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3 years ago

Solve the quadratic equation by completing the square.

Mathematics

1 answer:

Step2247 [10]3 years ago

6 0

Answer:

x1, x2 = 4.74 , -2.74

Step-by-step explanation:

To find the roots of a quadratic function we have to use the bhaskara formula

ax^2 + bx + c

x^2 - 2x - 13

a = 1 b = -2 c = -13

x1 = (-b + √ b^2 - 4ac)/2a

x2 =(-b - √ b^2 - 4ac)/2a

x1 = (2 + √ (2^2 - 4 * 1 * (-13)))/2 * 1

x1 = (2 + √ (4 + 52)) / 2

x1 = (2 + √ 56 ) / 2

x1 = (2 + 7.48) / 2

x1 = 9.48 / 2

x1 = 4.74

x2 = (2 - √ (2^2 - 4 * 1 * (-13)))/2 * 1

x2 = (2 - √ (4 + 52)) / 2

x2 = (2 - √ 56 ) / 2

x2 = (2 - 7.48) / 2

x2 = -5.48 / 2

x2 = -2.74

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Which equation represents the circle described?

faust18 [17]

ANSWER

${(x - 4)}^{2} + {(y - 3)}^{2} = {2}^{2}$

EXPLANATION

The equation of the circle with radius r and centre (a,b) is given by

$(x - a)^{2} + {(x - b)}^{2} = {r}^{2}$

The radius is

$r = 2$

We need to determine the center of the circle from the given equation of another circle, which is,

${x}^{2} + {y}^{2} - 8x - 6y + 24 = 0$

We complete the square to obtain,

${x}^{2} - 8x+ {y}^{2} - 6y + 24 = 0$

${x}^{2} - 8x+ {y}^{2} - 6y = - 24$
${x}^{2} - 8x+ {( - 4)}^{2} + {y}^{2} - 6y + {( - 3)}^{2} = - 24 + {( - 3)}^{2} + {( - 4)}^{2}$

${(x - 4)}^{2} + {(y - 3)}^{2} = - 24 + 9+ 16$

${(x - 4)}^{2} + {(y - 3)}^{2} = 1$

The centre of this circle is (4,3)

Hence the center of the circle whose equation we want to find is also (4,3).

With this center and radius 2, the required equation is,

${(x - 4)}^{2} + {(y - 3)}^{2} = {2}^{2}$

Therefore the correct answer is C.

3 0

3 years ago

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On a number line what is the difference between -3/7 and -2/3?

Yakvenalex [24]

Answer: -5/21

Step-by-step explanation:

-3/7 & -4/6

common detonator is 42

-3/7 = -18/42 reduced to -9/21

-4/6 = -28/42 reduced to -14/21

difference between -9/21 and -14/21 = -5/21

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3 years ago

What is -7/2y = 21/2 what is the solution_______? Brainliest is on the mark if 10 point will be added as well!

miss Akunina [59]

Answer:

y= -3

Step-by-step explanation:

(-7/2)y =21/2

Divide both sides by (-7/2) = Multiply by (-2/7)

On the left side ,after cancellation you have only y

On the right side you multiply 21/2 by (-2/7)

y= (21*-2) / 2*7

y=(-42)/14

y=(-21)/7

y=- 3

check:

-(7/2) of- 3 is 10.5 21/2=10.5

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3 years ago

Mina drew 15hearts,6stars and 16 circles.What is the ratio of stars to hearts to circles?

GenaCL600 [577]

answer

6:15:16

step-by-step explanation

the ratio of stars to hearts to circles is stars:hearts:circles

plug in 6 for stars, 15 for hearts, and 16 for circles

6:15:16

since these do not have a common factor, this is your final answer

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3 years ago

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Sean bought 68 3/4 inches of rope . How many 15-inches ropes can he make from it

choli [55]

Length of rope bought by Sean = 68 3/4 inches
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Then
The number of 15 inch rope that can be made by Sean = (275/4)/15
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   = 4.58
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2 years ago

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