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fiasKO [112]
3 years ago
8

Answer pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee omg

Mathematics
1 answer:
Sphinxa [80]3 years ago
3 0
The best estimate of r is 0.
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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
  • Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

6 0
3 years ago
Read 2 more answers
Ryan has 25 tiles and 12% of them are green. how many tiles are green
Lady_Fox [76]

Answer:

208.33. this is it your welcome

6 0
3 years ago
When the temperature of an object increases, what happens to the kinetic energy of the particles in the object?
valentina_108 [34]
C.) It increases ............
8 0
3 years ago
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Masha biked 20km 20 minutes faster than Dasha biked 20km. Find the speed of each cyclist if one biked 2km/h faster than the othe
motikmotik

Answer:

  • 12 km/h and 10 km/h

Step-by-step explanation:

Let the speed of Masha = s, speed of Dasha = d

  • Distance = 20 km
  • Time difference = 20 min = 1/3 hr
  • Speed difference  = 2 km/h

<u>As per above info we get following equations:</u>

  • s = d + 2
  • 20/s + 1/3 = 20/d

<u>Substitute s and solve for d:</u>

  • 20/(d + 2) + 1/3 = 20/d

<u>Get rid of fraction by multiplying all terms by 3d(d + 2):</u>

  • 60d + d(d + 2) = 60(d + 2)
  • 60d + d² + 2d = 60d + 120
  • d² + 2d = 120
  • d² + 2d + 1 = 121
  • (d + 1)² = 11²
  • d + 1 = 11
  • d = 10

<u>Find s:</u>

  • s = 10 + 2 = 12

<u>The answer is</u>

  • Masha's speed 12 km/h and Dasha's speed 10 km/h
3 0
3 years ago
Please I need help ASAP, please tell me how you know
mixas84 [53]

Answer: D it the For the way they have as examples

what do you need help on. what the problem

7 0
3 years ago
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