Answer:
5. 8
6. 18
Step-by-step explanation:
5.
a(a^2 + a - 1) + 7 =
= a^3 + a^2 - a + 7
For a = -1,
= (-1)^3 + (-1)^2 - (-1) + 7
= -1 + 1 + 1 + 7
= 8
6.
2ab(a + b) - 3ab(a - b) =
= 2a^2b + 2ab^2 - 3a^2b + 3ab^2
= -a^2b + 5ab^2
For a = 1 and b = 2,
= -(1)^2(2) + 5(1)(2)^2
= -1(2) + 5(4)
= - 2 + 20
= 18
Let any integer be represented by x.
Then, the consecutive integer (the number that follows) should be x+1.
The statement wants us to prove;
(x+1)²-x²=x+(x+1) <-- solve left hand side
x²+x+x+1²-x²
2x+1 (solution for left hand side)
Now solve for right hand side.
x+(x+1)= 2x+1
As noticed, the LHS=RHS (left hand side= right hand side), therefore, the difference of squared consecutive numbers subtracted is equal to the sum of the two integers.
Hope I helped :)
<h3>
Answer: 14 km per hour</h3>
=====================================================
Work Shown:
x = rowing speed when there is no current
c = speed of the current
speeds are in km per hour
-----------
Going downstream, i.e. with the current:
x+c = faster speed since the current is pushing you
distance = rate*time
d = r*t
40 = (x+c)*2
x+c = 40/2
x+c = 20
c = 20-x
-----------
Going upstream, i.e. against the current:
x-c = slower speed since the current is working against you
d = r*t
16 = (x-c)*2
16 = 2x-2c
2x-2c = 16
2(x-c) = 16
x-c = 16/2
x-c = 8
x-(20-x) = 8 ... plug in c = 20-x
x-20+x = 8
2x-20 = 8
2x = 8+20
2x = 28
x = 28/2
x = 14 km per hour is the rowing speed when there is no current
Side note: the speed of the current is c = 20-x = 20-14 = 6 km per hour.
