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2 years ago

[(-2)²×3]÷[(-9)-5+2]

Mathematics

2 answers:

Law Incorporation [45]2 years ago

8 0

-1 is the correct answer

Elodia [21]2 years ago

6 0

Answer:

-1

Step-by-step explanation:

1. To simplify this expression, let's go through the steps of BODMAS.

$\frac{(-2)^2(3)}{-9-5+2}$
$\frac{(4)(3)}{-9-5+2}$
$\frac{12}{-9-5+2}$
$\frac{12}{-14+2}$
$\frac{12}{-12}$
$-1$

Therefore, the answer is -1.

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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

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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

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3 years ago

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Mila [183]

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3 years ago

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3 years ago

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strojnjashka [21]

Answer:

After 11 weeks, Darnell′s savings account will have a total of $8,360.

Step-by-step explanation:

The data provided is as follows:

n: 1 2 3 4

f (n): 260 360 460 560

Consider the data for f (n).

The series f (n) follows an arithmetic sequence with a common difference of 100 and first term as 260.

The nth term of an arithmetic sequence is:

$a_{n}=\frac{n}{2}[2a+(n-1)d]$

Compute the value of f (11) as follows:

$f(11)=\frac{11}{2}[(2\times260)+(11-1)\times 100]$

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3 years ago

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Answer:

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