The answer looks like it's A.
1. 31 2. 56ft 3. 16 4. 7 5. 20ft
Answer:
first piece = 5 m
second piece = 2(5) + 2 = 12 m
third piece = 3(2x + 2) = 6(5) + 6 = 36 m
Step-by-step explanation:
The question is incomplete, the length of the actual rope is unknown but it should be given . Let us assume the length of the rope is 53 meters.
The rope is cut into 3 pieces of different length.
first piece = x
second piece = 2x + 2
third piece = 3(2x + 2) = 6x + 6
Since the length of the actual rope is assumed to be 53 meters .The length of the first piece, second piece and third piece can be calculated as follows.
we add the length of the pieces to get the actual length of each piece. Therefore,
x + 2x + 2 + 6x + 6 = 53
collect like terms
9x + 8 = 53
9x = 53 - 8
9x = 45
x = 45/9
x = 5 meters
first piece = 5 m
second piece = 2(5) + 2 = 12 m
third piece = 3(2x + 2) = 6(5) + 6 = 36 m
I'm assuming that you meant:
1
f(x) = -------- and that you want to find the value of x at which f(x) = h(x).
x+1
Of course you could create a table for each f(x) and h(x), but setting f(x)=h(x) and solving for x algebraically would be faster and more efficient:
1
f(x) = -------- = 2x + 3 = h(x). Then 1 = (x+1)(2x+3) = 2x^2 + 3x + 2x + 3
x+1
or 1 = 2x^2 + 5x + 3, or 2x^2 + 5x + 2 = 0.
This is a quadratic equation with a=2, b=5 and c=2. The discriminant is b^2-4ac, or 5^2-4(2)(2), OR 25-16= 9.
Thus, the roots are
-5 plus or minus sqrt(9)
x = ------------------------------------
2(2)
-5 plus or minus 3
= ----------------------------------
4
= {-1/2, -2}
Thus, f(x) = h(x) at both x=-1/2 and x= -2.
Answer:
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.