Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0). y = one fourth(x − 5)2 + 1 y = one fourth(x + 1)2 − 5 y = −one fourth(x + 1)2 − 5 y = −one fourth(x − 5)2 + 1

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

Step-by-step explanation:

parabola with a directrix at y = 2 and a focus at (5, 0)

The focus is equal to ( h, k+ 1/(4a))  where ( h,k) is the vertex

The directrix is equal to  y = k - 1/ (4a)

We know h =5 and

0 = k + 1/(4a)

2 = k - 1 /(4a)

Add these two equations together

2 = 2k

k =1

The vertex is ( 5,2)

Now we find a

0 = 1 + 1/(4a)

-1 = 1/(4a)

-4a =1

a = -1/4

The equation for a parabola is

y = a ( x-h) ^2 + k

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

the correct answer is semicircle

step-by-step explanation:

the answer is semicircle because the shorter arc joining two points on the circumference of a circle is known as the minor arc, the larger arc is called the major arc, and a semicircle is a half circle, formed by cutting a whole circle along a diameter line.

hope i .

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841