1. Consider the rational numbers 4/13 and 3/10 .

2 answers:

4 0

There are infinite rational numbers between the two numbers you have given
Why not start with the one midway between the two?
Since 3/10 = 39/130 < 4/13 = 40/130
a = (39 + 40)/260 = 79/260
will do for a start.

yaroslaw [1]4 years ago

3 0

A. 4/13 3/10

find a common denominator which is 130

mult. by 10/10 and the second one by 13/13

40/130 and 39/130

so, that means 4/13 is larger because after you find a common denominator, compare the top numbers to find the larger and 40 is larger than 39.

B. a rational number between them would be 39.5/130

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It’s confusing, would the answer be square root 7 over 4?

Colt1911 [192]

Answer:

$\tan U = 1$

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$\text{Apply Pythagorean theorem,}\\\\~~~~~~\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2\\\\\implies UT^2 = UV^2 +VT^2\\\\\implies UV^2 = UT^2 -VT^2\\\\\implies UV^2 = \left(7\sqrt 2 \right)^2 - 7^2\\\\\implies UV^2 = 49(2)-49\\\\\implies UV^2 = 49\\\\\implies UV = \sqrt{49} \\\\ \implies UV = 7$