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:
50
Step-by-step explanation:
one teacher per 17 students
Answer:
-5 and -4
Step-by-step explanation:
It is far easier just to solve the equation than to determine appropriate integer bounds on the solution.
In the attachment, we show a couple of initial trials at solutions. The nearness of y=5 to being correct suggests that the next higher integer may be helpful, too. It is.
We find -4 and -5 to bracket the solution.
_____
The actual solution is (3.4 -1.3)/-0.5 = -4.2.
Answer:
The expression will be simplified into 
Step-by-step explanation:
It's like addition, when you multiply exponents that are on the same bases as each other.
