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Step2247 [10]
3 years ago
11

Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?

Mathematics
1 answer:
Sav [38]3 years ago
7 0
Circle: x^2+y^2=121=11^2 => circle with radius 11 and centred on origin.
g(x)=-2x+12   (from given table, find slope and y-intercept)
We can see from the graphics that g(x) will be almost tangent to the circle at (0,11), and that both intersection points will be at x>=11.
To show that this is the case, 
substitute g(x) into the circle
x^2+(-2x+12)^2=121
x^2+4x^2-2*2*12x+144-121=0
5x^2-48x+23=0
Solve using the quadratic formula,
x=(48 ± √ (48^2-4*5*23) )/10
=0.5058 or 9.0942
So both solutions are real and both have positive x-values.

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3 years ago
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serious [3.7K]

Answer:

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Step-by-step explanation:

4 0
3 years ago
Based on the sample of 500 people, 42% owned cats. Calculate the test statistic. Round to two decimal places.
Tanzania [10]

Answer:

z= 3.63

z for  significance level = 0.05 is ± 1.645

Step-by-step explanation:

Here p = 42% = 0.42

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We formulate our null and alternative hypotheses as

H0: p= 0.42     against Ha : p> 0.42 One tailed test

From this we can find q which is equal to 1-p= 1-0.42 = 0.58

Taking p`= 0.5

Now using the z  test

z= p`- p/ √p(1-p)/n

Putting the values

z= 0.5- 0.42/ √0.42*0.58/500

z= 0.5- 0.42/ 0.0220

z= 3.63

For one tailed test the value of z for  significance level = 0.05 is ± 1.645

Since the calculated value does not fall in the critical region we reject our null hypothesis  and accept the alternative hypothesis that more than 42%  people owned cats.

4 0
3 years ago
Which inequality is true when the value of R is 18? I'ma shower the answers i can choose in the picture ​
musickatia [10]

Answer:

See below:

Step-by-step explanation:

Hello! We can check to see if the inequality is true by replacing r with 18 as we have been told to find them in which 18 as r makes the equation true.

So our equations to test for are:

-r-3>-6\\-r+3

We can input 18 as r and then we see the following are correct:

1. No, as a -21 is not greater than -6

2. Yes, as -15 is less than 6.

3. No, as 21 is not greater than 6

4. No, as -15 is not greater than 6.

Cheers!

7 0
3 years ago
Which equation can be used to find A, the area of the parallelogram shown? A = 5 × 9 A = 4 × 9 A = 12 × 5 × 9 A = 12 × 4 × 9
Vlada [557]

Answer:

I believe it's A=5 times 9 but since the triangle is special (3-4-5), it could be 12 times 5. Hope this kinda help :)

5 0
3 years ago
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