You have to understand how piecewise functions first
I hope you do because I won't be explaining it here
1.
if it is continiuous at x=1 then the part of the function that approaches 1 from the left is the same value
so we have f(x)=3-x for x<1, so evaluate it for x=1,
we would get 3-1=2
so
if a=2 and b=3
f(x)=2x²+3x
for x=1, we get 2+3=5
it approaches 2 from the left but equals 5
2≠5
so it is not continuous because it doesn't approach the same value at x=1
2.
alright
so we established that it should approach 2 because we had the f(x)=3-x
so
f(1)=2=ax²+bx
2=a+b
the relationship is 2=a+b
3.
same as before, but use the other function, the one that is defined at x≥2
5x-10, 5(2)-10, 10-10, 0
it approaches 0
so
we must find one such that f(x)=0 for x=2 with the ax²+bx
0=a(2)²+b(2)
0=4a+2b
if we minus 2b both sides
-2b=4a
divide by 2
-b=2a
add b both sides
0=2a+b
4.
2=a+b
0=2a+b
2=a+b
minus b both sides
2-b=a
subsitute
0=2a+b
0=2(2-b)+b
0=4-2b+b
0=4-b
b=4
sub back
2-b=a
2-4=a
-2=a
a=-2
b=4
5.
graph f(x)=-2x²+4x from x=1 to x=2 and put a closed dot at (1,2) and an open dot at (2,0)
<span>YES..., because the whole number is 100%, 120% proves that the result is 20% more than the whole number.</span>
So, first you subtract 10 from 38 which gives three times of the money spent for the movie. Then you divide 3 from it to give you the answer.
38-10 = 28
28/3 = 9.37 dollars
For 1. To estimate how many sports cards Alberto had, you would round each number to the nearest ten, so 318 would become 320. 273 would then become 270. You would then add those two and would get 590. So, Alberto had 590 sports cards (estimated). If you were looking for the actual answer (not estimated) , you would get 591.
Answer:
1) 3x = 2x + 50
3x - 2x = 50
X= 50
2)6x = 2x + 44
6x - 2x = 44
4x = 44
divide both sides by 4
X = 11
3)8x = 2x + 36
8x - 2x = 36
4x = 36
divide both sides by 4
X = 9
4) 4x = X + 18
4x - X = 18
3x = 18
divide both sides by 3
X= 6
5) 7x + 10 = 3x + 120
collect like terms
7x - 3x = 120 - 10
4x = 110
divide both sides by 4
X = 27.5
6) 20 + 2x = X + 56
collect like terms
2x - X = 56 - 20
X = 36
7) already done
8)12x + 12 = 3x + 84
collect like terms
12x - 3x = 84 - 12
9x = 72
divide both sides by 9
X = 8
9) 3 + 6x = 2x + 27
collect like terms
6x - 2x = 27 - 3
4x = 24
divide both sides by the coefficient of X (4)
X = 6
10) 8x + 2 = 72 + X
collect like terms
8x - X = 72 - 2
7x = 70
divide both sides by the coefficient of X (7)
X = 10
11) 2x + 20 = X + 60
collect like terms
2x - X = 60 - 20
X = 40
12). 4x + 1 = 25 + 2x
collect like terms
4x - 2x = 25 - 1
2x = 24
divide both sides by the coefficient of X (2)
X = 12
I hope this helps
