Complete the square
to find the vertex
of this parabola.
x?+8y+2x - 23=0

Complete The Squareto Find The Vertexof This Parabola.x?+8y+2x - 23=0

Answers

Answer 1

Answer:

The vertex of the parabola is;

([-1], [3])

Step-by-step explanation:

The given quadratic equation is presented as follows;

x² + 8·y + 2·x - 23 = 0

The equation of the parabola in vertex form is presented as follows;

y = a·(x - h)² + k

Where;

(h, k) = The vertex of the parabola

Therefore, we have;

x² + 8·y + 2·x - 23 = 0

8·y = -x² - 2·x + 23

y = 1/8·(-x² - 2·x + 23)

y = -1/8·(x² + 2·x - 23)

y = -1/8·(x² + 2·x + 1 - 23 - 1) = -1/8·(x² + 2·x + 1 - 24)

y =  -1/8·((x + 1)² - 24) =  -1/8·(x + 1)² + 3

Therefore, the equation of the parabola in vertex form is y =  -1/8·(x + 1)² + 3

Comparing with y = a·(x - h)² + k, we have;

a = -1/8, h = -1, and k = 3

Therefore, the vertex of the parabola, (h, k) = (-1, 3).


Related Questions

How many solutions are there to the equation below?
5x - 2 - 3x(1 + 2) = 2(2 + 3)
A. O
B. infinitely many
C. 1

Answers

C. Only 1, you can tell by just looking at it, you can see that there will be a real number on one side and an x value on the other and by solving you can find only one answer that x will equal.

i need 4 more brainliest's

Answers

Answer:

What??

Step-by-step explanation:

Could I have a branliest?? You don't have to give it to me if you don't want to.

eli is going to make apple pie he buys 17 apples and put them and put the in paper bags to take home each bag holds 6 apples how many bags eli completely fill? how many appels are left

Answers

Answer:

Eli can only have 2 bags, and there will be 5 apples left

Step-by-step explanation:

17/6=2 with a remainder of 5

Answer:

17/6=2 with a remainder of 5

Step-by-step explanation:

what is the length of BC ?

Answers

The answer is c.

Since a^2+b^2=c^2, b^2=c^2-a^2 thus,
16=4-b^2= srt. of 12

Answer:

b = √12

Step-by-step explanation:

Pythogerom Thyrom

a^2 + b^2 = c^2

2^2 + b^2 = 4^2

4 + b^2 = 16

Find the value of b

4 - 4 + b^2 = 16 - 4

b^2 = 12

b = √12

Complete steps 2 and 3 to solve the system of equations.

y = 4x – 5,

y = –3

Answers

Answer:

Point form: ([tex]\frac{1}{2}[/tex],-3)

Equation form: x=1/2  y=-3

Step-by-step explanation:

hope it helps ;)

HELP NOW WITH EXPONENTS

Answers

PLZ MARK BRAINLIEST! :)

Answer:

[tex]7^{12}[/tex]

Step-by-step explanation:

When you divide two numbers that have exponents and have the same base, just subtract the exponents. In this case, 7 is the base of both the dividend and the divisor. So, simply subtract 14 - 2 to get 12. The final answer is [tex]7^{12}[/tex].

Hope this helps! :)

Consider -152 ÷ 19. Which statements are correct?
A) -152/19 = -8
B) 19/ -152 = -8
C) -152 ÷ 19 is rational
D) -152 ÷ 19 us irrational
E) -152 ÷ 19 = -152/19

Answers

Answer: A, C, E

Explanation:
-152/19 = 8
-8 = -8 ✅
-152 ÷ 19 = -8 the number -8 can be written as a fraction so it’s rational
-152 ÷ 19 = -152/19
-8 = -8 ✅

1. Find the volume of each cylinder ( use = 3.14 )

Answers

Answer:

1. volume = 1243.44ft^3

2. volume = 54259.2ft^3

Pls helpppppppppl!!!!

Answers

Answer:

I dont really understand it but I think it's the first one cuz that's the only one that makes sense to me hope it helped tho:))))))))

Answer:

Multiply the amount of milk by 4

Step-by-step explanation:

4x1=4

4x2=8

4x3=12

and it keeps going

hope this helps

help ill give brainliest

Answers

Answer: Choice B

==========================================

Explanation:

Here's a slightly more detailed breakdown of what's going on

3x + 2y = 15 ... start with the first equation

3x + 2( y ) = 15 .... the parenthesis don't change the expression

3x + 2( 3x+5) = 15 ... replace y with 3x+5; since y = 3x+5

From here, you solve for x like you would any other single variable equation. Once you know x, you can determine y through y = 3x+5.

SOS PLEASE HELP
write the equation for this line

Answers

If this is for slope-intercept, the equation is: y = 3x + 1

To find the slope, you would find the rise over run ( [tex]\frac{rise}{run}[/tex] ). So, you would start where the graph intersect at the y-axis, which is 1. You would go up 3 times, and right 1 time. So, [tex]\frac{3}{1}[/tex], or 3, would be your slope. To find the y-intercept, you would need to find where the graph intersects at the y-axis, which is 1, so it would be your y-intercept. Plug them into the y = mx + b formula and the answer is y = 3x + 1.

If you have any further questions, please reach out to me :)

The ratio of the side length of a square to the square's perimeter is always 1 to 4. Peter drew a square with a perimeter of 28 inches.
What is the side length of the square Peter drew?

Answers

Answer:

7 inches

Step-by-step explanation:

Answer:

perimeter of square = 4x

= 4x = 28/4

x = 7 inches

In triangle ABC, the sum of the measures of angle A and angle B is 57°. What is the measure of and C?

Answers

Answer:

I think it's 123 if not sorry

Step-by-step explanation:

all you need to do is 180 - 57 to get your answer

Will give brainlest

The figure is made up of a cylinder and a cone. What is the exact volume of the figure? Enter your answer in the box.​

Answers

Answer:

V=160.22114

Step-by-step explanation:

Volume of cone = 47.12389

Volume of cylinder = 113.09734

In your own words, describe what the word "congruent" means.

Answers

Answer:

heres a sentence using it

Eating five chocolate bars is not congruent with your plan for losing weight.

Triangles are considered congruent when they have the same angles.

it means

having the same size and shape

Answer:

Congruent

Step-by-step explanation:

Multiple objects the work well together.

Hope this helps (:

if a point a device line segment a b of length 10 centimetre internally In the ratio 2:3 then find the length of a d ​

Answers

Given:

Consider a point d divides line segment ab of length 10 centimetre internally in the ratio 2:3.

To find:

The length of ad.

Solution:

If a point d divides line segment ab internally in the ratio 2:3, then the length of ad and db are 2x and 3x receptively.

We know that,

[tex]ab=ad+db[/tex]

Length of the segment ab is 10 cm.

[tex]10=2x+3x[/tex]

[tex]10=5x[/tex]

Divide both sides by 5.

[tex]2=x[/tex]

Now,

[tex]ad=2x[/tex]

[tex]ad=2(2)[/tex]

[tex]ad=4[/tex]

Therefore, the length of segment ad is 4 centimetres.

Which best describes the slope of the given line

A. Negative
B. Positive
C. Vertical
D. Zero

Answers

D. because the line is flat and undefined making it 0.
D plz giv me a thank you

there is the screenshot

Answers

Answer:

11 Tenths

Step-by-step explanation:

Withouth the tenths, the bottom number would be 1.05. So we need 1.10 or 11 more. 10 tenths is one whole plus the 1 tenth we need to put in the tenths place.

Please do 37,39,41 kskdkjdnd sorry please and ty!!!!

Answers

37: 1 yard
39: to
41: 21000 mm

help me with this please

Answers

Answer:

.............

Step-by-step explanation:

Student Council is selling tickets to the Winter
Dance. Tickets cost $5 per person or $8 per
couple. To cover expenses, at least $1200
worth of tickets must be sold. No more than 500
students can fit in the gym where the dance is
being held.
List two combinations of tickets that could be sold, so
that Student Council makes a profit, yet stays under the
room capacity.

Answers

Answer:

Two possible combinations are;

1) 200 single and 30 couples

2) 150 single and 57 couples

Step-by-step explanation:

The given parameter in the question are;

The cost of ticket per person = $5

The cost of tickets per couple = $8

The minimum worth of tickets to be sold = $1,200

The maximum number of students that can fit in the gym = 500

Let 'x' represent the number of single persons that attend the dance and let 'y' represent the number of couple that attend, we have;

5·x + 8·y ≥ 1,200

x + y ≤ 500

Making 'y' the subject of both equations gives;

y ≥ 150 - 5·x/8

y ≤ 500 - x

From the graph of the inequalities created with Microsoft Excel, we have;

When x = 200, and y = 30, we get;

5 × 200 + 8 × 30 = 1240 > 1200

200 + 30 × 2 = 460 < 500

We also have;

x = 150, and y = 57, we get

Equating both values of 'y', we get;

5 × 150 + 8 × 57 = 1206 > 1200

150 + 57 × 2 = 264 < 500

Therefore, from the acceptable region in the graph, we have the following two possible combinations

1) 200 single and 30 couples

2) 150 single and 57 couples

Given: Quadrilateral ABCD is a kite. Prove: ΔAED ≅ ΔCED Kite A B C D is shown. Diagonals are drawn from point A to point C and from point B to point D and intersect at point E. It is given that quadrilateral ABCD is a kite. We know that AD ≅ CD by the definition of . By the kite diagonal theorem, AC is to BD This means that angles AED and CED are right angles. We also see that ED ≅ ED by the property. Therefore, we have that ΔAED ≅ ΔCED by .

Answers

Answer:

1. kite 2. perpendiclular 3. reflective 4. HL

Step-by-step explanation:

I hope this helps :)

Answer:

We know that AD ≅ CD by the definition of kite. By the kite diagonal theorem, AC is perpendicular to BD. This means that angles AED and CED are right angles. We also see that ED ≅ ED by the reflexive property. Therefore, we have that ΔAED ≅ ΔCED by HL.

Step-by-step explanation:

We know that AD ≅ CD by the definition of kite.

- adjacent sides in a kite are congruent

By the kite diagonal theorem, AC is perpendicular to BD.

- the kite diagonal theorem states that diagonals of a kite form right angles because they are perpendicular to each other.

We also see that ED ≅ ED by the reflexive property.

- any side or angle congruent to itself is identified by the reflexive property

Therefore, we have that ΔAED ≅ ΔCED by HL.

- the triangles formed are all right triangles, so we can they that the two triangles are congruent to each other by the Hypotenuse Leg theorem.

solve using the box method

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{Just SIMPLIFY the given EQUATION or find the DIFFERENCE}\\\large\text{OF the SQUARES... Here is the formula: }\mathsf{\bf a^2 - b^2 =(a+b)(a-b)}[/tex]

[tex]\large\text{Equation: }\mathsf{\dfrac{(4x^2-9)}{(2x + 3)}}[/tex]

[tex]\large\text{Rewrite }\mathsf{ 4x^9 - 9}\large\text{ in the formation of }\mathsf{a^2 - b^2}\large\text{ whereas}\mathsf{a = 2x \ \&\ b = 3.}[/tex]

[tex]\large\text{Equation: }\mathsf{\dfrac{(2x)^2-3^2}{2x + 3}}[/tex]

[tex]\large\text{This is where you try to do the DIFFERENCE OF its SQUARES}[/tex]

[tex]\mathsf{\dfrac{(2x + 3)(2x - 3)}{2x + 3}}[/tex]

[tex]\large\text{CANCEL out: }\mathsf{(2x + 3)\ - (2x +3)}\large\text{ because it gives you 0}[/tex]

[tex]\large\text{This leaves us with }\mathsf{\bf 2x - 3}\large\text{ as your POSSIBLE ANSWER}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge \bf 2x - 3}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\large\text{Note: There is/are many ways to solve for equations like this.... this was just}\\\large\text{the quickest and easiest way to understand it!}[/tex]

PLEASE BEED HELP ASAP​

Answers

Answer:

1. Complementary Angles.

2. x=60°

Step-by-step explanation:

Part 1:

*Note: A complementary angle is when the sum of two angles equal 90 degrees. A Supplementary angle is when the sum of 2 angles equals 180 degrees.

In this instance, the 2 angles equal 90 degrees, as indicarted by the box on the angle. Therefore, the the angles are complentary.

Part 2:

1. Since we know that the sum of the two angles (x-30 and x) is 90 degrees, we can write an equation which says: (x-30) + x=90.

2. Then we'd simplify the equation by adding the like variables, and adding 30 to both sides:

2x=120

3. Now we will divide both sides by 2

[tex]\frac{2}{2} x=\frac{120}{2} \\x=60[/tex]

4. As a result, we get x=60, now label your answer with the degree sign, and enjoy your answer.

Write an equation in standard form for the line.
Slope is 3, and (1, 6) is on the line.

Answers

Answer:

Step-by-step explanation:

m = 3

(1 , 6)

y - y1 = m(x -x1)

y - 6 = 3(x - 1)

y - 6 = 3x - 3

    y = 3x - 3 + 6

    y = 3x +3

Standard form:

-3x + y - 3 = 0

pls help will give brainliest when i can ​

Answers

Angle 1 is corresponding to angle 5.
This is where one angle has the same relative position as another angle.

I KNOW THIS ISNT MATH BUT PLEASE HELP! Which statements describe the
mountains region? Check all that apply

. It is the least populated region in the state

Its largest metropolitan area surrounds Asheville

It has a fall line running through the region's center

It has become a big industry for Christmas trees

It draws many people for outdoor adventures

It has large urban areas where most people live​

Answers

Answer:

lots of stuff

Step-by-step explanation:

snow lava and stone frfr

Answer:

I think A and D and E and maybe B

Step-by-step explanation:

(im not sure if they r right though)

In the triangle below, m ∠ 1 = 39 ° and m ∠ 4 = 85 ° . What is m ∠ 2 ?

Answers

Answer:

one sec

Step-by-step explanation:

please explain how to do this

Answers

Answer:

27.4

Step-by-step explanation:

Use your calculator for this.

Remember, use SOH CAH TOA

We have an opposite (O) and an adjacent side (A), so we use SINE

sin(41)=18/X......following?

Now, solve for X by multiplying both sides by X......sin(41)(X)=18

Then, divide both sides by sin(41).

Type into your calculator: 18/sin(41), and you'll get 27.44. Round to the nearest tenth, or 27.4!

Answer:

x = 11.8

Step-by-step explanation:

sine = [tex]\frac{opposite}{hypotenuse}[/tex]

⇒ sine 41 = [tex]\frac{18}{x}[/tex]

⇒ 0.656 = [tex]\frac{18}{x}[/tex]

multiply 18 on both sides:

⇒ 0.656 x 18 = [tex]\frac{18}{x}[/tex] x 18

⇒ 11.808 = x

round to the nearest tenth:

⇒ 11.808 = 11.8

WILL MARK BRAINLIEST NO LINKS: If you had a cube with a side length of 4, how can your write the calculations in exponential form?

Answers

The exponential form would be written as 4^3
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