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3 years ago

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

Mathematics

1 answer:

Vinvika [58]3 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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Graph the first six terms of a sequence where a1=5 and r=1.25

emmainna [20.7K]

The sequence above is geometric progression.
The nth term of such sequence is given by;

Tn = ar∧(n-1),
Where a⇒first term and
r⇒common ratio

So, 1st term = 5×1.25∧(1-1) = 5×1.25∧0 =5
2nd term = 5×1.25∧(2-1) = 5×1.25 = 6.25
3rd term = 5×1.25∧(3-1) = 5×1.25² = 7.8125
4th term = 5×1.25∧(4-1) =5×1.25³ = 9.765625
5th term = 5×1.25∧(5-1) = 5×1.25∧4 = 12.20703125
6th term = 5×1.25∧(6-1) = 5×1.25∧5 = 15.25878909

7 0

3 years ago

Transformation Rule:<br> Translate 4 units right and 3 units up.<br> B<br> Х<br> A

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

Translation of a point (h, k) by 'a' units to the right and 'b' units upwards is defined by,

(h, k) → (h + a, k +b)

Coordinates of A → (-4, -2)

Coordinates of B → (1, -1)

Coordinates of C → (0, -5)

If these points are shifted 4 units right and 3 units up,

By applying rules of the translation,

Coordinates of image point A' → (-4 + 4, -2 + 3)

→ (0, 1)

Coordinates of B' → (1 + 4, -1 + 3)

→ (5, 2)

Coordinates of C' → (0 + 4, -5 + 3)

→ (4, -2)

Now plot these points on the graph.

6 0

2 years ago

What is 1.5% of 30? (please I have no idea and I need to know ASAP)

xxMikexx [17]

Answer:

30 x 1.5% = .45

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3 0

3 years ago

Read 2 more answers

What else would need to be congruent to show that AABC=A DEF by the

Pepsi [2]

Answer:

D. AC ≅ DF

Step-by-step explanation:

According to the AAS Theorem, two triangles are considered congruent to each other when two angles and a mon-included side of one triangle are congruent to two corresponding angles and a corresponding non-included side of the other.

Thus, in the diagram given:

<A and <B in ∆ABC are congruent to corresponding angles <D and <E in ∆DEF.

The only condition left to be met before we can conclude that both triangles are congruent by the AAS Theorem is for a mon-included side AC to be congruent to corresponding non-included side DF.

So, AC ≅ DF is what is needed to make both triangles congruent.

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3 years ago

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Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

3 0

3 years ago