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777dan777 [17]
2 years ago
14

Determine the points of intersection of the line y=2x+5 and the circle x²+y²=36

Mathematics
1 answer:
Vladimir79 [104]2 years ago
5 0

The two intersection points are (-2.79,  -0.58) and (0.79,  6.58).

<h3>How to find the points of intersection?</h3>

Here we want to solve the system of equations:

y = 2x + 5

x² + y² = 36

To solve this, we need to replace the first equation into the second one:

x² + (2x + 5)² = 36

Now we can solve this for x:

x² + 4x² + 10x + 25 = 36

5x² + 10x - 11 = 0

This is a quadratic equation, to solve it we use the general formula:

x = \frac{-10 \pm \sqrt{10^2 - 4*5*(-11)} }{2*5} \\\\x = \frac{-10 \pm 17.9 }{10}

So we have two solutions for x:

x = (-10 - 17.9)/10 = -2.79

x = (-10 + 17.9)/10 = 0.79

To get the y-values of the solutions, we evaluate the linear equation in these values of x:

y = 2*(-2.79) + 5 = -0.58

y = 2*( 0.79) + 5 = 6.58

Then the two intersection points are (-2.79,  -0.58) and (0.79,  6.58).

If you want to learn more about intersection points:

brainly.com/question/17206319

#SPJ1

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2 years ago
Graph a line that is perpendicular to y=7/8x+3
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4 0
3 years ago
Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?
damaskus [11]

Answer:

f(x)= (x+8)^2 + 200

Step-by-step explanation:

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3 years ago
Linda is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
MA_775_DIABLO [31]

Answer: as company A charges a fix amount $93 for any distance and company B charges variable amount starting from $65.there will be a certain mileage after that the amount charged by company B should be greater than company A.

let for greater than m mileage company A will

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charge for company A for m mileage= $93

charge for company B for m mileage= $65 + $0.70*m

 

so,

   93  ≤ 65+0.70*m

93-65 ≤ 65+0.70*m -65

  28   ≤ 0.70*m

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280     ≤ 7m

280/7  ≤ 7m/7

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Ans: greater than 40 mileage  Company A will charge less than Company B

Step-by-step explanation:

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4 0
3 years ago
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