The answer would be 9 because
Let, one leg be x units.
since the other leg is 9.0 units shorter than the other,
the measure of the other leg =x-9
hypotenuse =13.0 units
According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.
x^2 +(x-9)^2 =13^2
x^2 + x^2 -18x +81 = 169
2x^2-18x-88=0
Divide the whole equation by 2
x^2 - 9x -44 =0
Let's use the quadratic formula to find the roots.
formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a
a=1 b=-9 c=-44
x= [9±sqrt(81+176)]/2
=[9±sqrt(257)]/2
=[9±16.03]/2
=25.03/2 or -7.03/2
length of a triangle cannot be negative,
Therefore, x=25.03/2 =12.52
one leg =12.5 units
other leg =12.52-9 =3.5 units
Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
<h3>What is the Inscribed Angle Theorem?</h3>
Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
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The lengths of the two segments below then tell whether they are congruent
YZ = 4
XW = 12
not congruent
This is further explained below.
<h3>What is a number line?</h3>
Generally, A number line is a depiction of a graded straight line that serves as an abstraction for real numbers, which are symbolized by the
Number lines are used in introductory mathematics. It is generally accepted that a real number may be assigned to each point on a number line and that each point can be assigned to a real number.
YZ = Z - Y = 1 -(-3) = 4
XW = W -X = 5 -(-7) = 12
Because the segments are not the same length, they cannot be considered congruent.
In conclusion, It is self-evident that segment YZ will not have the same length as segment XW since it is just a portion of the latter.
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