Which statement is best supported by the information in the box plots?

The coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.

The set of all points in a plane that are equidistant from a fixed line and a fixed point (not on the fixed line) in the plane is a parabola. The fixed line is the ‘directrix’ and the fixed point is the ‘focus’. The point of intersection of the parabola with the axis is the vertex.

For the given situation,

The equation of parabola is [tex](x-1)^2=12(y+2)[/tex] ------ (1)

The diagram below shows the parabola and the vertex of the equation of parabola.

The general form of the equation of parabola is

[tex](x-h)^{2} =4a(y-k)[/tex]

Here the vertex is (h,k)

Now compare the equation 1 with this general form, we get

⇒ [tex]h=1[/tex] and [tex]k=-2[/tex]

Hence we can conclude that the coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.

Learn more about equation of the parabola here

https://brainly.com/question/20333425

#SPJ2

Answer:

The scale factor is 1/4

Step-by-step explanation:

20/5 = 4

Answer:

22 feet

Step-by-step explanation:

A=lw

28=l(4)

7=l

P=2l+2w

P=2(7)+2(4)

P=14+8

P=22

Hope it helped! (:

Answer:

The perimeter of the rug is 22.

Step-by-step explanation:

The formula for perimeter of a rectangle is side + side + side + side .

The width of the rug is 4 and the length of the rug is 7.

And 4 + 4 + 7 + 7 = 22.

Answer:

x=24.9

Step-by-step explanation:

Use pythagoras theorem to find half of x which is 12.45 then multiply by 2 to get x

Answer: I think the red one I am not 100%

Step-by-step explanation:

Given:

Leon had 84 paper clips.

He gave [tex]\dfrac{3}{4}[/tex] of them to Joe.

Joe gave [tex]\dfrac{2}{7}[/tex] of what he received to Justin.

To find:

How many paper clips did Justin get?

Solution:

Leon had 84 paper clips and he gave [tex]\dfrac{3}{4}[/tex] of them to Joe.

Number of paper clips Joe has = [tex]\dfrac{3}{4}\times 84[/tex]

                                                    = [tex]63[/tex]

Joe gave [tex]\dfrac{2}{7}[/tex] of what he received to Justin.

Number of paper clips Justin has = [tex]\dfrac{2}{7}\times 63[/tex]

                                                       = [tex]18[/tex]

Therefore, Justin has 18 paper clips.

Step-by-step explanation:

Answer:

it's b on edge

Step-by-step explanation:

Answer:

(random name) drinks 3/8 of the lemonade then later drinks 6/8 of the cranberry juice before (random name) goes to bed they put the lemonade and the cranberry juice together. How much is in the cup now?

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Let the equation of the given exponential function is,

y = a(b)ˣ

Graph of the given exponential function passes through (0, 2) and (-1, 6)

For a point (0, 2),

2 = a(b)⁰

a = 2

For another point (-1, 6),

6 = 2(b)⁻¹

3 = b⁻¹

b = [tex]\frac{1}{3}[/tex]

Therefore, equation of the exponential function will be,

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

Answer:

C

Step-by-step explanation:

Answer:

(0,1) is the answer

Step-by-step explanation:

hope it helped!!!

Answer:

1) x = 50 m

2) Max area = 22500 m²

3) Max area of each pen = 1500 m²

4) y = 150 m

5) dimensions of pen are 50m and 30m

6) Graph is attached

Step-by-step explanation:

Area of a rectangle is length × width

Let length be y and let width be x

Thus;

A = xy

Fencing material is 600m

Thus,perimeter = 600

Perimeter is; P = 6(length) + 2(width)

Thus;

600 = 6x + 2y

y = (600 - 6x)/2

y = 300 - 3x

Thus,

A = x(300 - 3x)

A = -3x² + 300x

We can see that the coefficient of x² is negative. This means that the parabola will open downward and has a maximum value at the vertex.

The vertex formula is;

x = -b/2a

a = -3

b = 300

Thus;

x = -300/(2 × -3)

x = 50 m

Since y = 300 - 3x, then;

y = 300 - 3(50)

y = 150 m

Maximum area of entire garden = xy = 50 × 150 = 7500 m²

There are 5 pens, thus;

Max area of each pen = max area of entire garden/5 = 7500/5

Max area of each pen = 1500 m²

Dimensions of each pen will be;

x and y/5

>> x = 50 m and y/5 = 150/5 = 30m

Answer:

i think its (687.79)

Step-by-step explanation:

Answer:

687.79

Step-by-step explanation:

since when the number before the digit is five above

And 8 is the hundredth , the one after eight is 5 so it gives 1 to eight that's how you get your answer

Answer:

987 milmeters equal to 98.7 centimeters

Step-by-step explanation:

To figure these kinds of problems divide the millimeter by 10 and you will get the centimeter value.

Hope that helps!

Answer:

The rate of change per week is $6.

Step-by-step explanation:

56 - 14 = 42

42/7 = $6

6 dollars were added each week.

Step-by-step explanation:

7.B

8.C

9.A

10.D

.......

Answer:

One way to check is 102 ÷ 6 = 17 is 100 ÷ 5 = 20. 

Answer:

letter a

Step-by-step explanation:

Answer:

2 because it holds the same value as -2 and its the additive inverse

Answer: the answer is 29.3

Step-by-step explanation:

Answer:

BAC=15

Step-by-step explanation:

angle BOA= 180-30= 150

triangle BAO is   isosceles because it has two equal sides, radii of a circumference so the angles ABO=BAO=(180-150)/2=15

1200/240=5

so 240 goes into 1200 5 times, just like 20% goes into 100% 5 times.

The answer would be 20%.

Hope this helps!

Answer:

Let x represent minutes.

The inequality derived from the question is...

58 > 18 + 5x

Solve for x...

58 > 18 + 5x

58 - 18 > 5x

40 > 5x

40/5 > x

8 > x

So it will take more than 8 minutes to have 58 liters.

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

Subtract them

5/9-4/9=1/9 Answer

Answer:

The equation of the circle is;

(x - [(-1))² + (y - [7])² = 8

Step-by-step explanation:

The given coordinates of the points P and Q are;

P = (-3, 5) and Q = (1, 9)

To find the equation of the circle that has segment PQ as a diameter

The equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

Given that segment PQ is the diameter of the circle, we have;

The center of the circle, O = The midpoint of PQ

The coordinates of the midpoint of segment PQ, O = ((-3 + 1)/2, (5 + 9)/2) = (-1, 7)

∴ The coordinates of the center of the circle, O = The coordinates of the midpoint of segment PQ = (-1, 7)

Therefore;

h = -1, k = 7

From PQ = The diameter of the required circle, we also have;

The length of PQ = 2 × (The radius of the circle) = 2 × r

The length of segment PQ = √((1 - (-3))² + (9 - 5)²) = √32 = 4·√2

Therefore;

The length of PQ = 4·√2 = 2 × r

r = (4·√2)/2 = 2·√2

r = 2·√2

r² = (2·√2)² = 8

r² = 8

The equation of the circle is therefore;

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - 7)² = 8.

Answer: 87

Step-by-step explanation: