What is one of the solutions to the following system of equations?y^2+x^2=53
y-x=5
a)(-10,-5)
b)(-7,-2)
c)(7,2)
d)(5,10)

Answers

Answer 1

Answer: $y^2+x^2=53 \ny-x=5 \n \n\hbox{solve the 1st equation for y:} \ny-x=5 \ny=5+x \n \n\hbox{substitute 5+x for y in the 1st equation:} \n(5+x)^2+x^2=53 \n25+10x+x^2+x^2=53 \n2x^2+10x+25-53=0 \n2x^2+10x-28=0 \n2x^2+14x-4x-28=0 \n2x(x+7)-4(x+7)=0 \n(2x-4)(x+7)=0 \n2x-4=0 \ \lor \ x+7=0 \n2x=4 \ \lor \ x=-7 \nx=2 \ \lor \ x=-7 \n \ny=5+x \ny=5+2 \ \lor \ y=5-7 \ny=7 \ \lor \ y=-2 \n \n(x,y)=(2,7) \ or \ (x,y)=(-7,-2)$

The answer is B.

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An investment counselor calls with a hot stock tip. he believes that if the economy remains strong, the investment will result in a profit of $50 comma 000. if the economy grows at a moderate pace, the investment will result in a profit of $10 comma 000. however, if the economy goes into recession, the investment will result in a loss of $50 comma 000. you contact an economist who believes there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. what is the expected profit from this investment?

Answers

Answer: $ 16,000 profit

Step-by-step explanation:

Given the following :

Profit when economy is strong = 50,000

Profit when economy is moderate = 10,000

Loss when economy goes into recession = 50000

Resulting probabilities of the three probable occurrences are:

Probability of strong economy; p(strong) = 30/100 = 0.3

Probability of moderate; P(moderate) = 60/100 = 0.6

Probability of recession; P(recession) = 10/100 = 0.1

Expected profit :

Summation of the product of each probability and its accompanying profit or loss.

P(strong) × profit of strong = 0.3 × 50000 = 15000

P(moderate) × profit of moderate = 0.6 × 10000 = 6000

P(recession) × loss on recession = 0.1 × 50000 = 5000 = - 5000 ( loss)

Expected profit :

$(15,000 + 6000 - 5000) = $16,000 profit

Assume that the line passes through the point (−2,4) and is parallel to the line through the points ( −4,4) and (−5,−1).find the equation of this line in slope intercept form.

Answers

let m be the slope and b the y-intercept.

m=(y₂-y₁)/(x₂-x₁)

m= (-1-4)/(-5-(-4))

m= 6

y=mx+b

4=6(-4)+b

b=28

y=6x+28

(-2,4)

parallel means the slopes are the same:

4=6(-2)+b

4=-12+b

b=16

y=6x+16

103 is 20% of what number