Answer:
NOT CONGRUENT
Step-by-step explanation:
Given:
AB ≅ CD
∠DCB ≅ ∠DAB
To prove:
ΔABD ≅ ΔDCB
Statements Reasons
1). AB ≅ CD 1). Given
2). ∠DCB ≅ ∠DAB 2). Given
3). DB ≅ DB 3). Reflexive property
4). ΔABD ≅ ΔDCB 4). SSA property of congruence.
But in the given options SSA property is not given.
So the answer is NOT CONGRUENT.
Solution :
Given
= weight of the first side
= 6 kg = 6000 g
= distance of the first weight from the triangle.
= 3 m = 300 cm
= distance of the first weight from the triangle.
= 600 cm
Let, 
= weight of the second side
So, x = x
or 
= 3000 g
Therefore, the quantity that is used to replace the question mark in order to make the scale balance is 3000 g.
Answer:
V = 40 1/2cm^3 OR 40.5cm^3
Step-by-step explanation:
A Prism is given it's name from the nature of it's base.
If it's a triangular base, it's call a TRIANGULAR PRISM.
If the base is of a rectangle shape, it's called a RECTANGULAR PRISM and so on!
From the question given, we'll treat the prism as a RECTANGULAR PRISM.
The volume of a prism is expressed as:
V = Bh
B means the BASE AREA
h means the height
Base Area for the prison is RECTANGLE.
Area of a rectangle (A) = lw
l means height
w means weight.
From the dimensions given in the question:
Length = 4 1/2cm
Width = 6cm
Height = 1 1/2cm
Let's start with the BASE AREA of the Rectangle
A = lw
A = 4 1/2cm * 6cm
A = 9/2cm * 6cm
A= 27cm^2
Volume = Base Area (A) * height (h)
V = Bh
V= 27cm ^2 * 1 1/2 cm
V = 27 * 3/2
V = 81 / 2
V = 40 1/2cm^3 OR 40.5cm^3
Answer:
Integers are 7, 8, 9
Step-by-step explanation:
Let three positive consecutive integers are (n - 1), n, (n + 1)
If the product of the second and the third integer is 72,
n(n + 1) = 72
n² + n = 72
n² + n - 72 = 0
n² + 9n - 8n - 72 = 0
n(n + 9) - 8(n + 9) = 0
(n - 8)(n + 9) = 0
(n - 8) = 0 ⇒ n = 8
(n + 9) = 0 ⇒ n = -9
For n = 8,
Integers will be ⇒ 7, 8, 9
For n = -9,
Integers will be ⇒ -10, -9, -8
Since, all integers are positive,
7, 8, 9 will be the answer.
