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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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Answer: 49, 35, and 32

Step-by-step explanation:

7 * 7 = 49

7 * 5 = 35

4 * 8 = 32

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How many lbs are in a metric ton​
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Step-by-step explanation:

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Marta is making 3 servings of fruit salad.she adds 3/8 cup blueberries for each serving.her measuring cup holds 1/8 cup.how many
quester [9]
To solve this problem you must follow the proccedure shown below:

 1. You have the following information given in the problem above:

 - <span>Marta is making 3 servings of fruit salad.
 - Marta adds 3/8 cups blueberries for each serving.
 - Her measuring cup holds 1/8 cup.

 2. Then, you have:

 1 time----1/8 cup 
         x----3/8 cups

 x=(3/8)/(1/8)

 x= 3x8/1x8
 x=24/8
 x=3 times

 H</span><span>ow many times must Marta measure 1/8 cup of blueberry to have enough for the fruit salad?

 The answer is: 3 times</span>
3 0
3 years ago
14.Y = Mx + b. Identify the slope and the y intercept. <br><br> -help meh
lakkis [162]

Answer:

y=mx+b is slope intercept form

In slope intercept form, m represents the slope, b represents the y-intercept and x and y represent the values of x and y on a graph.

Therefore, the slope is m and the y-intercept is b

Step-by-step explanation:

8 0
3 years ago
(05.03)Calculate the area of the regular pentagon below: A regular pentagon with side length of 22.3 inches and dotted line from
Marat540 [252]

Answer:

The area of the regular pentagon is A=858.55\ in^{2}

Step-by-step explanation:

we know that

The area of a regular polygon is equal to

A=\frac{1}{2}Pa

where

P is the perimeter of the regular polygon

a is the apothem

Find the perimeter P

P=5(22.3)=111.5\ in ----> the regular pentagon has five equal sides

a=15.4\ in ---> distance from center to middle of side

substitute

A=\frac{1}{2}(111.5)(15.4)

A=858.55\ in^{2}

5 0
2 years ago
Read 2 more answers
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