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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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gtnhenbr [62]

Answer:

(-12, -12)

Step-by-step explanation:

Since the scale factor is 3, you would multiply the x-coordinate and y-coordinate by it.

-4×3=-12

Hope this helps!!

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2 years ago
You and a friend take pictures at a motocross event. Your camera can take 24 pictures in 3.75 seconds. Your friend's camera can
UkoKoshka [18]

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2 years ago
How many different ways are there to choose a dozen donuts from the 4 varities at a donut shop so that you get atleast one donut
Leno4ka [110]

There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)

<h3>How to calculate the number of ways to select items?</h3>

There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by

The number of ways =  _{n+r-1}C_r

Where the combination _{n}C_r is calculated as

_{n}C_r=\frac{n!}{r!(n-r)!}

<h3 /><h3>Calculation:</h3>

It is given that there are 4 varieties of donuts in a shop. I.e., n = 4

Number of donuts to be selected r = 12 (one dozen)

And also given that at least one donut of every variety has to be selected.

Since there are 4 varieties, at least one from each of these means the count is 4.

So, the remaining number of donuts to be selected is 12 - 4 = 8.

So, r becomes 8 i.e., r = 8

On substituting,

the number of ways of selecting the remaining 8 donuts = _{4+8-1}C_4

⇒ _{11}C_4

⇒ \frac{11!}{4!(11-4)!}

⇒ \frac{11!}{(4!)(7!)}

⇒ 330

Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.

Learn more about combinations here:

brainly.com/question/11732255

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5 0
1 year ago
Henry wants to know the height of an outdoor sculpture. He measures the shadow of the outdoor sculpture and finds that it is 12
coldgirl [10]
Height of sculpture/shadow of sculpture = height of tower/shadow of tower

x/12 = 12/16
16x = 12*12
16x = 144
x = 144/16
x = 9

The sculpture is 9 meters tall
3 0
3 years ago
Solve for - 2/5 x = 12
LenaWriter [7]
X is -30
(-2/5) times -30 is 12
8 0
3 years ago
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