Find the value of x
A.) 46
B.)31
C.)52
D.)107

x = 52

Step-by-step explanation:

These angles are vertical angles meaning they are equal to each other.

4x - 101 = 2x + 3

2x - 101 = 3

2x = 104

x = 52

C) 52

Step-by-step explanation:

Note that these angles are vertical angles, meaning that their measurements will be the same. Set the two angles equal to each other:

4x - 101 = 2x + 3

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 101 and subtract 2x from both sides:

4x (-2x) - 101 (+101) = 2x (-2x) + 3 (+101)

4x - 2x = 3 + 101

2x = 104

Divide 2 from both sides of the equation:

(2x)/2 = (104)/2

x = 104/2

x = 52

C) 52 is your answer.

~

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .