Answer:
43°
Step-by-step explanation:
(x + 53)° + (x + 74)° + 73° = 180°
(x + 53 + x + 74)° = 180° - 73°
(2x + 127)° = 107°
2x + 127 = 107
2x = 107 - 127
2x = - 20
x = - 20/2
x = - 10

The different ratios are 2 : 7, 2 : 9 and 7 : 9
<h3>How to determine the ratio?</h3>
The statement is given as:
8 out of 36 squares unfilled
This means that:
- There are 36 squares
- 8 are unfilled
- 28 are filled
The part-to-part ratio is represented as:
Ratio = Unfilled : Filled
This gives
Unfilled : Filled = 8 : 28
Simplify
Unfilled : Filled = 2 : 7
The part-to-whole ratios are represented as:
Ratio = Unfilled : Total
Ratio = Filled : Total
So, we have:
Unfilled : Total = 8 : 36
Filled : Total = 28 : 36
Simplify
Unfilled : Total = 2 : 9
Filled : Total = 7 : 9
Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9
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Answer:
A, C, D
Step-by-step explanation:
Consider triangles NKL and NML. These triangles are right triangles, because

In these right triangles:
- reflexive property;
- given
Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so
![\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]](https://tex.z-dn.net/?f=%5Coverline%7BKN%7D%5Ccong%20%5Coverline%7BNM%7D%5C%5C%20%5C%5C%5Coverline%7BKL%7D%5Ccong%20%5Coverline%7BLM%7D%5C%20%5B%5Ctext%7Boption%20D%20is%20true%7D%5D)
Since

then
![7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}]](https://tex.z-dn.net/?f=7x-4%3D5x%2B12%5C%5C%20%5C%5C7x-5x%3D12%2B4%5C%5C%20%5C%5C2x%3D16%5C%5C%20%5C%5Cx%3D8%5C%20%5B%5Ctext%7Boption%20A%20is%20true%7D%5D%5C%5C%20%5C%5CMN%3DKN%3D7%5Ccdot%208-4%3D56-4%3D52%5C%20%5B%5Ctext%7Boption%20C%20is%20true%7D%5D)
Option B is false, because KN=52 units.
Option E is false, because LN is congruent KN, not LM
Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder
Area of the base of the cylinder =

Area of the cylinder 'wall' = width × length =

×

=

×

=

Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by

where

is the slanted height of the cone
SA of cone =

Hence total painted surface area is