Answer:
0.280
Step-by-step explanation:
Answer:
a)g: 3x + 4y = 10 b) a:x+y = 5 c) c: 3x + 4y = 10
h: 6x + 8y = 5 b:2x + 3y = 8 d: 6x + 8y = 5
Step-by-step explanation:
a) Has no solution
g: 3x + 4y = 10
h: 6x + 8y = 5
Above Equations gives you parallel lines refer attachment
b) has exactly one solution
a:x+y = 5
b:2x + 3y = 8
Above Equations gives you intersecting lines refer attachment
c) has infinitely many solutions
c: 3x + 4y = 10
d: 6x + 8y = 5
Above Equations gives you collinear lines refer attachment
i) if we add x + 2y = 1 to equation x + y = 5 to make an inconsistent system.
ii) if we add x + 2y = 3 to equation x + y = 5 to create infinitely system.
iii) if we add x + 4y = 1 to equation x + y = 5 to create infinitely system.
iv) if we add to x + y =5 equation x + y = 5 to change the unique solution you had to a different unique solution
surface area (S) of a right rectangular solid is:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
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you have:
L = 7
W = a
H = 4
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formula becomes:
S = 2*7*a + 2*7*4 + 2*a*4
simplify:
S = 14*a + 56 + 8*a
combine like terms:
S = 22*a + 56
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answer is:
S = 22*a + 56 (equation 2)
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to prove, substitute any value for a in equation 2:
let a = 15
S = 22*a + 56 (equation 2)
S = 22*15 + 56
S = 330 + 56
S = 386
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since a = 15, then W = 15 because W = a
go back to equation 1 and substitute 15 for W:
S = 2*L*W + 2*L*H + 2*W*H (equation 1)
where:
L = length
W = width
H = height
-----
you have:
L = 7
W = 15
H = 4
-----
equation 1 becomes:
S = 2*7*15 + 2*7*4 + 2*15*4
perform indicated operations:
S = 210 + 56 + 120
S = 386
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surface area is the same using both equations so:
equations are good.
formula for surface area of right rectangle in terms of a is:
S = 22*a + 56
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Assume that each material in each category has an equal chance of being selected.
Categories:
(a) Type of wood used to make the cabinet: birch, maple, cherry.
Each type of wood has a probability of 1/3 to be selected.
(b) Type of finish: transparent, semi-transparent.
Each type of finish has a probability of 1/2 to be selected.
(c) Knob: bronze, steel, wood.
Each material has 1/3 probability to be selected.
Each event (selecting material for the cabinet, for the finish, and for the knob) is an independent event.
Therefore
Probablity(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cheryy wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6
Answer:
(x+1)^2
Step-by-step explanation:
(g ° f) (x) = g(f(x))
g ( f(x)) means that you are going to replace x in g(x) for f(x)
g(x) = x^2
f(x) = x+1
So you have to solve g(x) when x = x+1
g (x+1) = (x+1)^2
