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4 years ago

Find the number of pairs (a,b) of integers such that a+2/a+5=b/3

Mathematics

1 answer:

Viktor [21]4 years ago

3 0

Answer:

Step-by-step explanation:

The expression can be rearranged to ...

b = 3 -9/(a+5)

In order for b to be an integer, (a+5) must be an integer divisor of 9. There are exactly 6 of those: ±1, ±3, ±9.

The attached table shows the values (a, b) = (x₁, f(x₁)).

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Answer:

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Step-by-step explanation:

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Fine length of BC on the following photo.

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Answer:

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Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

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step 2

In the right triangle ACD

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substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

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step 3

In the right triangle ABC

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$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

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Answer: look at the picture

Step-by-step explanation: Hope this help :D

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3 years ago

Your averages and values are the following:

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Answer: You need a grade of 78 on the final exam to earn a final grade average of at least 87 in each grading system.

Step-by-step explanation:

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