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inna [77]
3 years ago
9

Does 23^-1 (mod 1000) exist? If yes solve it.

Mathematics
1 answer:
sweet [91]3 years ago
3 0

Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).

Let <em>x</em> be the inverse. Then <em>x</em> is such that

23<em>x</em> ≡ 1 (mod 1000)

Use the Euclidean algorithm to solve for <em>x</em> :

1000 = 43×23 + 11

23 = 2×11 + 1

→   1 ≡ 23 - 2×11   (mod 1000)

→   1 ≡ 23 - 2×(1000 - 43×23)   (mod 1000)

→   1 ≡ 23 - 2×1000 + 86×23   (mod 1000)

→   1 ≡ 87×23 - 2×1000 ≡ 87×23   (mod 1000)

→   23⁻¹ ≡ 87   (mod 1000)

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The size of angle aob is equal to 132 degrees and the size of angle cod is equal to 141 degrees. find the size of angle dob.
Varvara68 [4.7K]

angle AOB = 132 and is also the sum of angles AOD and DOB. Hence 
angle AOD + angle DOB = 132°    ---> 1 

angle COD = 141 and is also the sum of angles COB and BOD. Hence 
angle COB + angle DOB = 141°    ---> 2

Now we add the left sides together and the right sides of equations 1 and 2 together to form a new equation. 

angle AOD + angle DOB + angle COB + angle DOB = 132 + 141       ---> 3 

We should also note that: 
angle AOD + angle DOB + angle COB = 180° 

Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180 and solving for angle DOB:
180 + angle DOB = 132 + 141 
angle DOB = 273 - 180 = 93° 

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8 0
2 years ago
Write 0.0059 in scientific notation.
polet [3.4K]
Hi!

When we write a number in scientific notation, we write it like this:
N × 10^{x}

N = a number between one and 10
x = negative if the decimal is moved to the right. positive if moved to the left.

Okay, so we need to move the decimal in the number <span>0.0059 to the right to make it between one and 10.
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Since we moved the decimal to the right 3 times,
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7 0
3 years ago
Read 2 more answers
Jay King, owner of a local Bed and Bath Store knows that his customers will only pay at most, $299 for a blow up bed. Assuming J
Roman55 [17]
If you would like to know the price Jay can pay the manufacturer for the blow up bed, you can calculate this using the following steps:

100% + 40% = 140%

140% of x is $299
140% * x = 299
140/100 * x = 299      /*100/140
x = 299 * 100 / 140
x = $213.6

40% of $213.6 = 40% * 213.6 = 40/100 * 213.6 = 85.44
$213.6 + $85.44 = $299

The correct result would be $213.6.
6 0
3 years ago
The product of a number and the difference of the number and 5
tatiyna
X(x-5)
this is because product is multiplcation and difference is subtraction. The multiplication of a subtraction problem is distribution

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