Number of zids=x
number of zods=y
number of zid legs=5x
number of zod legs=7y
so
5x+7y=140
try to get it into slope intercept from so you can graph is (y=mx+b)
5x+7y=140
subtract 5x from both sides
7y=140-5x
divide both sides by 7
y=20-5/7x
y=-5/7x+20
plug in numbers for x and get numbers for y (you can only plug in multiples of 7 for x so that there are a whole number of zids and since you are counting, x and y must never be negative)
lets try 0 for x
y=-5/7(0)+20
y=20
so x=0 and y=20 is an answer (if you can have only one of that species)
lets try 7 for x
y=-5/7(7)+20
y=-5+20
y=15
so x=7 and y=15 is an answer
lets try 14 for x
y=-5/7(14)+20
y=-10+20
y=10
so x=14 and y=10 is another answer
lets try 21 for x
y=-5/7(21)+20
y=-15+20
y=5
so x=21 and y=5 is another answer
lets try 28 for x
y=-5/7(28)-20
y=-20+20
y=0
so x=28 and y=0 is an answer (if there can be only one of a species)
if we go further, then y will be negative so the answers are
(x,y)
(0,20)
(7,15)
(14,10)
(21,5)
(28,0)
if it is allowed that only one species exists then there are 5 possible answers
if both must exist simultaneously, then there are only 3 answers
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Answer: 12
Step-by-step explanation:
6y - 3z
6(4) - 3(4)
24 - 12
12
Answer:
45cm
Step-by-step explanation:
Volume of a sphere = 4/3πr³
Volume of an hemisphere = 1/2 of volume of a sphere
Volume of hemisphere = 1/2{4/3πr³}
Volume of hemisphere = 2/3πr³
Given
Volume of the hemisphere = 60,750πcm³
60,750π = 2/3πr³
π cancels out
60,750 = 2/3r³
Multiply both sides by 3
2r³ = 60,750×3
2r³=182,250
Divide both sides by 2
r³ = 91,125
Find the ∛ of 91,125 to eliminate the cube on r
r = ∛91,125
r = 45cm
After solving ![\sqrt[5]{128x^8y^2}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B128x%5E8y%5E2%7D)
we get ![2x\sqrt[5]{4}\sqrt[5]{x^3}\sqrt[5]{y^2}](https://tex.z-dn.net/?f=2x%5Csqrt%5B5%5D%7B4%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D)
Step-by-step explanation:
We need to solve
Applying the rule: ![\sqrt[a]{xy}=\sqrt[a]{x}.\sqrt[a]{y}](https://tex.z-dn.net/?f=%5Csqrt%5Ba%5D%7Bxy%7D%3D%5Csqrt%5Ba%5D%7Bx%7D.%5Csqrt%5Ba%5D%7By%7D)
![\sqrt[5]{128x^8y^2}\\=\sqrt[5]{128}\sqrt[5]{x^8}\sqrt[5]{y^2}\\We\,\,know\,\,that\,\,128=2\times2\times2\times2\times2\times2\times2=2^7\,\,or\,\,2^5.2^2\\=\sqrt[5]{2^5.2^2}\sqrt[5]{x^5.x^3}\sqrt[5]{y^2}\\=(2^5)^{\frac{1}{5}}\sqrt[5]{2^2}\sqrt[5]{x^5}\sqrt[5]{x^3}\sqrt[5]{y^2}\\=2x\sqrt[5]{4}\sqrt[5]{x^3}\sqrt[5]{y^2}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B128x%5E8y%5E2%7D%5C%5C%3D%5Csqrt%5B5%5D%7B128%7D%5Csqrt%5B5%5D%7Bx%5E8%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5CWe%5C%2C%5C%2Cknow%5C%2C%5C%2Cthat%5C%2C%5C%2C128%3D2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%5Ctimes2%3D2%5E7%5C%2C%5C%2Cor%5C%2C%5C%2C2%5E5.2%5E2%5C%5C%3D%5Csqrt%5B5%5D%7B2%5E5.2%5E2%7D%5Csqrt%5B5%5D%7Bx%5E5.x%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5C%3D%282%5E5%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%5Csqrt%5B5%5D%7B2%5E2%7D%5Csqrt%5B5%5D%7Bx%5E5%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D%5C%5C%3D2x%5Csqrt%5B5%5D%7B4%7D%5Csqrt%5B5%5D%7Bx%5E3%7D%5Csqrt%5B5%5D%7By%5E2%7D)
So, After solving we get
Keywords: Solving with Exponents
Learn more about Solving with Exponents at:
#learnwithBrainly
