Question 2 unsaved triangle abc has vertices at (-4,0), (-1,6) and (3,-1). what is the perimeter of triangle abc, rounded to the nearest tenth. question 2 options: 21.84 22 21.8 21.9

According to the geometry program used to draw the triangle, the lengths of the sides add to 21.841 units*. Rounded to the nearest tenth, the appropriate answer choice is ...

... 21.8

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You can use your test-taking skill to choose this answer without doing a single calculation. The answer choices appear to be about rounding, not about accurate calculation of the length. The choice 21.84 tells you that is probably the value before any rounding. Then choices 22 and 21.9 are obviously incorrectly rounded. The correctly rounded answer is then 21.8.

Coordinate differences are ...

AB = (-1, 6) -(-4, 0) = (3, 6) . . . . ║AB║=√(3²+6²)=3√5

BC = (3, -1) -(-1, 6) = (4, -7) . . . . ║BC║=√(4²+7²)=√65

CA = (-4, 0) -(3, -1) = (-7, 1) . . . . ║CA║=√(7²+1²)=5√2

The sum of these lengths is about 21.8415, so rounds to 21.8.

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* If you follow the math, you find that the final sum should be displayed using 3 decimal digits as 21.842. The error in the least-significant digit of the sum comes from rounding each length to 3 decimal digits.

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!