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3 years ago

Why is the product of negative reciprocals always -1?

Mathematics

1 answer:

erik [133]3 years ago

3 0

Answer:

please check the explanation.

Step-by-step explanation:

Let suppose we have a number = n

n≠0

The negative reciprocal of 'n' = -1/n

Taking the product of 'n' and its negative reciprocal '-1/n':

$n\left(-\frac{1}{n}\right)$

remove parentheses: (-a) = -a

$=-n\frac{1}{n}$

$\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}$

$=-\frac{1\times \:n}{n}$

$\mathrm{Cancel\:the\:common\:factor:}\:n$

$=-1$

Canceling the common factor (the number itself) will bring -1.

It proves that the multiplication of any number and its negative reciprocal will always yield -1.

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Need help on 9 don’t know if I did it right or not but I need help :p

solmaris [256]

Answer:

9b) -8 = y

9a) 72° = m∠ABC

Step-by-step explanation:

Since you have an angle trisector, in this case, m∠CBE ≅ m∠DBA, therefore you set x equal to 8, plus, according to Morley's Trisector Theorem, all three angles form an equilateral triangle, so m∠BOC also has to equal 24°:

${8}^{2} - 5(8) = 64 - 40 = 24 \\ \\ 6(8) - 24 = 48 - 24 = 24 \\ \\ 2(8) - y = 24 >> 16 - y = 24 >> -8 = y$

Then, m∠ABC comes from multiplying 3 by 24 [three twenty-four's], which results in 72°.

I am joyous to assist you anytime.

4 0

3 years ago

a triangle has a perimeter of 49 inches. the medium side is 7 more than the short side, and the longest side is 5 times the leng

slavikrds [6]

Short side length = x
Medium side = x + 7
Long side = 5x
Total 49, so
x + x + 7 + 5x = 49
If you combine like terms:
7x + 7 = 49
Subtract 7 from both sides
7x = 42
Divide both sides by 7
x = 6 inches

4 0

2 years ago

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A new Community Center is being built in Alston. The perimeter of the rectangular playing field is 308 yards. The length of the

Blababa [14]

Answer:

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Step-by-step explanation:

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3 years ago

For each container of tea, McKenzie uses 16 tea bags and 3 cups of sugar. If McKenzie uses 64 tea bags, how many cups of sugar w

cestrela7 [59]

So tis is a ratio 16 is to 3 or 16:3
if use 64 tea bags then how many cups of sugar so
turn 16:3 into fraction
16:3=16/3 or 3/16, it doesn't matter
then you want to find 64:x or 64/x or x/64

we know that 16/3=64/x because it tis an equivalent ratio
so 16/3=64/x
multiply both sdies by (3 times x)
16 times x times 3/3=64 times 3 times x/x
16 times x=64 times 3
16x=192
divide both sdies by 16
x=12
theanswer is 12 cups of sugar

5 0

3 years ago

Question 2 of 5

AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$

$f(n)=5+3(n-1)$

Therefore, the correct option is D, i.e., $f(n)=5+3(n-1)$ .

6 0

3 years ago

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