Answer:
The gcd(259, 621) = 1 and gcd(108, 156) = 12
Step-by-step explanation:
The Euclidean algorithm solves the problem:
Given integers a, b, find d = gcd(a,b)
These are the steps of the Euclidean algorithm:
- Let a = x, b = y.
- Given x, y use the division algorithm to write
where q is quotient and r is the remainder - If r = 0, stop and output y; this is the gcd of a, b.
- if r ≠ 0, replace (x, y) by (y,r). Go to step 2.
These are the steps for the division algorithm:
- Subtract the divisor from the dividend repeatedly until we get a result that lies between 0 and the divisor
- The resulting number is known as the remainder, and the number of times that the divisor is subtracted is called the quotient.
To find the greatest common divisor of 621 and 259 by the Euclidean algorithm you need to:
- Divide 621 by 259, applying the division algorithm you get
next you need to write the expression 
- Divide 259 by 103 to write
- Divide 103 by 53 to write
- Divide 53 by 50 to write
- Divide 50 by 3 to write
- Divide 3 by 2 to write
- Divide 2 by 1 to write
The greatest common divisor of 621 and 259 is 1
To find the greatest common divisor of 156 and 108 by the Euclidean algorithm you need to:
- Divide 156 by 108 to write
- Divide 108 by 48 to write
- Divide 48 by 12 to write
The greatest common divisor of 156 and 108 is 12
The complete question in the attached figure
we know
In a rhombus ABCD<span> , </span>AC <span> = 26 , </span>AB<span> = 14
</span><span>the diagonals of a rhombus are perpendicular bisectors of each other
</span>AX<span> = </span>XC<span> = 13. triangle </span>ABX<span> is a right triangle with hypotenuse 14.
</span>
From the pythagoras theorem AB² =<span> AX</span>² + BX²
14² = 13² + BX²
196 = 169 + BX²
27 = BX²----- > BX=√27
BX = 5.20
Area of ABX<span> triangle=(1/2)*5.2*13=33.77
</span>
The four triangles formed by construction of the diagonals are all congruent since the diagonals are perpendicular bisectors.
Total area of the rhombus is 4 times of ABX triangle
<span>Area = 4* 33.77=135.10 units</span>²
the answer is the option D) 135.1 units ²
Answer:
The reasonable domain to plot the growth function is the interval [0,9]
Step-by-step explanation:
In this problem we have a exponential function of the form
where
f(d) is the radius of the algae in mm
d is the number of days
a is the initial value or y-intercept
b is the base
r is the rate of growth
b=1+r
we have
we have
For f(d)=12.81 mm
substitute in the function and solve for d
Apply log both sides
therefore
The reasonable domain to plot the growth function is the interval [0,9]
To find the answer, just divide 77 by 6. This gets you 12.83. (simplified) 12.83 is also your answer. I hope this helps!
