramid its distinctive shape. Each base edge and the apex form a triangle. The given object does not appears like this.
So, the given object is Polyhedron and Prism(rectangular).
The lowest common denominator is 340.
Answer:
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
Step-by-step explanation:
Let the cost of tacos be x and the cost of quesadillas be y.
<h3><u>Given condition:</u></h3>
x + 3y = 26.50 ------------------(1)
3x + y = 19.50 -------------------(2)
Multiply Eq. (2) by 3
3(3x + y) = 19.50 * 3
9x + 3y = 58.5 -----------------(3)
Subtract Eq. (3) from (1)
x + 3y - 9x - 3y = 26.50 - 58.50
x - 9x = -32
-8x = -32
8x = 32
Divide 8 to both sides
x = $4
Put x = 4 in (1)
4 + 3y = 26.50
Subtract 4 to both sides
3y = 26.50 - 4
3y = 22.50
Divide 3 to both sides
y = $7.50
So,
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
