Answer:
Step-by-step explanation:
![\frac{1}{2} x=a=\frac{2}{3} y\\\frac{1}{2}x=a\\x=2a \\\frac{2}{3} y=a\\y=\frac{3}{2} a\\x+y=2a+\frac{3}{2} a=\frac{4a+3a}{2} =\frac{7}{2} a=na\\n=\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x%3Da%3D%5Cfrac%7B2%7D%7B3%7D%20y%5C%5C%5Cfrac%7B1%7D%7B2%7Dx%3Da%5C%5Cx%3D2a%20%5C%5C%5Cfrac%7B2%7D%7B3%7D%20y%3Da%5C%5Cy%3D%5Cfrac%7B3%7D%7B2%7D%20a%5C%5Cx%2By%3D2a%2B%5Cfrac%7B3%7D%7B2%7D%20a%3D%5Cfrac%7B4a%2B3a%7D%7B2%7D%20%3D%5Cfrac%7B7%7D%7B2%7D%20a%3Dna%5C%5Cn%3D%5Cfrac%7B7%7D%7B2%7D)
Answer:
8 and 16
Step-by-step explanation:
Answer: 8
You just need to multiply the numerator (top number) by the 12
2x12=24
so now its 24/3
24/3 simplified is 8
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
<h3>Completing the square </h3>
From the question, we are to solve the given quadratic equation by completing the square
The given equation is
z² +8z - 44 =20
First, add 44 to both sides of the equation
z² +8z - 44 + 44 = 20 + 44
z² +8z = 64
Now, divide the coefficient of z by 2, square the value and add to both sides
The coefficient of z is 8
Dividing
8/2 = 4
Squaring
4²
Now, add this to both sides
That is,
z² +8z +4² = 64 + 4²
(z + 4)² = 64 + 16
(z + 4)² = 80
The equation after completing the square is
(z + 4)² = 80
Continuation
(z + 4)² = 80
Take the square root of both sides
√(z + 4)² = ±√80
z + 4 = ±√80
z = -4 ± √80
z = -4 ± 4√5
z = -4 + 4√5 and z = -4 - 4√5
Hence,
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
Learn more on Completing the square here: brainly.com/question/49444
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Answer:
Yes
Step-by-step explanation: