A)
Earlier, The length of the angelfish = 
inches
Now, the length of angelfish = 
inches
We have to determine the grown length of angelfish
= -
= 
LCM of '2' and '3' is '6',
= 
= 
inch
Therefore, the angelfish has grown by inch.
B)
We have to determine the increased length of angelfish in feet.
Since 
foot
So, 
= 0.069 foot.
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:
A
Step-by-step explanation:
Given the zeros are x = - 1 and x = 3 then the factors are
(x + 1) and (x - 3) and the parabola is the product of the factors, that is
y = a(x + 1)(x - 3) ← where a is a multiplier
To find a substitute (0, - 9) into the equation
- 9 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
3 = a, thus
y = 3(x + 1)(x - 3) ← expand the factors using FOIL
= 3(x² - 2x - 3) ← distribute by 3
= 3x² - 6x - 9 → A
