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kvv77 [185]
2 years ago
12

Find the focus and the directrix of the parabola with the equation y = 1∕4(x – 6)2+ 5

Mathematics
1 answer:
strojnjashka [21]2 years ago
5 0

Answer:

B)

Focus = (6,6), directrix is y = 4

Step-by-step explanation:

A parabola is the locus of a point that is equidistant from a fixed line (known as directrix) and a fixed point (known as focus).

The equation of a parabola in vertex form is given as:

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

It can be further simplified to:

(x-h)^2=4p(y-k)

The directrix of this parabola is given at line y = k - p and the focus is at (h, k + p)

Given that:

y = \frac{1}{4}(x-6)^2+ 5 \\(y-5)=\frac{1}{4}(x-6)^2\\(x-6)^2=4(y-5)

Comparing (x-6)² = 4(y-5) with (x-h)² = 4p(y-k), It can be gotten that h = 6, p =1 and k = 5

The directrix of this parabola is given at line y = k - p = 5 - 1 = 4 and the focus is at (h, k + p) =  (6, 5+1) = (6, 6)

Focus = (6,6), directrix is y = 4

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Which inequality represents all the solutions of -5x + 5 ≥ 160 − 10x? A. x ≤ -33 B. x ≥ 33 C. x ≥ 31 D. x ≤ 31
ikadub [295]

Answer:

The answer is B.

Step-by-step explanation:

Solve for x.

-5x + 5 \geq 160 - 10x

Add 10x to both sides, and subtract 5 from both sides.

5x \geq 155

Now, divide by 5.

x \geq 31          is the answer

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2 years ago
If Adrianna can read 7 pages in 10 minutes. At this rate, how many page can she read in 25 minutes?
lesya692 [45]

3.5 : 5

7 : 10

14 : 20

17.5 : 25

At that rate, she can read 17.5 pages in 25 minuets.

Divide both 7 and 10 by 2, which gets 3.5 and 5

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I need this done please help me
levacccp [35]

Answer:

see explanation

Step-by-step explanation:

A

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Here diameter = 12 , then radius = 12 ÷ 2 = 6 , then

A = π × 6² = 3.14 × 36 = 113.04 m²

B

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C = 2πr ( r is the radius )

Here C = 28.26 , then

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