Answer:
1. value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice
2. evaluates at x = -1; remainder is -11 . . . . first choice
Step-by-step explanation:
Dividing f(x) by (x -a) gives ...
f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r
If we multiply this expression by (x -a), we see ...
f(x) = (x -a)g(x) +r
so
f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a
f(a) = 0 +r
f(a) = r . . . . . . . . . a statement of the remainder theorem
If r=0, then x-a is a factor of f(x) = (x-a)g(x).
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1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.
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2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.
Answer:
33
Step-by-step explanation:
Answer:
13% chance
Step-by-step explanation:
Area of backyard = length * width
A = 30 ft * 20 ft
A = 600 
Area of bathtub = π 
A = π * 
A = 78.54
Probability of arrow landing in tub can be found by dividing Area of the bathtub by the area of the backyard, and then multiplying by 100 for a percentage
Prob. = 78.54/600
Prob. = 0.13
Prob. = 0.13 * 100
Prob. = 13%
Answer:
16 bicycles and 21 tricycles
Step-by-step explanation:
Both bicycles and tricycles have 1 set of handlebars. Bicycles have 2 wheels while tricycles have 3.
Using this information, set up a system of equations, where b is the number of bicycles and t is the number of tricycles:
b + t = 37
2b + 3t = 95
Solve by elimination by multiplying the top equation by -2:
-2b - 2t = -74
2b + 3t = 95
t = 21
Then, plug in 21 as t into one of the equations:
b + t = 37
b + 21 = 37
b = 16
So, there are 16 bicycles and 21 tricycles
