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Ulleksa [173]
3 years ago
6

X^2 + 4y^2 =100; 4y - x^2 = -20

Mathematics
1 answer:
deff fn [24]3 years ago
7 0
x^2+4y^2=100\implies x^2=100-4y^2
\implies 4y-(100-4y^2)=-20
\implies 4y^2+4y-80=0
\implies y^2+y-20=0
\implies (y-4)(y+5)=0
\implies y=4,y=-5

When y=4, you have

4(4)-x^2=-20\implies x^2=36\implies x=\pm6

When y=-5,

4(-5)-x^2=-20\implies x^2=0\implies x=0

So there are three solutions, (x,y)\in\{(6,4),(-6,4),(0,-5)\}.
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Anna11 [10]

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Blababa [14]
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5 0
4 years ago
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aliya0001 [1]

Answer:

x + 3y = 21

Step-by-step explanation:

(x_{1},y_{1})=(12,3) \\\\(x_{2},y_{2})=(-3,8)\\\\Slope= \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \dfrac{8-3}{-3-12}= \dfrac{5}{-15}\\\\= \dfrac{-1}{3}

Equation of the line: y =mx+ b

y =  \dfrac{-1}{3}x+b\\\\\\Plugin \ x = 12 \ and \ y=3 \ in \ the \ above \ equation\\\\3= \dfrac{-1}{3}*12+b\\\\3= -4+b\\\\3+4 = b\\\\b = 7\\\\\\\y=  \dfrac{-1}{3}x+7\\\\

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6 0
3 years ago
A factory employs skilled laborers at$25 per hour and unskilled laborers at $12 per hour. The total hourly cost of the factory’s
yarga [219]
For this case what you should do is the following system of equations:
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 y: unskilled laborers
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 x = 24-15
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 Answer:
 skilled laborers = 9
 unskilled laborers = 15
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saw5 [17]
R:{-46, 52}. You cannot repeat any numbers and the order is from least to greatest.
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