3x^2=375
x^2=125
x=11.18
c or d, they say the same thing
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:
B
Step-by-step explanation:
Using the determinant to determine the type of zeros
Given
f(x) = ax² + bx + c ( a ≠ 0 ) ← in standard form, then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct zeros
• If b² - 4ac = 0 then 2 real and equal zeros
• If b² - 4ac < 0 then 2 complex zeros
Given
f(x) = (x - 1)² + 1 ← expand factor and simplify
= x² - 2x + 1 + 1
= x² - 2x + 2 ← in standard form
with a = 1, b = - 2, c = 2, then
b² - 4ac = (- 2)² - (4 × 1 × 2) = 4 - 8 = - 4
Since b² - 4ac < 0 then the zeros are complex
Thus P(x) has no real zeros
now, with that template above in mind, let's see this one
A=3, B=1, shrunk by AB or 3 units, about 1/3
C=2, horizontal shift by C/B or 2/1 or just 2, to the left
D=4, vertical shift upwards of 4 units
check the picture below
