Answer:
45
Step-by-step explanation:
AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.
now, what is f ?
we know this from the relation of AC to FA.
FA = 12 mm
AC = 12 + 28 = 40 mm
so, going from AC to FA we multiply AC by f so that
AC × f = FA
40 × f = 12
f = 12/40 = 3/10
all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).
the area of a triangle is
baseline × height / 2
aABC = 500
and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.
baseline small = baseline large × f
height small = height large × f
we know that
baseline large × height large / 2 = 500
baseline large × height large = 1000
aAEF = baseline small × height small / 2 =
= baseline large × f × height large × f / 2 =
= baseline large × height large × f² / 2 =
= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =
= 500 × 9/100 = 5 × 9 = 45 mm²
Answer:
0.875
Step-by-step explanation:
they're proportional.
Answer:
The students where asleep and did not have phones turned on.
Step-by-step explanation:
Answer:
<h2>C</h2>
Step-by-step explanation:
To determine a function rule, look at the table. Input the x and y value from one column into the function to see if it is correct.
<h3>Function a: y = 10 - 2x</h3>
Input values
22 = 10 - 2(6)
22 = 10 - 12
22 ≠ -2 ❌
As we can see, function a gives us a false statement, so a is incorrect.
<h3>Function b: y = 2 - 10x</h3>
Input values
22 = 2 - 10(6)
22 = 2 - 60
22 ≠ -58 ❌
We once again get a false answer, so b is also not correct.
<h3>Function c: y = 10 + 2x</h3>
Input values
22 = 10 + 2(6)
22 = 22 ✔
Finally, we get a true statement, so option c is correct.
<h3>Function d: y = 2 + 10x</h3>
Just to check that option c is correct, we need to prove that d is incorrect.
Input values
22 = 2 + 60
22 ≠ 62 ❌
This is also wrong, so that proves that c is correct.
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