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4 years ago

How many real solutions does this system of equations have? x^2 + y^2 = 36

Mathematics

1 answer:

Vinvika [58]4 years ago

4 0

Answer:

C: there are two real solutions

Step-by-step explanation:

x^2 + y^2 = 36 is the equation of a circle centered at the origin and with radius √36, or 6. Even a rough sketch of this circle would enable you to visualize what is happening here.

3x – y + 1 = 0 may be solved for y: y = 3x + 1. The y-intercept of this straight line is (0, 1). Plot this point inside the circle of radius 6 mentioned above and then draw a straight line with slope m = 3 through it. This line will intersect the circle in two places; they represent real solutions.

Alternatively, substitute 3x + 1 for y in x^2 + y^2 = 36:

x^2 + (3x + 1)^2 = 36, or

x^2 + 9x^2 + 6x + 1 = 36, or

10 x^2 + 6x + 1 - 36 = 0, or

10 x^2 + 6x - 35 = 0. This is a quadratic equation. We'll use the quadratic formula to find solutions which represent the intersections of this line with this circle:

The coefficients are a = 10, b = 6 and c = -35. Thus, the discriminant is

b^2 - 4ac, or 6^2 - 4(10)(-35), or 1436.

Because the discriminant is positive, we can safely conclude that there are two real solutions, that is, two different, real x-values, each representing the x-coordinate of a point of intersection of the circle and the line.

The correct answer to this prolem is C: there are two real solutions.

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In a horse race with 5 horses, you make a bet by predicting the ranking of all 5 horses. Suppose you place your bet at random. W

lapo4ka [179]

Answer:

P( top two horses are predicted incorrectly in incorrect order)

= $\frac{1}{2}$

Step-by-step explanation:

In the horse race the outcome can be predicted in 5! = 120 ways.

Now suppose the top two horses were predicted incorrectly in incorrect order. Now, the top horse can be predicted incorrectly in 4 ways.

Suppose the top horse was predicted to be in k-th position where k = 2, 3 ,4,5

so the second horse can be predicted to be in place from 1 to (k - 1)

So, the top two horses can be predicted incorrectly in incorrect order

in $\sum_{k =2}^{5}(k - 1)$ = 10 ways

and for each prediction of the two the remaining horses may be predicted in 3! = 6 ways.

Hence ,

P( top two horses are predicted incorrectly in incorrect order)

= $\frac{6 \times 10}{120}$

= $\frac{1}{2}$

8 0

3 years ago

2 3/4-3 3/8÷4 1/2 plus show ur work

sladkih [1.3K]

Answer:

149/60

Step-by-step explanation:

11/4-27/8*1/4*1/2

11/4-27/64

149/64

8 0

3 years ago

A price is decreased by 24% and is now £372.40.<br>Work out the original price.

goldfiish [28.3K]

Answer:

Step-by-step explanation:

Subtract the discount from 100 to get the percentage of the original price.

Multiply the final price by 100.

Divide by the percentage in Step One

5 0

3 years ago

Can somebody help me asap.

ehidna [41]

Answer:

Step-by-step explanation:

1) m∠1 +m∠2 + m∠3 = m∠LAM (Angle addition postulate)

2) m∠1 + m∠2 + m∠3 = 180 (def. of straight angle)

3) y║z (Given)

4) ∠1 ≅ ∠5 (alternate interior angles theorem)

5) ∠3 ≅ ∠6 (alternate interior angles theorem)

6) Since m∠1 + m∠2 + m∠3 = 180

m∠5 + m∠2 + m∠6 = 180

Hence proved.

7 0

3 years ago

D • (-4) = 32 solve for d

RSB [31]

Answer:

d = -8

Step-by-step explanation:

Isolate the variable, d. Note the equal sign, what you do to one side, you do to the other. Divide -4 from both sides of the equation:

$d * -4 = 32\\\frac{d * -4}{-4} = \frac{32}{-4}\\d = \frac{32}{-4}\\d = -8$

d = -8 is your answer.

7 0

2 years ago

Read 2 more answers