Find the perimeter of the shape.
a. 17.6
b. 21.4
c. 26.7
d. 32.9

  B.  21.4 units

Step-by-step explanation:

The distance formula is used to find the length of each segment. That formula tells you the distance is the square root of the sum of the squares of the x-length and the y-length.

  AB = √(4² +1²) = √17 ≈ 4.12

  BC = √(2² +2²) = √8 ≈ 2.83

  CD = √(2² +7²) = √53 ≈ 7.28

  DA = √(4² +6²) = √52 ≈ 7.21

The perimeter is the sum of these lengths:

  P = AB +BC +CD +DA = 4.12 +2.83 +7.28 +7.21 = 21.44 ≈ 21.4 . . . . units

Comment on distance measures

Here, AB and CD have an "aspect ratio" (x:y or y:x) that is more than 3:1. This means that a reasonable estimate of the length can be made simply by using the length of the longest side of the right triangle. That estimate will be well within 10% of the actual length.

For aspect ratios closer to 1, you can add about 1/3 of the length of the shortest side to the length of the longest side. (DA ≈ 6+4/3 ≈ 7.3, for example) For an aspect ratio of 1, like segment BC, you know the length of it is √2 ≈ 1.414 times the length of either side.

Using such estimates, you get ...

  P = AB +BC +CD +DA ≈ 4 +2.8 +7 +7.3 ≈ 21.1 . . . . . close to choice B

By using estimates in this way, we have saved a lot of work and chosen the correct answer.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

2 apples

step-by-step explanation:

taking away equals subtraction. 6-4=2