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laila [671]
3 years ago
14

Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. Steps Reasons 1.

A over b plus c over d Given 2. Ad over bd plus cb over bd Multiply to get a common denominator 3. Simplify Fill in the missing step in the proof. ad times cb all over bd ad plus cb all over bd ad minus cb all over bd ad plus cb all over two times bd
Mathematics
2 answers:
harkovskaia [24]3 years ago
6 0

Answer:

\dfrac{ad+bc}{bd}

Step-by-step explanation:

Let \frac{a}{b} and \frac{c}{d} be two rational numbers, where b and d are not zero and a, b, c and d are integers.

1. Given:

\dfrac{a}{b}+\dfrac{c}{d}

2. Multiply to get a common denominator :

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}

3. Simplify:

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}=\dfrac{ad+bc}{bd}

4. Since b\neq 0,\ d\neq 0, then bd\neq 0.

If a,b,c,d are integers, then bd, ad,bc, ad+bc are integers too. So the fraction

\dfrac{ad+bc}{bd}

is a rational number

LuckyWell [14K]3 years ago
3 0

Answer:

c

Step-by-step explanation:

i took the test

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Answer:

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Step-by-step explanation:

Distribute the Negative Sign:

=3v5+8v3−10v2+−1(−12v5+4v3+14v2)

=3v5+8v3+−10v2+−1(−12v5)+−1(4v3)+−1(14v2)

=3v5+8v3+−10v2+12v5+−4v3+−14v2

Combine Like Terms:

=3v5+8v3+−10v2+12v5+−4v3+−14v2

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Answer:

=15v5+4v3−24v2

Hope this helps! :)

5 0
3 years ago
Tiana has already taken 1 page of notes on her own, and she will take 1 page during each hour of class. In all, how many hours w
Novosadov [1.4K]

Answer:

<u>42 Hours.</u>

Step-by-step explanation:

As an equation where y is the total pages and x is hours of class:

y=1+1x since she started with 1 page and does 1 page per hour.

Setting the total pages she needs as 43 (y=43) we get:

43=1+1x

Subtract one on both sides

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x=42

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