The focus of a parabola is [tex](0, 2)[/tex], and its directrix is the vertical line [tex]x=-6[/tex]. Identify the axis of symmetry, the vertex, and the direction the parabola opens.

Answers

Answer 1

Answer:

[tex]\huge\boxed{\text{Axis of Symmetry: } y = 2}[/tex]

[tex]\huge\boxed{\text{Vertex: } (-3, 2)}[/tex]

The parabola opens to the right (horizontally)

Step-by-step explanation:

We need to note a few basic rules about focuses and directrix’s of a parabola.

1. The directrix never touches the parabola, however it is perpendicular to the axis of symmetry

2. The focus never touches the parabola, however it lies on the axis of symmetry of the parabola

3. The directrix is always the same distance away from the vertex as the focus

If we know that the focus of the parabola is (0, 2) and the directrix lies on x=-6. that means these points are 6 units apart as we can assume the line x = -6 crosses the point (-6, 2), making these points 6 units apart (since |-6 - 0| = 6)

These are 6 points apart horizontally, via the x-axis, meaning that this is a horizontally facing parabola, and it opens to the right. We know it can’t open to the left because then the directrix (x = -6) would touch the parabola and then it wouldn’t be a directrix!

The vertex of the parabola will be the same distance away from the focus and the directrix. Since these are 6 units apart, that means the focus will lie [tex]6 \div 2 = 3[/tex] units away from either one.

Halfway between 0 and -6 is -3, so we know the vertex lies on x-coordinate -3. We also know that the focus is on y-value 2, meaning that the vertex will also be on y = 2, since the focus is always on the axis of symmetry.

So our vertex is at [tex](-3, 2)[/tex].

We know that this is a horizontally facing parabola, meaning that our axis of symmetry is going to lay on a y coordinate. The axis of symmetry always contains the vertex, so that means that we can just take the y value of the vertex and use that as the axis of symmetry. The vertex lies at y value 2, meaning that the axis of symmetry is [tex]y=2[/tex]

In conclusion

The vertex is at [tex](-3, 2)[/tex] The axis of symmetry is at [tex]y=2[/tex] The parabola opens to the right (horizontally)

Hope this helped!


Related Questions

Work out, giving your answer in its simplest form:
5/
14
x
7/
30​

Answers

x in (-oo:+oo)

((5/14)*x^7)/30 = 0

1/84*x^7 = 0 // : 1/84

x^7 = 0

x = 0

x = 0

Type the correct answer in the box. If necessary, use / for the fraction bar and simplify the fraction. cos(75°)cos(15°) =

Answers

Answer:

1/4

Step-by-step explanation:

If you type cos(75)cos(15) into a scientific calculator, the answer comes out as 1/4.

The value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a trigonometric expression:

= cos(75°)cos(15°)

As we know the trigonometric identity:

cos(a)cos(b) = (1/2)[cos(a + b) + cos(a - b)]

a = 75

b = 15

Plug the above values in the trigonometric identity:

cos(75)cos(15) = (1/2)[cos(75 + 15) + cos(75 - 15)]

cos(75)cos(15) = (1/2)[cos(90) + cos(60)]

The trigonometric ratio is the ratio of the pair of a right-angled triangle.

The value of cos90 = 0

cos60 = 1/2

cos(75)cos(15) = (1/2)[0 + 1/2]

cos(75)cos(15) = 1/4

Thus, the value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.

Learn more about trigonometry here:

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help please i need it



dhhdkhdkjhdkdhkshdksj

Answers

Answer:

26 percent sodium

also can i have brainliest please

Two students are taking a math test. After 5 minutes, one student is 13 done and the other is 28 done. How much ahead of the second student is the first

Answers

Given :

Two students are taking a maths test.

After 5 minutes, one student is 13 done and the other is 28 done.

To Find :

How much ahead of the second student is the first.

Solution :

Number of questions second student is ahead is :

[tex]n = 28 - 13\\\\n = 15[/tex]

Therefore, second student is ahead by first by 15 questions.

Hence, this is the required solution.

rob bought 15 concert tickets worth $322.50. Floor tickets cost $25 each while balcony tickets cost $17.50 each. How many tickets of each type did rob bye?

Answers

Answer:

8 floor tickets and 7 balcony tickets.

Step-by-step explanation:

f+b=15

25f+17.50b=322.50

Answer:

8 floor tickets, 7 balcony tickets

Step-by-step explanation:

F + B = 15

25F + 17.50B = 322.50

Can someone please help me? I can't find the h(x) for 0. I also need help with the last question. Please I need it very soon.

Answers

9514 1404 393

Answer:

  see attachments for a table and graph

Step-by-step explanation:

I find it convenient to use a graphing calculator or spreadsheet to do repetitive computations reliably.

__

Your specific question asks for h(0):

  h(0) = -|0 +2| +1 = -2 +1

  h(0) = -1

You may want to check your other table values.

I need help with this question -3/8 + 1/6

Answers

Answer:

5/24

Step-by-step explanation:

Step-by-step explanation:

[tex] - \frac{3}{8} + \frac{1}{6} [/tex]

[tex] (- \frac{3}{8} \times \frac{3}{3} ) + ( \frac{1}{6} \times \frac{4}{4} )[/tex]

[tex] - \frac{9}{24} + \frac{4}{24} [/tex]

[tex] - \frac{5}{24} [/tex]

plss help ASAP
What is the ratio of blue shapes to all shapes in the set below?
4.9
5.9
4.5
5.4​

Answers

Answer:

5:9

Step-by-step explanation:

There are 5 blue shapes out of 9 total shapes.

5:9 would be the answer

What is the trademark of a linear equation? WILL GIVE BRAINLIEST. Will report if answer is absurd

Answers

Answer: They can be represented in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Step-by-step explanation:

Select all that apply.
The figures below are not similar because
the corresponding angles are congruent
the corresponding sides are not proportional
the corresponding sides are proportional
they are not the same shape

Answers

I think b and d sorry if I am wrong

The two given figures are not similar because they are not the same shape. Option D is correct.

Given that,
A figure of two shapes has been shown, we have to discuss why the two shapes are not similar,

What is congruent geometry?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Here,
The two shapes are not similar because one is square and the other is a rectangle, There is why both are not the same shape, because they are cyclic and regular shapes their corresponding angles are congruent.

Thus, the two given figures are not similar because they are not the same shape. Option D is correct.

Learn more about congruent geometry here.

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Jasmine bought 6.4 pounds of chewy candy from the local confectionary store. If she gave 2.06 pounds of the candy to her little brother Sam, how many pounds did Jasmine have left for herself?
A.
3.8 pounds
B.
4.34 pounds
C.
3.98 pounds
D.
4.3 pounds

Answers

Answer:

4.34 lbs

Step-by-step explanation:

6.4-2.06= 4.34

The answer would be B. All you would do is subtract 6.4-2.06 and annex a zero after the four.

What is the slope of the line that passes through the points (-4, 4)(−4,4) and (-6, 6) ?(−6,6)? Write your answer in simplest form.

Answers

The answer is -1 and here’s the steps

An airplane flying at an altitude of 2600 m is approaching an airport run away located 56 km away (from the airplane to the run away). Calculate the airplane’s angle of decent. (Hint: the angle of decent is the same as the angle of depression.)

Answers

Given :

An airplane flying at an altitude of 2600 m is approaching an airport run away located 56 km away.

To Find :

The airplane’s angle of decent.

Solution :

Height of plane, h = 2600 m.

Horizontal distance of airplane from vertices is, d = 56 km = 56000 m.

Let, angle of depression is Ф.

So,

[tex]tan \ \phi = \dfrac{56000}{2600}\\\\tan \ \phi = 21.54\\\\\phi = 87.34^o[/tex]

Therefore, the angle of decent is 87.34°.

Hence, this is the required solution.

Three cubic feet of seawater weigh 192 pounds.
What is the weight of the seawater in an aquarium that is 4.4 ft long, 2.5 ft wide, and 5.3 ft high?

Answers

Answer:

3731.2 pounds

Step-by-step explanation:

Aquarium will hold 4.4 * 2.5 * 5.3 = 58.3 cubic feet of sea water.

For 3 cubic feet of sea water, weight is 192 pounds

For 58.3 cubic feet of sea water,

( 192 * 58.3) / 3 = 11193.6 / 3 = 3731.2 pounds

Use the graph below to answer the question. Quadrilateral PQRS will be rotated 90° clockwise about the origin resulting in quadrilateral P'Q'R'S'. Which statement is true

Answers

Answer: it’s D

Step-by-step explanation:

You have $22 to spend on four raffle tickets. After buying them you had $6. How much did each raffle ticket cost?

Answers

Answer:

$4 each

Step-by-step explanation:

Answer:

each ticket cos $4

Step-by-step explanation:

because is you multiply 4 × 6 is 16

and 22-16=6

Which two points on the number line are opposites? A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is 1 mark to the left of negative 1. Point B is half-way between negative 1 and 0. Point C is half-way between 0 and 1. Point D is half-way between 1 and 2. points A and B points B and C points C and D points A and D

Answers

Answer:

Points B and C are opposite

Step-by-step explanation:

0 on the number line marks the center of the number line. To the right on the number line are positive integers and to the left from zero are negative integers.

Points B and C are opposite because they are each half way between 0 and 1 on the right and 0 and -1 on the left

Answer:

b and c are opposites

Step-by-step explanation:

other guy was right

Misaki cut some wood for a bookcase she is building.She needs to find how many 13 ft boards she can make from a 5 ft board.Explain how to model with fraction bars to solve the problem.

Answers

Complete question :

Misaki cut some wood for a bookcase she is building.She needs to find how many 1/3 ft boards she can make from a 5 ft board.Explain how to model with fraction bars to solve the problem

Answer:

15

Step-by-step explanation:

Total Size of board = 5 feets

Size of board to be made = 1/3 feets

Number of 1/3 feets board to be made from 5 feets board :

Total size of board / size of board to be made

5 feets ÷ 1/3 feets

5 feets * 3 / 1 feets

= 15

Hence, number of 1/3 feets board that can be made from 5 feets board = 15

(Geometry) Please help! 50 points

Answers

Answer:

A) similar; SSS similarity

Step-by-step explanation:

You have to find the proportion by dividing each side to the according side

35/14 = 2.5  -  S/D

20/8 = 2.5  -  R/E

30/12 = 2.5  - Q/F

Answer:

A B AND C

Step-by-step explanation:

The answers are

abc

Scott bought three bags of candy with 75 pieces in each one. He plans to divide all the candy evenly among seven friends. How many pieces of candy will Scott have left for himself?​

Answers

He will have left 28.125
Explanation: 3x75 / 8

Answer:

he will have 28 pieces

Step-by-step explanation:

75*3=250

250/8=28

A newspaper surveyed households to determine how likely they were to subscribe to their publication. The results are shown below by annual household income.

Household Income
< $60,000 > $60,000
I would never purchase a newspaper subscription. 40 63
I might or might not purchase a newspaper subscription. 53 70
I would probably purchase a newspaper subscription. 65 32
I already purchase a newspaper subscription. 73 16
Identify the percentage of families with an income more than $60,000 who might or might not purchase a newspaper subscription. What does this number represent?

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is  C

Step-by-step explanation:

The  sample  

                                                                                          Household Income

                                                                                     < $60,000    > $60,000

I would never purchase a newspaper subscription.          40                63

I might or might not purchase a newspaper subscription. 53                70

I would probably purchase a newspaper subscription.     65                 32

I already purchase a newspaper subscription.                   73                 16

Generally the sample size is mathematically represented as

       [tex]n = 40 + 53 + 65+ 73 + 63 + 70 + 32+ 16[/tex]

=>    [tex]n = 412[/tex]

Generally the number of the sample with an income greater $60,000 is mathematically represented as

        [tex]N = 63 + 70 + 32 + 16[/tex]

=>     [tex]N = 181[/tex]

Generally the number of  families with an income more than $60,000 who might or might not purchase a newspaper subscription is

      [tex]X = 70[/tex]

Generally the percentage of families with an income more than $60,000 who might or might not purchase a newspaper subscription is

           [tex]P(X) = \frac{70}{181} * 100[/tex]

=>        [tex]P(X) = 39\%[/tex]

   

       

How do you find slope? like...what's the equation? Cause nothing in my math class makes sense rn and finding the slope of things is the reason why

Answers

slope is y=mx+b

m=slope aka rise/run
b=base aka, where the line starts at

1 Admission to the local movie theater is $3 for each child and $7 for each adult. A group of 12 people pay $64 admission. How many children are in this group?

Answers

Given:

Admission to the local movie theater is $3 for each child and $7 for each adult.

A group of 12 people pay $64 admission.

To find:

The number of children in a group.

Solution:

Let the number of children be x and number of adults be y.

According to the question,

Total persons : [tex]x+y=12[/tex]          ...(i)

Total cost : [tex]3x+7y=64[/tex]     ...(ii)

Multiply equation (i) by 7 and subtract the result from (ii).

[tex]3x+7y-7(x+y)=64-7(12)[/tex]

[tex]3x+7y-7x-7y=64-84[/tex]

[tex]-4x=-20[/tex]

Divide both sides by -4.

[tex]x=5[/tex]

Therefore, the number of children is 5.

Please please help! Its due soon!! Ill mark brainliest!!
I need side b, using tangent!! Thank you!!

Answers

Answer:

tan 68 degrees = b/60

60 * tan 68 degrees = b

b = 148.5 in tenths, 149 as a whole number, and 148.51 in hundredths

Step-by-step explanation:

Hope it helps!

Answer:

tan 68 degrees = b/60

60 * tan 68 degrees = b

b = 148.5 in tenths, 149 as a whole number, and 148.51 in hundredths

  . Step-by-step explanation:

Hope it helps!

Sarge completed 1/10 of his report in 4/5 of an hour. At this rate, how much of the report will Sarge complete in 1 hour?

Answers

Answer:

1/8

Step-by-step explanation:

Rate is the change of a quantity per unit time

We are told Sarge completed 1/10 of his report in 4/5 of an hour.

We are going to equate the rate at 4/5hour to that of 1hour to get how much of the report Sarge will complete in 1 hour

(1/10)/x=(4/5)/1

0.10/x=0.8

Make x subject of the formula we have

X=1/8

Hence 1/8 of the report needed to be completed

Help ASAP plz
Jacob bought 5 boxes of pencils for his drawing class. Each box contains 12 pencils. Which point on the graph shows the number of pencils he bought?

Answers

Answer:

it would be (5,60)

Step-by-step explanation:

he bought 5 boxes

each box has 12 pencils

5*12=60

Randy bought 6 candy bars for $7.20. What is the cost per candy bar? PLS HELP FAST IT IS WORTH 45 POINTS AND MY GRADE

Answers

Answer:

$1.20 per candy bar

Step-by-step explanation:

7.2 ÷ 6 = 1.2

What does x an y represent

Answers

Answer:

x represents the bottom and y represents the top

Step-by-step explanation:

Answer:

grid

Step-by-step explanation:

So they x in the grid it a straight line in the middle ok. Then we have the y which is the one that's up and down in the grid. Also when the numbers are added that are ploted somewhere on the x goes first because x goes first in the alphabet.

is y=x/4 a proportional relationship

Answers

Answer:

yes

Step-by-step explanation:

The function f(x) = x/4 represents a proportional relationship.

What is a proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent.  A straight line represents a proportional relationship. Mathematically -

y = mx + b

(y - b)/x = m       [m is constant]

or

y = mx

m = y/x               [m is constant]

Given is the following function -

y = x/4

We have -

f(x) = x/4

Now, we know a straight line represents a proportional relationship. The general form of equation representing the proportional relationship is -

y = mx

where -  [m] is constant

y = x/4

y = (1/4)x

On comparing, we get -

m = 1/4

Hence, the function f(x) = x/4 represents a proportional relationship.

Therefore, the function f(x) = x/4 represents a proportional relationship.

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Write a function g whose graph represents a reflection in the x-axis of the graph of f(x)=1/2x−3.

Answers

g(x) = -1/2 - 3
(I'm not sure)
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