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3 years ago

The points A-1,-9) and K(5,1) are endpoints of a diameter of circle 5. Which equation represents circle S?

Mathematics

1 answer:

Lilit [14]3 years ago

4 0

Answer:

Step-by-step explanation:

if (x1,y1) and (x2,y2) are the extremities of diameter,then eq. of circle is

(x-x1)(x-x2)+(y-y1)(y-y2)=0

reqd. eq. is (x+1)(x-5)+(y+9)(y-1)=0

$x^{2} +x-5x-5+y^2+9y-y-9=0\\x^{2} -4x+y^2+8y-14=0\\compare with x^2+y^2+2gx+2fy+c=0\\center (-g,-f) \\radius r=\sqrt{g^2+f^2-c}$

center is (2,-4)

r=√(2²+(-4)²-(-14))

=√(4+16+14)

=√(34)

eq. of circle is (x-2)²+(y+4)²=34

(x²-4x)+(y²+8y)=14

(x²-4x+4)+(y²+8y+16)=14+4+16

(x-2)²+(y+4)²=34

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the straight line L has the equation 4y=5x+3. Point A has the coordinates (3,-2) Find the equation of the line straight line tha

Aleonysh [2.5K]

Answer:

y = - $\frac{4}{5}$ x + $\frac{2}{5}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4

y = $\frac{5}{4}$ x + $\frac{3}{4}$ ← in slope- intercept form

with slope m = $\frac{5}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{5}{4} }$ = - $\frac{4}{5}$ , thus

y = - $\frac{4}{5}$ x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = - $\frac{12}{5}$ + c ⇒ c = - 2 + $\frac{12}{5}$ = $\frac{2}{5}$

y = - $\frac{4}{5}$ x + $\frac{2}{5}$ ← equation of perpendicular line

4 0

2 years ago

Una botella tenía agua hasta de su capacidad. Luego, se agregó litro de agua y la botella quedó llena. Si x representa la capaci

Elena L [17]

Responder:

3 / 4x + 1/2 = x

Explicación paso a paso:

Dado que:

Capacidad total = x

Volumen inicial = cierta fracción * capacidad total

Volumen adicional agregado para llenar = 1/2

Por eso,

Inicial. Volumen + volumen adicional = volumen total

De las opciones:

Un volumen inicial de 3 / 4x

Volumen adicional de 1/2

Volumen total = x

Sumar todo hace que la ecuación:

3 / 4x + 1/2 = x

x - 3 / 4x = 1/2

Por lo tanto, la ecuación correcta de la opción es: 3 / 4x + 1/2 = x

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2 years ago

Triangles ABC and DEF have the following characteristics B and Eare right angles A = D BC = EF which congruence theorem can be u

kvasek [131]

AAS Angles A and D are one pair of congruent angles, then angles B and E are congruent because they are both right angles, following that you have line BC as congruent to EF so that is an angle, an angle, and a side so AAS

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2 years ago

One number is five more than another number. If the square of the smaller number is 3 more than 3 times the larger number, what

11111nata11111 [884]

Answer:

6 and 11

Step-by-step explanation:

n1 = n + 5

ns^2 = 3 + 3nb

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