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kenny6666 [7]
3 years ago
14

How many four-digit positive integers are multiples of 3?

Mathematics
1 answer:
Musya8 [376]3 years ago
7 0

Answer:

  3000

Step-by-step explanation:

There are 9000 positive 4-digit numbers (all between 1000 and 9999, inclusive). 1/3 of those are multiples of 3, so there are ...

  3000 four-digit multiples of 3

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Step-by-step explanation:

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3 years ago
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Perform the indicated operations. Write the answer in standard form, a+bi.<br> 5-3i / -2-9i
Vsevolod [243]

\huge \boxed{\mathfrak{Answer} \downarrow}

\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\

Multiply both numerator and denominator of \sf \frac{5-3i}{-2-9i} \\ by the complex conjugate of the denominator, -2+9i.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)})  \\

Multiplication can be transformed into difference of squares using the rule: \sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}})  \\

By definition, i² is -1. Calculate the denominator.

\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85})  \\

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85})  \\

Do the multiplications in \sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right).

\large \bf \: Re(\frac{-10+45i+6i+27}{85})  \\

Combine the real and imaginary parts in -10+45i+6i+27.

\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85})  \\

Do the additions in \sf-10+27+\left(45+6\right)i.

\large \bf Re(\frac{17+51i}{85})  \\

Divide 17+51i by 85 to get \sf\frac{1}{5}+\frac{3}{5}i \\.

\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i)  \\

The real part of \sf \frac{1}{5}+\frac{3}{5}i \\ is \sf \frac{1}{5} \\.

\large  \boxed{\bf\frac{1}{5} = 0.2} \\

3 0
2 years ago
HELP “The vertical supports in this truss bridge are built so that
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Answer:

The statement that is not true is;

c) m∠ABO = m∠ODC

Step-by-step explanation:

With the assumption that the lengths AO, and OD are equal, we have that in ΔABO and ΔOCD, the following sides are corresponding sides;

Segment AO on ΔABO is a corresponding side to segment OD on ΔOCD

Vertices B and C on ΔABO and ΔOCD are corresponding vertices

Therefore;

Segments AB and OB on ΔABO are corresponding sides to segments OC and OD on ΔOCD respectively

Therefore, ∠ABO on ΔABO is the corresponding angle to ∠OCD on ΔOCD

Given that ΔABO ≅ ΔOCD, we have that ∠ABO ≅ ∠OCD

Therefore;

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Answer:

yes it is true

Step-by-step explanation:

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