Answer:
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.
Step-by-step explanation:
Since it is a cube, all sides lengths are the same.
Surface area = 2lw+2lw+2hw
if you substitute all the sides for 13 you get
2(169) three times
so you multiply and get 338 three times so you do 338x3 which is 1014 cm
its messy to explain so i attached a photo
2/3(6c+4)-(8c-5)
1) Get rid of the negative signs
New equation (the ones in bold are the changes): 2/3(6c+4)+(-8c)+(5)
2) Use distributive property for the first part by multiplying 2/3*6c= 4c and 2/3*4= 2 2/3
New equation: 4c+2 2/3+ (-8c) + 5
3) Combine like terms: 4c+(-8c)= -4c and 2 2/3+5= 7 2/3
New and simplified equation: -4c+ 7 2/3
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:
add, subtract, multiply and divide complex numbers much as we would expect. We add and subtract
complex numbers by adding their real and imaginary parts:-
(a + bi)+(c + di)=(a + c)+(b + d)i,
(a + bi) − (c + di)=(a − c)+(b − d)i.
We can multiply complex numbers by expanding the brackets in the usual fashion and using i
2 = −1,
(a + bi) (c + di) = ac + bci + adi + bdi2 = (ac − bd)+(ad + bc)i,
and to divide complex numbers we note firstly that (c + di) (c − di) = c2 + d2 is real. So
a + bi
c + di = a + bi
c + di ×
c − di
c − di =
µac + bd
c2 + d2
¶
+
µbc − ad
c2 + d2
¶
i.
The number c−di which we just used, as relating to c+di, has a spec
