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Ulleksa [173]
3 years ago
5

A parabola and a circle are graphed into the standard (x,y) coordinate plane. The circle has a radius of 4 and is centered at (1

,1). The parabola, which has a vertical axis of symmetry, has its vertex at (1,5) and a point at (2,4). How many points of intersection exist between the parabola and the circle?
Mathematics
1 answer:
Gala2k [10]3 years ago
6 0

Answer:

Correct answer: Two point of intersection and one touch point.

Step-by-step explanation:

Cartesian form of parabola is: y= a(x-1)² + 5  and point named A(2,4)

when we replace the coordinates of the point A in the formula we get

a = - 1 and parabola is  y= - (x-1)² + 5 which means that it faces the opening downwards. The parabola touches the circle in vertex.

God is with you!!!

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Evaluate the discriminant of the equation. Tell how many solutions each equation has and whether the solutions are real or imagi
cupoosta [38]

Answer:

D=-4<0, the equation has no real solutions, it has two imaginary solutions.

Step-by-step explanation:

The quadratic equation x^2 +4x+5=0 has coefficients

a=1,

b=4,

c=5.

The discriminant D is the expression

D=b^2-4ac.

Hence,

D=4^2-4\cdot 1\cdot 5=16-20=-4

Since the discriminant is negative, the equation has no real solutions, it has two imaginary solutions.

4 0
3 years ago
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What is the value of x in the equation 6(х + 1) — 5х = 8 + 2(x — 1)?
Licemer1 [7]

Multiply the first bracket by 6.

Multiply the second bracket by 8

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6(x)+6(1)-5x= 8+2(x)+2(-1)

6x+6-5x= 8+2x-2

6x-5x+6= 8-2+2x

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Move +2x to the other side. Sign changes from +2x to -2x.

x-2x+6= 6+2x-2x

-x+6= 6

Move +6 to the other side. Sign changes from +6 to -6.

-x+6-6= 6-6

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6 0
3 years ago
What is the quotient of 1.728 x 109 and 4.8 x 106 expressed in scientific notation?​
fenix001 [56]

Step-by-step explanation:

\to 1,728 \times {10}^{9}

= 1,728 \times {10}^{9}

= 1,728 \times 1.000.000.000

= 1.728.000.000

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\:

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= 4,8 \times {10}^{6}

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2 years ago
Geometry question for homework.
mars1129 [50]

So remember that the distance formula is \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} .

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Distance between (4,-5) and (4,-2) is 3 units.

2.

\sqrt{(1-(-1))^2+(1-4)^2}\\ \sqrt{2^2+(-3)^2}\\ \sqrt{4+9}\\ \sqrt{13}

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