9514 1404 393
Answer:
   470.16 cm²
Step-by-step explanation:
The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.
The apothem of the base for side length s is ...
   s/2 = a·tan(π/8)
   a = s/(2·tan(π/8)) ≈ 7.24 cm
The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...
   x² = 10² + a² = 100 +52.46
   x ≈ √152.46 ≈ 12.35
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The area of the 8 triangular faces will be ...
   A = 1/2Px . . . . where P is the perimeter of the pyramid
The area of the base will be ...
   A = 1/2Pa
So, the total surface area is ...
   A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²
 
        
                    
             
        
        
        
Final Answer is 4.5
= 4.5hours more time was used on games than on research.
 
        
             
        
        
        
Answer:
21) 12 cm
22) 5.9 cm
Step-by-step explanation:
21) The base is 10, and if the other two sides are congruent and the perimeter is 36, we can figure out with simple algebra that the sides are 13 cm long. 
Half of 10 is 5, so we can use the pythagorean theorem. 
5^2+x^2=13^2
Rearranging the variables we have 169-25=x^2
144=x^2
x can be plus or minus 12, but since negative length is impossible we find that x is positive 12 cm. 
22) We want to use sine, because we have opposite and hypotenuse. A simple and easy way to memorize this is the SohCahToa method. If we have opposite (O) and hypotenuse (H) we have OH. Soh has the letters O and H, and the S means we should use sine. 
sine 36=a/10
Plug this into a calculator or desmos scientific calculator to get a=5.9
 
        
             
        
        
        
I agree with what that person told you. The expression -2(x+10) is equivalent to -2x-20
Multiply the outer -2 with the inner x to get -2 times x = -2x
Multiply the outer -2 with the inner term 10 to get -2 times 10 = -20
So overall, -2(x+10) = -2x-20
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So that's how we're able to go from this 

 to this 

The only thing that changes is the left side. The inequality sign will not flip. It only flips if we multiply both sides by a negative number. 
 
        
        
        
Answer:
Slope = 2/3 Y intercept +3
Step-by-step explanation:
Plot the y-intercept (0,+3) in the xy axis. Remember, this point always lies on the vertical axis y.
Starting from the y-intercept, find another point using the slope. Slope contains the direction how you go from one point to another.
The numerator tells you how much steps to go up or down (rise) while the denominator tells you how many units to move left or right (run).
Connect the two points generated by the y-intercept and the slope using a straight edge (ruler) to reveal the graph of the line.