Confused on number 10. I put one solution, but I don’t know if it’s right. I got

Mathematics

1 answer:

velikii [3]3 years ago

4 0

4(3x + 12) = -6(-8-2x)
12x + 48 = 48 +12x
12x + 18 = 12x + 48
0 = 0
answer is A. infinitely many solutions

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How do you write out.32ft/sec to meters/min

marta [7]

32 ft
this is meters per second >>> 9.7536

6 0

3 years ago

Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

4 0

3 years ago

$10,000 at an annual rate of 7%, compounded semi-annually, for 2 years

forsale [732]

Answer:

$\$13,107.96$

Step-by-step explanation:

Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.

Therefore, we can set up the following equation to find the new balance after 2 years:

$\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}$