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
1/5 of a foot
Simply subtract the height of Pancho’s sandcastle (3/5 of a foot) minus the height of his sister’s sandcastle (2/5 of a foot) to find a difference of 1/5 of a foot, meaning Pancho’s sandcastle was 1/5 of a foot taller than his sister’s sandcastle.
That’s the answer because I couldn’t type it out! Hope it helped!
It’s 35 and 23 and also it can be mans at the the cakes
From the remainder theorem, the remainder will be -2 and the relationship between f(x) and x + 2 is an inverse relationship.
<h3>What is the remainder of the division of the given polynomial?</h3>
The remainder theorem is used to determine the remainder where a polynomial is divided by a binomial.
The remainder theorem states that if a polynomial p(x) is divided by a binomial x - a, the remainder of the division is p(a).
Given the following division, f(x)/ x + 2
We can rewrite the binomial in this form:
x + 2 = x - (-2)
The division then becomes:
f(x)/ x - (-2)
From the remainder theorem, the remainder will be -2.
Therefore, the relationship between f(x) and x + 2 is an inverse relationship such that f(2) = -2
Learn more about remainder theorem at: brainly.com/question/13328536
#SPJ1
