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

Question 16 options:

A)

Focus = (5,–6), directrix is y = –7

B)

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

C)

Focus = (6,–6), directrix is y = –4

D)

Focus = (–5,6), directrix is y = –4

Answers

Answer 1

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:

[tex]y=a(x-h)^2+k[/tex]

It can be further simplified to:

[tex](x-h)^2=4p(y-k)[/tex]

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

Given that:

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

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


Related Questions

6.5+(-8.3)-(-1.6)+0.7-9.9

Answers

Answer:

-12.6

Step-by-step explanation:

OK so I might have done something wrong but just remember when you're adding a negative and and a positive number you're technically just subtracting

What shape will you get if you take a cross section of a square pyramid parallel to its base? ANSWERS: A rectangle A triangle A square A parallelogram

Answers

Answer:

A square

Step-by-step explanation:

Since the base is a square, any plane of the pyramid parallel to the base is shaped like a square (except the very top one which is a point).

Square shape will you get if you take a cross section of a square pyramid parallel to its base

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

'A square pyramid is a  three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'

According to the given problem,

If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.

Hence, we concluded that square could be formed by slicing the square pyramid by a plane.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

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4. Which regions contain more than 3 million males?

Answers

Europe and Australia and the us

Answer:

The Eastern region has more than 3 million males.

Graph the line that passes through the points (4, 3) and (1,6) and determine the equation of the line.

Answers

Answer:

y = -x + 7

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]

Step 1: Find slope

m = (6 - 3)/(1 - 4)

m = -1

Step 2: Find b

y = -x + b

6 = -1 + b

b = 7

Step 3: Rewrite linear equation

y = -x + 7

Answer:

y = -x + 7

Step-by-step explanation:

(x1, y1) = (4 , 3)

(x2, y2) = (1 , 6)

[tex]slope=\frac{y_{2}-y{1}}{x_{2}-x_{1}}\\\\=\frac{6-3}{1-4}\\\\=\frac{3}{-3}\\\\=-1\\\\y-y_{1}=m(x-x_{1})\\\\[/tex]

m = - 1;  (4,3)

y - 3 = (-1)(x -4)

y - 3 = -x + 4

y = -x + 4 + 3

y = -x + 7

Helpppp meeee do ths

Answers

Answer:

7/10

Step-by-step explanation:

10 dishes

3 meat dishes = ( chicken, hamburger, meatloaf)

10-3 = 7 that are not meat

P ( not meat) = not meat / total

                      =7/10

Answer:

7/10

Step-by-step explanation:

There are a total of 10 meals to choose from. There is 1 chicken, 1 hamburger, and 1 meatloaf. Together they make 3 meat choices. So there are 3/10 of probability of choosing meat. We are looking for the probability of not choosing meat which would be 7/10. This is because the whole amount of meals 10- 3 meat chooices equals 7 total of meals that are not meat. Which gives us the probability of 7/10.

Hope that was helpful!

(Brainliest???) :P

Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 3, 4, B at ordered pair negative 4, 2, C at ordered pair negative 1, 1. A triangle A prime B prime C prime has A prime at ordered pair 3, 4, B prime at ordered pair 4, 2, C prime at ordered pair 1, 1.

Which equation shows the correct relationship between the measures of the angles of the two triangles?

The measure of angle ABC = The measure of angle A prime B prime C prime

The measure of angle ABC = The measure of angle B prime C prime A

The measure of angle BCA = The measure of angle A prime B prime C prime

The measure of angle BCA = The measure of angle C prime A prime B prime

Answers

Answer:

The measure of angle ABC = The measure of Angle A' B' C'

Step-by-step explanation:

Because

<A = <A'

<B = <B'

<C = <C'

The answer above is right.

Which Anna quality graft is the solution to X/ < -3

Answers

Answer:

Well the following inequality [tex]x<-3[/tex] as a graph is in the image below.

The triangular prisms are similar. Find the volume of the larger prism. Round your answer to the nearest hundredth.
A. 85.33 in³
B. 86.38 in³
C. 87.07 in³
D. 88.16 in³​

Answers

The correct answer is A. 85.33 in^3

85.33 in^3 will be your answer, hope this helps!

sin law or cos law?!!!!!!!!!!!!! ​

Answers

Answer:

Law of Sines

Step-by-step explanation:

Law of Sines: [tex]\frac{A}{sina} =\frac{B}{sinb} =\frac{C}{sinc}[/tex]

Step 1: Solve for m∠B

[tex]\frac{25}{sin36} =\frac{27}{sinx}[/tex]

25sinx = 27sin36°

sinx = 27sin36°/25

[tex]x = sin^{-1}(\frac{27sin36}{25} )[/tex]

m∠B ≈ 39.4°

Step 3: Find m∠C

180 - (36 + 39.4)

180 - 75.4

m∠C = 104.6°

Which of the following best describes the slope of the line below?



O A. Undefined
O B. Negative
O c. Positive
O D. Zero

Answers

Answer:

zero or undefined

Answer:

it's d zero.

Step-by-step explanation:

just took the test

Please help with this

Answers

Answer: x = 10

Step-by-step explanation:

Hi, to answer this question we have to apply proportions, since the sides are equivalent.

15/25

6/x

So, for equal ratios:

15/25 = 6/x

Solving for the missing side x:

x = 6 / (15/25)

x = 10

In conclusion, the correct option is D) 10

Feel free to ask for more if needed or if you did not understand something.  

there are 4 blue counters and 3 red counters in a bag. Suzy put some more red counters into the bag. The ratio between blue and red counters is now 2:5. How many red counters did suzy put into the bag​

Answers

Answer:

i think suzy will put 15 red counters into the bag​

Step-by-step explanation:

Suzy will put 15 red counters

Find the value of the trigonometric ratio, cos L.

Answers

Answer:

b/h

Step-by-step explanation:

remember SOH CAH TOA. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. So in this case use CAH for cos L. Adjacent to L is b, and the hypotenuse is h. Therefore the answer is b/h.

PLEASE HELP

Prison M and pyramid N and have the same base area and the same height. Cylinder P and prism Q have the same height in the same base perimeter. Come Z has the same base area of cylinder y, but its height is three times the height of the cylinder y. The figures? And? Have the same volume

Answers

9514 1404 393

Answer:

  Cone Z, cylinder Y

Step-by-step explanation:

Pointy objects such as pyramids and cones have 1/3 the volume of a prism (or cylinder) with the same base area. So, for a cone and cylinder of the same base area to have the same volume, the cone must be 3 times as high.

The figures described as having that relationship are ...

  cone Z, cylinder Y

_____

Additional comment

The perimeter of a prism is not sufficient to define its base area, unless the shape of the base is well-enough defined. However, the perimeter of the base is useful for determining the lateral surface area. Unfortunately, that is not of any interest in this problem.

PRE CALC, please help 22 POINTS

Answers

Answer:

D. f(x)=3^x+5

Step-by-step explanation:

D. have a domain and range

In a recent television survey, participants were asked to answer ʺyesʺ or ʺnoʺ to the question ʺAre you in favor of the death penalty? ʺ Six thousand five hundred responded ʺyesʺ while 4100 responded ʺnoʺ. There was a fifty-cent charge for the call.
A) stratified B) random C) cluster D) convenience E) systematic

Answers

Answer:

D) Convenice

Step-by-step explanation:

People who called in were already wiilling to answer with a 50 cent charge and had available time to answer the survey

Expand to write an equivalent expression: -1/4(-8x+12y)

Answers

Answer:

 

8x -12

Step-by-step explanation:

Use the distributive property. 16 outside wishes to go inside and multiply each term; you get 16x/2 which is 8x minus ¾ of 16 which is 12.

 

Answer:

2x-3y

Step-by-step explanation:

To expand this expression, use the distributive property.

[tex]-\frac{1}{4}(-8x+12y)[/tex]

To distribute, multiply each term inside the parentheses by the number outside the parentheses.

[tex](-\frac{1}{4}*-8x)+(-\frac{1}{4} *12y)[/tex]

Multiply -1/4 and -8x first.

[tex]((-\frac{1}{4}*-8)x)+(-\frac{1}{4} *12y)[/tex]

[tex]2x+(-\frac{1}{4} *12y)[/tex]

Next, multiply -1/4 and 12y.

[tex]2x+ ((-\frac{1}{4} *12)y)[/tex]

[tex]2x+ -3y[/tex]

A +- becomes a -

[tex]2x-3y[/tex]

40 points!!! please tell me how to do it not what the answer is :D

Answers

Answer:

C

Step-by-step explanation:

You first distribute within the parentheses which is -(-z-2). This is going to make everything positive as everything in the parentheses is negative. You should get z+2. Next, you plug that back in. It should be-3z+z+2. You simplify to get -2z+2. Hope this helps!

Answer:

see below

Step-by-step explanation:

-3z -( -z -2)

The first step is to distribute the minus sign

-3z  --z  --2

A negative negative is a positive

-3z +z +2

Then combine the like terms

-3z+z   +2

Answer

-2z+2

There are eight marbles in a bag. Four marbles are blue (B), two marbles are red
(R) and two marbles are green(G)
Steve takes a marble at random from the bag.
(i) What is the probability that Steve will take a blue marble.
(ii) What is the probability that Steve will take a green marble.
(iii) What is the probability that Steve will take a yellow marble.

Answers

Answer:

i. 4/8 or 1/2, ii. 2/8 or 1/4, iii. 0/8

Step-by-step explanation:

In the problem it says that there are 8 marbles in total, so for number 1 it'll be 4/8 or 1/2 since 4 of the marbles are blue. Number 2 will be 2/8 because there are only 2 green marbles and you can simplify 2/8 to 1/4. The last one would be 0 since the problem didn't mention that there are yellow marbles. Hope this helps :)

does this graph represents a function? why or why not?

Answers

Answer:

Yes, it passes the vertical line test

Step-by-step explanation:

This graph has a one to one correspondence and will pass the vertical line test, there fore it is a function

Please help with this

Answers

I would go with A as it seems the most logical answer
A. Should be right.

Est. Length: 2:00:00
x
Wyatt Stewart: Attempt 1
(06.01 MC)
What is the value of the expression shown below?
(2) 12 point)
4 + 16 +2244
O 1) 20
O 2 16
0 3 2
O 4) 5​

Answers

Answer:

Step-by-step explanation:

B

Find the area of this circle. Area = _______ in2. Use 3.14 for pi and round to the nearest tenth. A. 35.8 B. 28.3 C. 254.3 D. 1017.4

Answers

Answer:

A ≈ 254.5 in²

Option C

Step-by-step explanation:

Area of a Circle Formula: A = πr²

d = 2r

Since we are given diameter d, we simply divide by 2 to get radius r:

r = 18/2 = 9

Then we simply plug it into the formula:

A = π(9)²

A = 81π

A = 254.469

A circle with a radius of 9 inches has an area of 254.3 square inches. The of aarea  circle is calculated using the formula πr², where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.

Hence, the correct option is C.

The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius of the circle. In this case, the radius is 9 inches, so the area is given by:

In this case, the radius is 9 inches, so the area of circle is given by,

Area = pi × [tex]9^{2}[/tex]

Area = 3.14 × 81

Area= 254.3

The value of pi is approximately 3.14, so the area of the circle is approximately 254.3. However, the question asks for the area rounded to the nearest tenth, so the answer is 254.3.

Learn more about area here: brainly.com/question/30307509

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In 6 years, John will be 3 times the age he was 2 years ago. What is his current age?
7
U8
5

Answers

Answer:

John is currently 6 years old.

Step-by-step explanation:

2 years ago: x years

Current time: x+2

In 6 years: x+8

EQUATION:

3(x)=x+8= 3x=x+8

(subract x from both sides)

2x=8

x=4

Therefore, John is 6 years old in current time

Help please, I'm not timed

Answers

Answer:

B 30% you can divide 160 the total by 10then multiply and you can check B and C

Can someone help me out please :)
Students in a class sit two major exams.
75% of students pass the maths exam.
80% of those who pass
the maths exam
also pass the science exam. 40% of those
who fail the maths exam pass the science
exam. Find the probability that a student
chosen at random:
(b) fails both exams.
%​

Answers

Answer:

15%

Step-by-step explanation:

25% fail math

60% of the 25% above fail science

thus,

[tex] \frac{25}{100} \times 60\%[/tex]

=15% of total student

Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides.

A) X → Z: If a shape has three sides, then it's a triangle.
B) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
C) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
D) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°.

Answers

Answer: X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.

Step-by-step explanation:

Answer: The answer is C.

Step-by-step explanation: I did the test and it was right


Jerry's motorcycle tank holds 6gallons of gas. There are 3 gallons of gas currently in the tank. How much more gasoline will
it take to fill the tank? (Simplify your answer and write it as a mixed numner

Answers

Answer:

It takes 3 more gallons to fill the tank.

Step-by-step explanation:

6-3=3

Gabe can wrap 1 2/3 presents in 1/3 hour. how many presents can Gabe wrap per hour?

Answers

Answer:

5.06

Step-by-step explanation:

1 2/3 = 1/3

x = 1                                         (cross multiply)

1/3 x = 1 2/3                             (divide both sides by 1/3)

x = 5.06

Sorry the final answer is in decimal. I think better in decimal.

Answer:

Gabe can wrap 5 presents in an hour.

Step-by-step explanation:

So, to find the answer all you have to do is just multiply how many presents he can wrap in 1/3 hours and multiply that by 3. That is then your answer.

Brainliest would be appreciated.

I hope that I was able to help you.

Isabel purchased bananas and apples at a grocery store. She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas. If the apple cost 3 times as much per pound as bananas, what is the cost per pound of apples??

A) $0.90

B) $1.80

C) $2.70

D) $3.60

Answers

Answer:

C. $2.70

If one pound of apples cost 3 times the amount of a pound of bananas, then a pound of apples costs; $2.70.

The cost per pound of apples will be $2.70, which is the correct answer would be option (C).

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the cost per pound of apples be x, and the cost per pound of banana be y

She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas.

So, 3x + 2y = 9.90 ....(i)

And the apple cost 3 times as much per pound as bananas.

So, x = 3y

y = x/3  ....(ii)

Substitute the value of y = x/3 in the equation (i), and solve

3x + 2(x/3) = 9.90

3x + 2x/3 = 9.90

11x/3 = 9.90

11x = 2.97

x = 2.97/11

x = 2.70

Thus, the cost per pound of apples will be $2.70.

Learn more about the equation here:

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