Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.

Complete The Square To Write Each Equation In Vertex Form. Then, State Whether The Vertex Is A Minimum

Answers

Answer 1

Answer:

          vertex form:    y = (x + 3)² + 1           the vertex is minimum           coordinates of the vertex:  (-3, 1)

Step-by-step explanation:

[tex]y=x^2+6x+10\\\\y=x^2+6x+9-9+10\\\\\bold{y=(x+3)^2+1}[/tex]

a = 1 > 0  ← it means the parabla opens up, so, the vertex is minimum

The vertex form is  y = a(x - h)² + k, where (h, k) is the vertex

So, from  y = (x + 3)² + 1   the vertex is:  (-3, 1)


Related Questions

The length of AB (the minor arc) is 40 cm. What is the circumference of C?

A. 360 cm
B. 120 cm
C. 60 cm
D. 240 cm
E. 6.67 cm
F. 24 cm

Answers

Answer: 240 cm

Explanation : the circumference of C is: 6 X 40=240

1/2y+3.2y=20 need some help, not very good with functions :/ asap tho pls-

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Answer:

hopefully this will help you on your journey!

NEED HELPP QUICK NO LINKS PLEASE!!

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Answer:

May be only relation 3 is the function.

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Answers

Answer:

I think a but I'm not sure

If 4, 6 and 8 and 14, 21, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x

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When you add all the numbers up and then divide by two you get the answer

b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
Cost (in dollars)
2
10
3
9
15 45
The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $50:

Answers

Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.

The best way to find out how many people will go to movie with $50 is by looking at the table.

So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,

Step-by-step explanation:

In the diagram below, what is the value of x rounded to the nearest whole number? If necessary, round your answer to the nearest tenth of a unit. 17 с х D 10 24 O A. 24 O B. 17 O O C. 7 O D. 12​

Answers

Answer:

12

Step-by-step explanation:

There is no specific work, but  this is assuming that the triangles are cut in the middle equally, and 24/2 = 12  

Which equation shows how to use equivalent fractions to evaluate 7/6-4/5

Answers

Answer:How do you evaluate equivalent fractions?

Summary:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

You only multiply or divide, never add or subtract, to get an equivalent fraction.

Only divide when the top and bottom stay as whole numbers.

Step-by-step explanation:

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly.After 11months he weighed 140 Kilograms. He gained weight at rate of 5.5 kilograms per month.
Let y represent the sumo wrestler’s weight (in kilograms)after x month.
Complete the equation for the relationship between the weight and number of months.

Answers

The equation that shows the relationship between the weight and number of months. y =  79.5 + 5.5x

What is weight ?

In science and technology, the weight of an object is the force acting on an object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on an object. Others define weight as a scalar quantity, the magnitude of  gravitational force. Still others define it as the size of the reaction force applied to the body by mechanisms resisting the influence of gravity: weight is a quantity measured, for example, by a spring balance.

Given that ; Total Month = 11 months

Gained weight at the rate =  5.5 kilograms per month.

Assume initial weight W,

The initial weight + total month  x rate = 140

w + 11 x 5.5 = 140

w = 79.5

if y is total weight after x months

y = 79.5 + 5.5x

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Please help ASAP will give 5 stars and brainliest if possible!!

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answer

the dot will be shaded and the line goes to the positive part because x is more than or equal to 3

A kite is attached to a 20 foot string that is staked to the ground . how far above the ground is the kite?

Answers

Answer:

12ft

Step-by-step explanation:

Answer:

The kite is 15ft from the ground

Step-by-step explanation:

What is the negation of ∃?

Answers

In order to find the negation of an expression we simply put the not operator in front of them . Therefore, the negation of ∃ is that â is not ^ to f.

The term negation means opposite , that is the negation of a statement is the opposite of the given mathematical statement. If we will take the example of P , let P be a statement, then the negation of P will be represented by ~P.

There are two  symbols which are  used to represent the negation of a statement which are “~” or “¬”. Therefore, ~P is known as the negation of P.

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The diameter of a circle is 8 cm. Find its area in terms of π.

Answers

Answer:

[tex]16\pi[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

Area of a circle is equal to [tex]\pi r^2[/tex], where r is the radius

[tex]A=\pi r^2[/tex]

A diameter is twice the length of the radius. ([tex]8/2[/tex])

So the radius is 4 cm.

[tex]r^2=4^2=16[/tex]

so the Area is [tex]16\pi[/tex]



3. ) Copy Center charges $0. 08 a page for machine fed copies and $0. 20 per page for hand-fed copies. I lagan's

bill for 80 copies of his movie script is $13. 00, how many copies of each type were made?

Answers

The number of machine fed copies are 25 and the number of hand fed copies are 55. This is solved forming simultaneous equations.

What are simultaneous equations?

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an infinite number of solutions.

Given cost per page of machine fed copies = $0.08

          cost per page of hand fed copies = $0.20

Let,

  number of machine fed copies = x

 number of hand fed copies = y

Given the total number of copies = 80

So we can write the equation as

  x + y = 80  ⇒   (1)

It is also given that the total cost of the movie script is $13

So we can the equation as

0.08x + 0.20y = 13 ⇒ (2)

Solving the simultaneous equations (1) and (2)

From (1),

x = 80 - y

Substituting the above in (2)

0.08(80 - y) + 0.20y = 13

0.12y = 6.6

y = 55

x = 80 - 55 = 25

Therefore the number of machine fed copies are 25 and the number of  hand fed copies are 55.

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Select the correct image.
Barry wants to host an event at a hotel that has four conference rooms. Each conference room has a maximum capacity of 150 people, but the
hotel limits the capacity to 1 person for every 4 square feet.
Sketches of the four conference rooms are shown below. Which room will stop Barry from hosting the event at the hotel?
25 ft
24 ft
28 ft
28 ft

Answers

The room that would stop Barry from hosting the event is the semicircular room.

Which room has a capacity that is less than 1 person per 4 square feet?

Would the first rectangular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a rectangle = length x width

25 x 30 = 750 feet²

Number of people per square foot - 750 / 150 = 1 person for every 5 feet

Would the trapezoidal room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a trapezoid = 1/2 x (sum of parallel sides) x height

1/2 x (24 + 36) x 28 = 840 feet²

Number of people per square foot = 840 / 150 = 1 person for every 5.6 feet

Would the square room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a square = length x width

28 x 28 = 784 feet²

Number of people per square foot - 784 / 150 = 1 person for every 5.2 feet

Would the semi circular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a semicircle = 1/2πr²

Where:

r = 3.14

r = radius = diameter / 2 = 28 / 2 = 14 feet

1/2 x 3.14 x 14² = 307.72 feet²

Number of people per square foot - 307.72/ 150 = 1 person for every 2.05 feet

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Answer:

The semicircle

Step-by-step explanation:

ewomazinoade's answer is correct, not sure why at time of writing the rating is so low for their answer (3.7).

See pic!

Hiiooo! Can someone please help with this!❤️:)

Answers

It will be 256.20 I hope I helped

el numero decimal 3,1 representa a la fraccion 3 entre 10

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Answer:

ne cheaso le uprenta singil layu ka bts dung lyr

pleaseeee helpppppppppp

Answers

Answer:

A

Step-by-step explanation:

heyy! i’ll give brainliest please help

Answers

Answer:

Name as a person

Step-by-step explanation:

Answer:

In the name of a person.

Step-by-step explanation:

The seasons are not written with capital letters unless they form part of a name. For example:

I am leaving in the winter.

I live near Winter Mountain River.

What is a real solution example?

Answers

Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.

What do you mean by a solution?

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

What are ideal and real solutions?

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

x+2=0

x=-2

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Which answer choice correctly identifies the extraneous information in the problem?

Anna babysat 2 children on Saturday night. She charges $8 an hour to babysit. She wants to save the money she earns babysitting to buy a stereo system that cost $225. If Nina babysat for 5 hours, how much money did she earn?
A. She charges $8 an hour and babysat for 5 hours.
B. She babysat 2 children on Saturday night and she wants to buy a stereo system that costs $225.
C. She babysat 2 children on Saturday night and she charges $8 an hour to babysit.
D. She wants to save the money she earns babysitting to buy a stereo system that costs $225 and she babysat for 5 hours.

Answers

Answer: B

explanation: I took the test ^w^

If Nina babysat for 5 hours,  then she earn 141 of money and option B choice correctly identifies the extraneous information in the problem

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Anna babysat 2 children on Saturday night.

She charges $8 an hour to babysit

She wants to save the money she earns babysitting to buy a stereo system that cost $225

If Nina babysat for 5 hours,  then we need to find how much money money did she earn.

8/225=5/x

Apply cross multiplication

8x=225(5)

8x=1125

x=1125/8

x=140.6=141

Hence, If Nina babysat for 5 hours,  then she earn 141 of money and option B choice correctly identifies the extraneous information in the problem

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Question content area top
Part 1
A computer store buys a computer system at a cost of ​$. The selling price was first at ​, but then the store advertised a markdown on the system. Answer parts a and b.
Question content area bottom
Part 1
a. Find the current sale price.
The sale price is ​$

enter your response here.
​(Round to the nearest cent as​ needed.)
Part 2
b. Members of the​ store's loyalty club get an additional ​% off their computer purchases. How much do club members pay for the computer with their​ discount?
The price for club members is ​$

enter your response here.
​(Round to the nearest cent as​ needed.)

Answers

a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

How to obtain the prices?

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

Missing Information

The problem is given by the image presented at the end of the answer.

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Find the lengths of the diagonals of rectangle WXYZ
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.

Answers

A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)

Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.

Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.

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Answer: 66

Step-by-step explanation:

I skipped it to see the answer hope this helps

please help me with math!! :(

Answers

Answer:

addition property of equality

Step-by-step explanation:

if jimmy had had 9 apples and karl has 10 how mush togheter

Answers

19? Lol........................

Please help me! Urgent, thanks!

The lowest common multiple of 60, 156 and n is 10920. Find the smallest possible value of n.

60 = 2² x 3 x 5
156 = 2² x 3 x 13
10920 = 2³ x 3 x 5 x 7 x 13

Answers

Answer:

2 cube into 3 into 5 into 13 into 7

2 cube into 5 something

When Souta went to Sweden, 1 Swedish krona was worth about 0. 12 US

dollar. He took d dollars on the trip. Which equation could be used to find

the value in Swedish krona, k, of the dollars?

A

k = 0. 12d

B

d

k=

0. 12

с

0. 12

k=

d

D k= 1. 12d

Answers

If 1 Swedish krona was worth 0.12 US dollar , and if he took d dollars for the trip then the equation that is used to find the value in Swedish krona (k) of the dollars is option (a) [tex]k = 0.12\times d[/tex] .

The value of 1 Swedish krona is = 0.12 US dollar ,

the number of dollar that Souta took on the trip is = d dollars ;

we have to find the equation that can be used to find the equation in Swedish krona "k" of the dollars ,

According to the question ,

the equation for Swedish krona can be represented as [tex]k = 0.12\times d[/tex] ;

Therefore , the required equation is [tex]k = 0.12\times d[/tex] .

The given question is incomplete , the complete question is

When Souta went to Sweden, 1 Swedish krona was worth about 0.12 US dollar. He took d dollars on the trip. Which equation could be used to find the value in Swedish krona, k, of the dollars ?

(a) k = 0.12d

(b) dk = 0.12

(с) 0.12k = d

(d) k = 1.12d

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Quadrilateral ABCD below is reflected about line m. After the reflection, how is the perimeter of A'B'C'D' related to the perimeter of ABCD?
Quadrilateral ABCD below is rotated 180°. After the rotation, how is the area of A'B'C'D' related to the area of ABCD?

Answers

Reflection and rotation will not alter the perimeter of the quadrilateral

What is transformation?

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformations has basically classifications

non rigid transformationRigid transformation

Non rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation

In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are

rotationreflectiontranslation

Because the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved

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Given the circle below with chords NO and PQ. Find the length of OR. Round to the nearest tenth if necessary.

Answers

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

Circle – what is it?

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

For each secant, the sum of the lengths from R to the circle's intersection points is the same:

=>RS*RT = RQ*RP

=>40(40 +31) = (44)(PQ +44)

=>40(71)/44 = PQ +44

=>PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11

=>PQ ≈ 20.5

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

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What is the value of 2/21 - 1/3


1. -5/21

2. 1/18

3. 5/21

4. 3/7


Whoever helps gets 15 points

Answers

answer: -5/21
explanation:
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