Find the focus and the directrix of the parabola with the equation y = –1∕2 (x – 8)2 – 6.


A) Focus = (–8,–61∕2), directrix is y = –51∕2

B) Focus = (–8,–51∕2), directrix is y = –61∕2

C) Focus = (8,–61∕2), directrix is y = –51∕2

D) Focus = (8,–51∕2), directrix is y = –61∕2

Answers

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

The focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

We have an equation for the parabola:

The parabolic equation also in the form of quadratic equation.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

y = (-1∕2)(x – 8)² – 6

The vertex of the parabola is (h, k)

h = 8, k = -6

The focus of the parabola:

(c, d)

c = -6

d = -6 - 1/2 = -13/2 = -6 1/2

Directrix of the parabola:

y = -6 - (-1/2)

y = -6 + 1/2

y = -11/2 = -5 1/2

Thus, the focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

Learn more about the parabola here:

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Related Questions

A spinner numbered 1 through 12 is spun. Find the probability that
the number spun is an 11 given that the number spun was an odd
number. Please write your answer as a fraction.

Answers

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Let A be the event of getting an odd number.

P(A) be the probability of getting an odd number.

Total odd numbers here are 6 i.e. [tex]\{1,3,5,7,9,11\}[/tex]

Here, total numbers in the game are 12 i.e [tex]\{1,2,3,....,12\}[/tex].

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}[/tex]

Let B be the event of getting 11.

P(B) be the probability of getting 11.

Total number of possible cases is 1.

[tex]P(B) = \dfrac{1}{12}[/tex]

[tex]P(A \cap B)[/tex] is the probability that we get 11 and an odd number.

Possible number of cases = 1

[tex]P(A\cap B) = \dfrac{1}{12}[/tex]

P(B/A) is the probability that we get an 11 given that it is an odd number.

[tex]P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}[/tex]

Hence, P(B/A) = [tex]\dfrac{1}{6}[/tex]

Answer:

The probability in fraction is [tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Total number of outcomes is = 12

Now we have to find the probability that spun number is 11.

That means favorable outcome is 1.

In this case, the probability can be determined by dividing the number of favorable outcomes by the total outcome. Accordingly, the total outcomes are 12 and favorable outcome is 1.  

[tex]\text{P(The spun number is 11)}= \frac{\text{Favorable outcomes}}{\text{total outcomes}} \\\text{P(The spun number is 11)}= \frac{1}{12} \ (in \ fraction)\\\text{P(The spun number is 11)} = 0.083 \ (in \ decimal)[/tex]

The sum of two numbers is 198. If one number is 20% larger than the other number, what are the numbers?

Answers

x + y = 198

y = 1.20 x

x + 1.2 x = 198

2.2x = 198

x = 198/2.2 = 90

y = 198 - 90 = 108

Answer: 90 and 108

Answer:

108 and 90

Step-by-step explanation:

let the two numbers be x and y

from the question let y be the greater number

therefore, y = 20%x +x

y=20/100x + x

y=(20x+100x)/100

y=120x/100

y=1.2x

from the question

x+y=198______(1)

x+1.2x=198

2.2x=198

x=198/2.2

x=90

from (1)

x+y=198

90+y=198

y=108

x=90 y=108

The perimeter of quadrilateral ABCD is 640. The perimeter of quadrilateral LMNO is 144. What is LM

Answers

Answer:

LM = 36

Step-by-step explanation:

A quadrilateral is a shape with 4sides. There are different type of quadrilateral such as square, rectangle, trapezium, parallelogram, kite and rhombus.

Perimeter of a quadrilateral is the addition of all 4 sides.

Since the shape is not specified neither is there a diagram, let's assume the quadrilateral is a square.

See attachment for diagram used in solving the question.

Perimeter of square = length+ length+ length+ length

= 4× length

Perimeter of quadrilateral ABCD:

640 = 4×length

Length = 640/4

Length = 160

Perimeter of quadrilateral LMNO:

144 = addition of all 4 lengths

144 = LM + MN + NO +OL

Since we are considering a square all the sides are equal.

LM = MN = NO = OL

144 = 4×LM

LM = 144/4

LM = 36

What is it that when you take away the whole, you still have some left over?

Answers

Answer:

wholesome!!! brainliest pls :)

Answer:

wholesome

Step-by-step explanation:

you take away the first word which is whole

and u still have the word some left over

hope this helped if this isnt what ur looking for plz tell me

okay who can tell me pi divided by 5.6 squared times 2

Answers

Answer:

0.20035667433

Step-by-step explanation:

Answer:

0.20035667433 , is the answer.

Step-by-step explanation:

Honestly whenever it comes to pi in maths , you can usually always use a calculator so on a calculator write in 'pi (5.6) *squared* x 2'

I need help Whats the Domain and range

Answers

Domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Whether ab is tangent to circle c at point b

Answers

Answer:

No

Step-by-step explanation:

If segment AB is tangent to the circle, then angle CBA will be a right angle, making triangle ABC a right triangle. If triangle ABC is a right triangle, it's sides will fit the Pythagorean theorem...

(leg)^2 + (leg)^2 = (hypotenuse)^2

Does 8^2 + 16^2 = 19^2 ?

64 + 256 does not equal 361!

Triangle ABC is NOT a right triangle, so segment AB is not tangent to the circle.

The inside of a refrigerator in a medical laboratory measures 17 inches long by 18 inches wide by 42 inches high. How many cubic inches can it hold?

Answers

7,852 cubic inches

17*18*42

Answer:

12,852

Step-by-step explanation:

V= l*w*h

V=17*18*42

V= 12,852

caroline works 8 hours a day 5 days a week she earns £440 each week
how much does she earn per hour ?

Answers

Answer:

She earns £11 per hour

Step-by-step explanation:

You divide £440 with 5 days of the week and then you get how much she earns in a day. And then you devide with 8 and u get £11.

Caroline will earn £11 for working per hour.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that caroline works 8 hours a day 5 days a week she earns £440 each week.

The earnings for an hour will be calculated as,

Total hours = 8 x 5 = 40 hours

Earning per hour = £440 / 40

Earning per hour =  £11

To know more about an expression follow

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Rebecca earns $6.25 per hour working after school. She needs at least $125.00 if she wants to buy a new bicycle. Which inequality shows the solution to how many hours Rebecca must work to earn the money for the bicycle? Let h equal the number of hours Rebecca must work.

Answers

Answer: the answer is in the steps.

Step-by-step explanation:

6.25h ≤ 125.00

Find the quotient.

3 divided by 3636

A. 1,212
B. 1,202
C. 122
D. 112
E. 102

help asap!!

Answers

The answer to the question is B

A cow can give 5 gallons of milk if it eats 2 pounds of grass. Express x in terms of y, where y is the number of gallons of milk the cow gives, and x is the number of pounds of grass it eats.

Answers

Answer:y=2.5 x

Step-by-step explanation:

Given

Cow give 5 gallon of milk if it eats 2 pound of grass

i.e. it gives 2.5 gallon of milk if it eats 1 pound of grass

So we can say cow given 2.5 times of milk in gallon for each pound it eats

If cow eats x pounds of grass then it must yield 2.5 times of milk

Suppose milk is denoted by y  

therefore we can write

y=2.5 x

Therefore y=2.5 x represent the relation between grass and milk produced

AB
Round your answer to the nearest hundredth.
B
5
?
40°​

Answers

Answer:

y

Step-by-step explanation:

y\

Answer: 6.53 on khan academy

Step-by-step explanation:

Ming would like to buy a plane ticket so she can visit her family this Thanksgiving, which is November 26. She has found that tickets for flights on days closer to Thanksgiving are more expensive than flights on days further away from Thanksgiving. A calendar from an airline company showing ticket prices by day is below.

Answers

Answer:

$165

Step-by-step explanation:

Answer:

156$

Step-by-step explanation:

Find the area of the following parallelogram

Answers

Answer:

6 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh where b is the base and h is the height

A = 3 *2 = 6 cm^2

An art teacher buys 9 bags of cotton balls. There are 68 cotton balls in each bag.
Which expression is best to estimate the number of cotton balls the teacher
buys?
9+70
9*60
9*70
9+60

Answers

Answer:

9*70

Step-by-step explanation:

It is not 9+70 or 9+60 because for this problem multiplication is required.

This problem seems to want you to round to the nearest ten's place.  Because the one's place in 68 is above 5, the number will round up.

This means that the answer will be 9*70

Answer:

9*70

Step-by-step explanation:

If 99 people have a mean incame of doolar 400, how much is the mean incame increased by the addition of a woman with an incame of doolar 1500​

Answers

The new mean will be (400*99+1500)/100=411
The mean increased by 11.

Answer:

Step-by-step explanation:

Mean income of 99 people = $ 400

Sum of income of 99 people = 400 * 99 = $ 39600

Income of a woman = $ 1500

Income of 100 people = 39600 + 1500 = $41100

Mean of 100 people = 41100/100 = $411

411 - 400 = $11

Mean income increases by $11

There are 197 oak trees in the park. There are 27 more pine trees than oak trees in the park how many trees are there in all

Answers

just add.................

197 + 27 = 224

hope this helps

Yeah.. the answer is 224

(2,3) (7,4) point slope form

Answers

Answer:

[tex]y-3=\frac{1}{5} (x-2)[/tex]

Step-by-step explanation:

First you need to find the slope by using this formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{(4)-(3)}{(7)-(2)}\\m=\frac{1}{5}[/tex]

Now you can put it in point slope form which is: [tex]y-y_1=m(x-x_1)[/tex]

[tex]y-3=\frac{1}{5} (x-2)[/tex] is your answer.

PLZ HELP MATH!
ASAP MANY POINTS REWARDED!

Answers

Answer:

Isosceles

Step-by-step explanation:

Two sides are equal to each other and not the same length as the other side, so it'd be an isosceles triangle.

Which equation are correct set ups to solve for the hypotenuse ** 2 answers

(Solve and Round decimal to the nearest hundredths )

Answers

Answer:x^2=2^2+4^2. x=4.47

Step-by-step explanation:

Opposite=m=2

Adjacent=n=4

Hypotenuse=x

x^2=m^2+n^2

x^2=2^2+4^2

x^2=4+16

x^2=20

x=√20

x=4.47

A police department used a radar gun to measure the speed of a sample of cars on the highway. Assume that the distribution of speeds is approximately Normal with a mean of 71 mph and a standard deviation of 8 mph. Using this distribution what is the z-score of a 65-mph speed limit?

Answers

Answer:

The z-score of a 65-mph speed limit is -0.75

Step-by-step explanation:

Here, we want to calculate the z-score

To calculate the z-score, we make use of the z-score formula

Mathematically;

z-score =(x-mean)/SD

from the question we identify the values as x = 65 mph, mean = 71 mph, Standard deviation(SD) = 8 mph

Plugging these values into the equation above, we have

z-score = (65-71)/8 = -6/8 = -0.75

A cone is cut by a plane parallel to its base. The small cone on top is similar to the large cone, with a similarity ratio of 1 : 2. The ratio between the volume of the small cone to that of the frustum is _ : _.

Answers

Answer:

1:1

Step-by-step explanation:

The ratio between the volume of the small cone to that of the frustum is 1:1.

Notice that the bigger cone is double than the smaller cone, which means the smaller cone is half of the volume of the bigger cone, if you wipe the small one, you would have the frustum with the same volume as the wiped part, because if you delete the smaller cone, you would be deleting half volume of the bigger cone, giving at the end a relation 1 : 1 between the frustum and the smaller cone.

A rectangle perimeter and its are have the same numerical value. The width of the rectangle is 3 units. What is the length of the rectangle in units

Answers

Answer:

six

Step-by-step explanation:

3x6=18 and 3+3+6+6= 18.

At a camp, kids can choose swimming, art, or music.
40 kids choose swimming, 16 choose art, and 24 choose music.
What is the ratio of kids who choose art to kids who choose swimming?

Answers

Answer:

3:5

Step-by-step explanation:

all figures can be divided by 8, so

swimming- 40/8= 5

arts 16/8= 2

music 24/8= 3

therefore, the ratio would be 3:5

Answer:

3/5

Step-by-step explanation:

I took it but got it wrong so i did the math problem and got this 3/5

Please hurry!

Which of the following is true of the values of x and y in the diagram below?

A. y < x
B. y > x
C. y + x = 1
D. y/x = 1

Answers

Answer:

y/x = 1

Step-by-step explanation:

sin 45 = cos 45 = y /1 = x/1

so y = x

or y/x =1

Grace hit 12 balls in the batting cage out of 20 pitches. Tomorrow she is going to go to the same batting cage and get 30 pitches.
Use experimental probability to predict how many of the 30 pitches she will hit.

Answers

Answer:

she is expected to hit 18 out of the 30 pitches

Step-by-step explanation:

In this question, we are required to use experimental probability to make a prediction.

From the hits she has today, we can estimate the number of hits she might be getting tomorrow.

Since she made 12 hits out of 20 today, the probability that she has a hit will be 12/20 = 3/5

Now if she is having 30 pitches tomorrow, the expected number of hits would be the probability of getting a hit multiplied by the total number of pitches.

That would be 3/5 * 30 = 18 pitches

Question 11 point(s) Jared made Ask Your Teacher cups of snack mix for a party. His guests ate Ask Your Teacher of the mix. How much snack mix did his guests eat?

Answers

Answer:

[tex]8\frac{1}{2}[/tex] cups

Step-by-step explanation:

To determine the quantity of snack mix Jared guest ate, we multiply the quantity of snack mix the guest ate by the quantity of snack mix Jared made. i.e we determine [tex]\frac{2}{3}of12\frac{3}{4}[/tex] by multiplying both fractions together

quantity of snack mix Jared guest ate = [tex]\frac{2}{3}of12\frac{3}{4}=\frac{2}{3}*12\frac{3}{4}=\frac{2}{3}*\frac{51}{4}=\frac{17}{2} =8\frac{1}{2}[/tex]

Please please thank you

Answers

Answer:

option 2

452.16

You would need to use this equation...

V=πr²h

3.14 * (4)² * 9

= 452.16 cm³

SMART PEOPLE HELP ASAP

Answers

Answer:

Step-by-step explanation:

Area of this shape is L*W*H

All dimensions are given, now you just have to multiply it

turn all fractions into improper fractions

10 3/8 = 83/8

1 3/4 = 7/4

2 1/2 = 5/2

[tex]\frac{83}{8}[/tex] * [tex]\frac{7}{4}[/tex] * [tex]\frac{5}{2}[/tex] = ?

= 2905/64 =

app. 45.39

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