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2 years ago

What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4

Mathematics

2 answers:

ratelena [41]2 years ago

6 0

See the picture! Hope it helps!

tresset_1 [31]2 years ago

5 0

Answer:

$y=\frac{-1}{4} x+3\\$

Step-by-step explanation:

$(y-5)=\frac{-1}{4} (x--8)\\(y-5)=\frac{-1}{4} (x+8)\\y=\frac{-1}{4} x-\frac{8}{4}+5 \\y=\frac{-1}{4} x-2+5\\y=\frac{-1}{4} x+3\\$

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Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

mel-nik [20]

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

$(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2$

$\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y$

$\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y$

$\implies 4x +8x-10y+2y = 16 + 1 -25-4$

$\implies 12x - 8y = 17 - 29$

$\implies 12 x - 8 y = - 12$ ---------(1)

Similarly, QO = RO

$\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2$

$\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y$

$\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y$

$\implies - 8x -4x-2y-6y=4+9-16-1$

$\implies -12 x - 8 y = 13 - 17$

$\implies 12 x + 8 y = 4$ ------------(2)

By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

y = 2

7 0

2 years ago

The perimeter of a certain rectangle is 16 times the width. The length is 12 cm more than the width. Find the length and width o

Blizzard [7]

Check the picture below

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8 0

3 years ago

WILL MARK BRAINLIEST HELPPP ME

steposvetlana [31]

Answer:

x=47

Step-by-step explanation:

5 0

2 years ago

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Given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

Anit [1.1K]

<u>Your question: </u>given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

The correct answer would be D $\sqrt{3}$

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3 years ago

What is -2 sqrt 50 - sqrt 125 in simplest radical form

Gnoma [55]

Answer:

- 10√2 - 5√5

Step-by-step explanation:

- 2√50

√50 = √( 2 x 5 x 5 ) = 5√2

- 2√50

= - 2 x 5√2

= - 10√2

- √125

= - √( 5 x 5 x 5 )

= - 5√5

- 2√50 - √125

= - 10√2 - 5√5

6 0

2 years ago

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What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4​

What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4