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Mumz [18]
3 years ago
13

Graph the line given by 5x+6y=12 and the circle given by x²+y²=1.Find all solutions to the system of equations.

Mathematics
1 answer:
kenny6666 [7]3 years ago
3 0

Answer:

The system has no real solution.

Step-by-step explanation:

Hi there!

We have the following system of equations:

x² + y² = 1

5x + 6y = 12

The solutions of the system are those (x,y) pairs that satisfy both equations.

Let´s take the second equation and solve it for y:

5x + 6y =12

subtract 5x to both sides of the equation

6y = 12 - 5x

divide by 6 both sides

y = (12- 5x)/6

Now, let´s replace the y in the first equation:

x² + y² = 1

x² + [(12- 5x)/6]² = 1

Apply distributive property

x² + (12 - 5x)²/36 = 1

x² + (12 - 5x)(12 - 5x)/36 = 1

Apply distributive property

x² + (144 - 120x + 25x²)/36 = 1

Apply distributive property

x² + 4 - 10/3 · x + 25/36 · x² = 1

subtract 1 to both sides

61/36 · x² - 10/3 · x + 3 = 0

Using the quadratic formula, let´s find the solutions to this quadratic equation:

a = 61/36

b = -10/3

c = 3

[-b ± √(b² - 4ac)]/2a

[10/3 ± √(100/9 - 4(61/36)(3))]/2(61/36)

(10/3 ± √-83/9)/61/18

This expression has no real solution because √-83/9 is not defined in the set of real numbers. This means that both curves don´t intersect (see attached figure).

Have a nice day!

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3 years ago
Answer question below.
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The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

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Answer:

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Step-by-step explanation:

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3 years ago
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Blake is a member of a golf club. When he became a member, he deposited money into his club account. For each round of golf that
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Answer:

D)  Blake's account initially had $320, which is decreasing at the rate of $20 per round.

Step-by-step explanation:

Here, according to the question:

x: The total number of golf rounds played

y: Represents the amount, in dollars, left in his account after playing x rounds

Let as assume A is the amount deposited initially.

y = A  - n x    here n : rate of each round played

Also, here

if x  = 2, then y = 280

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If x  = 2 and y = 280, then:

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If x  = 4 and y = 240, then:

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Solving (1) and (2)  by (1) - (2),  we get:

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⇒ The amount initially deposited is $320 and the rate per round is  $20

Hence ,Blake's account initially had $320, which is decreasing at the rate of $20 per round.

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