X=5 and y=7 for algebraic expression 2(4x-3) + 6(3y-5)

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

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

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

brainly.com/question/8708520

Answer:

its 48

Step-by-step explanation:

Answer: 1.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

This is a fraction equal to

6 miles ÷ 2 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2

6 miles ÷ 2 2 hours ÷ 2= 3 miles1 hour= 3 miles hour = 3 miles per hour

Answer:

1:5

Step-by-step explanation:

13cm: 65cm = 13cm/65cm =13/65 = 1/5= 1:5

Answer:

$9.80

Step-by-step explanation:

Remember that the way to find the mean of a data set is by adding together all the values, and dividing by the number of the values. So, in this case, you add the 5 values together and get 49. Since there are 5 values, you divide 49 by 5 and get 9.8, or in a real world-money situation $9.80.

Answer:

your answer will be Option C.256

Step-by-step explanation:

hope it helps

Answer:

[tex]\boxed{C. 32}[/tex]

Step-by-step explanation:

Hello There!

If you didn't know the exterior angle of a triangle is equal to the opposite interior angles

so

100 = 68 + x

subtract 68

100-68=32

68-68 cancels out

we're left with

x = 32

Answer:

C

Step-by-step explanation:

A normal curve describes a unimodal curve... this has 2 peaks (bimodal)

**this looks like stats?**

The graph does not represent a normal curve since:

Graphically speaking, the probability density function of a normal distribution has the following characteristics:

The curve presented in the image only observes the condition described in 2. Therefore, we conclude that correct choices are:

We kindly invite to check this question on normal curves: https://brainly.com/question/15992479

Answer:

₹45000

Step-by-step explanation:

Let the selling price (SP) of the television be ₹x.

Therefore,

Profit [tex] =\frac{1}{9}x[/tex]

Cost price (CP) = ₹ 40000

[tex]Profit = SP - CP \\ \\ \frac{1}{9}x = x - 40000 \\ \\ \frac{x}{9} - x = - 40000 \\ \\ \frac{x - 9x}{9} = - 40000 \\ \\ - \frac{8}{9} x = - 40000 \\ \\ x = 40000 \times \frac{9}{8} \\ \\ x = 5000 \times 9 \\ \\ x = 45000[/tex]

All the answers are in the picture attached.

Answer:

48

Step-by-step explanation:

Cat = x

Dog = 8x

x + 8x = 54

9x = 54

x = 6, Dog = 8 * 6 = 48

Answer: a. 90

Step-by-step explanation: plz give me brainliest

Answer:

P=22cm

A=24cm²

Step-by-step explanation:

Answer:

290in

Step-by-step explanation:

Answer:

I think the anwser is 8

Step-by-step explanation:

Answer:

It will be 8

Step-by-step explanation:

because the triangle will be in a ratio of 1:[tex]\sqrt{3}[/tex]:2, here 1 corresponds to 4, so the sides will be 4, 4\sqrt{3} and 8!

Answer:

Raeyln bought 60 stickers, Beth bought 15 stickers

Step-by-step explanation:

simple math l.mao

Answer:

1. v = 72

2. b = 8

3. 0 or -2

4. C = -24

Step-by-step explanation:

Hope this helps.. Can I get brainiest

Answer:

p = $200

Step-by-step explanation:

90/p = 45/100

45p = 9000

p = 9000/45 = $200

Answer:

25 questions,

$18.75

Step-by-step explanation:

Remember, to change percents to decimals, divide the number by 100 and remove the parentheses.

1. 84%, or 21 questions of Roy's test were correct.

Let's set the number of questions on the test as "x". We can then write this equation:

84% * x = 21

Simplify.

0.84 * x = 21

Divide both sides by 0.84

x = 25

There were 25 questions on the test.

2. Cheesecake Factory question

We need to find 15% of 125.

15% * 125 =

0.15 * 125 =

18.75

They need to leave a $18.75 tip.

I hope this helps! Feel free to ask any questions!

Answer:

He pays $18 for the long distance calls because 0.06 x 300 is 18

and if you want to find how much that month do 18+20 which is 38

$38 that month

Answer:

To find out how any inches are in a certain amount of feet you have to multiply it by 12. For example 4 feet is equal to 48 inches. (4x12)

Step-by-step explanation:

Answer:

1 hour and about 15 minutes.

Step-by-step explanation:

because in an hour she walks 4.5 km. and 4.5•2=9 so just another km will be 10 so estimatly it'll be 1 hour and 15 minutes

2 hours 13 minutes 20 seconds

Answer:

1.(x+y)²

2. (x-4)²

3. (4a²-3b²)²

Answer:

Step-by-step explanation:

Answer:

y=3×+6

Step-by-step explanation:

bla bla bla bla bla bla bla hhhhhhhhhhhh

Answer:

13.2

Step-by-step explanation:

using the Pythagorean theorem:

L² = 20² - 5²

L² = 400 - 225 = 175

L = 13.23

You have a 3/6 chance of getting even number (there are 3 even numbers in the 6 die)

You have a 1/16 chance of getting a 16 on the other die

multiply them 1/3 × 1/16 then convert it to decimal form is your answer

Answer:

16

Step-by-step explanation:

8x2