Answer:
Isosceles triangle:
* two sides are equal.
* the base angle are always equal and
* the altitude is a perpendicular distance from the vertex to the base.
Since, the triangle ABC is an isosceles and AC is the base
⇒ AB=BC and 
Also, AD is the angle bisector of
, which implies that it cuts the angle at A in two equal halves,
let
, then the bisectors cuts it in
.
As per the given information, we know
is 110°, therefore, the line BDC forms a supplementary angle;
⇒
As shown in picture given below:
By sum of all interior angles in a triangle is 180 degree, thus
or

Simplify:

Therefore, the
.
Now, to find the angle B, we have;
[Sum of the measure of the angles in a triangle is 180 degree]
or
or

Simplify:
.
(a)
421₅ = 4×5² + 2×5¹ + 1×5⁰
… = 100 + 10 + 1
… = 111
(b)
11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
… = 16 + 8 + 4 + 0 + 1
… = 29
(c)
13T₁₂ = 1×12² + 3×12¹ + 10×12⁰
… = 144 + 36 + 10
… = 190
Answer:
(-6, 4)
Step-by-step explanation:
Given the coordinate points (-3,1). If The point (-3,1) is moved 3 places in the negative y direction and 2 places in the positive x direction the required coordinate will be expressed ss;
X' = (-3-3, 1+3)
X = (-6, 4)
Hence the resulting coordinate will be at:(-6, 4)
The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.
Step-by-step explanation:
The given is,
A cylinder and a cone have the same volume
Cylinder has a radius 2 inches and height of 3 inches.
Cone has a radius of 3 inches
Step:1
For Cylinder'
Formula to calculate the volume of cylinder is,
..................................................(1)
where,
r - 2 inches
h - 3 inches
From the equation (1)
=
×
× 3
= 37.70
V = 37.70 cubic inches
Step:2
For cone,
Formula to calculate the volume of cone is,
..................................................(2)
From the statement,
cylinder and a cone have the same volume
= 
37.70 =
×
× 
37.70 = 9.42478 × h
Height of the cone, h = 4 inches
Result:
Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.
Answer:
c=6
Step-by-step explanation: