Answer:
Step-by-step explanation:
To prove that
is a multiple of 7.
Proof by induction:
Let n =1. Then we have 8-1 =7 is a multiple of 7
Thus the P(1) is true.
Let us assume that P(n) is true.
= 7l is true for some integer l
To check for P(n+1)
=LHS
=
Thus we find that this is also a multiple of 7.
If true for n, then true for n+1
Hence we find that since true for 1, we have it is true for all natural numbers.
17. Subtraction. According to the order of operations, he should've done the exponent of 3 first.
18. He then did 15×2. According to the order of operations, he should've done the multiplication of 8×2, since, if there are only multiplication and/or division left, you work left to right. He isn't correct.
19. 16, I think, I did it in my head.
Answer:
13.9
Step-by-step explanation:
Use Pythagorean Theorem:
Both of the lengths given are the legs,
13.5^2 + 3.2^2 = c^2
182.25 + 10.24 = c^2
192.49 = c^2
13.87 = c
Just differentiate <em>G</em> and <em>H</em> :
• d<em>G</em>/d<em>x</em> = d(<em>x</em> ² <em>eˣ </em>)/d<em>x</em> = 2<em>x</em> <em>eˣ</em> + <em>x</em> ² <em>eˣ</em>
so <em>G</em> is not an antiderivative of <em>f</em>.
• d<em>H</em>/d<em>x</em> = d(2<em>x</em> <em>eˣ</em> - 2<em>eˣ</em> ) = (2<em>eˣ</em> + 2<em>x</em> <em>eˣ</em> ) - 2<em>eˣ</em> = 2<em>x</em> <em>eˣ</em> = <em>f(x)</em>
so <em>H</em> is indeed an antiderivative of <em>f</em>.
How many blocks away from school does she live now is 9 blocks away from school.
First step is to calculate the number of blocks between the house she was living before and the school
Blocks=42 blocks/3
Blocks=14 blocks
Second step is to calculate how many blocks away from school does she live now
Number of blocks=14 blocks- 5 blocks
Number of blocks=9 blocks
Inconclusion How many blocks away from school does she live now is 9 blocks away from school
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