Complete the square to rewrite y=x2 - 6x + 2 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates.

A. Maximum at (-3, -7)

B. Maximum at (3,-7)

C. Minimum at (3, -7)

D. Minimum at (-3, -7) ​

Answers

Answer 1

Answer:

C is the Answer

Step-by-step explanation:

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Answer 2

Answer:

C) Minimum at (3,-7)

Step-by-step explanation:

[tex]y=x^2-6x+2[/tex]

[tex]0=x^2-6x+2[/tex]

[tex]0+7=x^2-6x+2+7[/tex]

[tex]7=x^2-6x+9[/tex]

[tex]7=(x-3)^2[/tex]

[tex]0=(x-3)^2-7[/tex]

[tex]y=(x-3)^2-7[/tex]

Because the parabola opens upward, the vertex is the minimum of the function. Therefore, the vertex is the minimum at (3,-7).


Related Questions

The voltage E in an electrical circuit is modeled by E=3.8cos(110π t). What is the maximum voltage?

Answers

Answer:

Max E=3.8 Voltage

Step-by-step explanation:

[tex]maximum-value -of cos(\theta) =1, when \theta=0,360,720\\110\pi t=0, therefore t=0, 1.04, 2.08 etc[/tex]

The maximum voltage for the electric circuit is E = 3.8 when the value of the trigonometric function cos(110π t) has the maximum value = 1, from the range of cosine function.

What is the range of the trigonometric function cosine?

The range of the trigonometric function of cosine, that is, cos θ, is [-1, 1], that is, -1 ≤ cos θ ≤ 1.

How do we solve the given question?

We are given that the voltage E in an electrical circuit is modeled by E = 3.8cos(110π t).

We are asked to find the maximum voltage E that can be obtained from the circuit.

The voltage E = 3.8cos(110π t).

In the given formula 3.8 is constant and cos(110π t) is variable. The value of E is maximum when the trigonometric function cos(110π t) attains the maximum value.

Since its a cos function, the maximum value it can attain = 1, as the range of the trigonometric function of cosine, that is, cos θ, is [-1, 1], that is, -1 ≤ cos θ ≤ 1.

When the variable attains the maximum value = 1, the value of the voltage E  = 3.8*1 = 3.8.

∴ The maximum voltage for the electric circuit is E = 3.8 when the value of the trigonometric function cos(110π t) has the maximum value = 1, from the range of cosine function.

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a square garden has an area of 6400 square find its perimeter

CAN SOMEONE HELP ME PLZ​

Answers

Answer:

what is it's perimeter?

5 x 1/7


The question



































Answers

as a fraction the answer is: 5/7

Answer:

5/7 or 0.71 is the answer

17. Find the area of a triangle whose base is 6 cm and height is 8 cm.
48 square cm
24 square cm
48 cm
24 cm

Answers

Answer:

24 square cm

Step-by-step explanation:

Answer:

48cm

Step-by-step explanation:

Because 6 times 8= 48cm

The weight of three articles is 856 kg. If two of the articles weigh 502kg, what is 1/2 the weight of the third article?

Answers

Answer:

177 kg

Step-by-step explanation:

Find the weight of the third article by finding the difference between 502 and 856, since 856 kg is the total weight and 502 kg is the weight of the other 2 articles:

856 - 502

= 354

Now, find 1/2 of the weight, by dividing this by 2:

354/2

= 177

So, 1/2 the weight of the third article is 177 kg

You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 145 feet tall. You measure the angle of elevation to the top of the lighthouse at 5 degrees. How far are you from the bottom of the lighthouse? *

Answers

Answer:

1657.14 ft

Step-by-step explanation:

Tan = opposite / adjacent

tan 5 = 145 / adjacent

0.0875 =  145 / adjacent

adjacent = 145 / 0.0875

= 1657.14 ft

If you put 700 into a savings account that's earns 1% interest compound monthly how much will you have in 5 years

Answers

Answer:

In 5 years I will have $ 1,151.71.

Step-by-step explanation:

To determine, if I put 700 into a savings account that's earns 1% interest compound monthly, how much will I have in 5 years, the following calculation must be performed:

700 x (1 + 0.01 / 12) ^ 12x5 = X

700 x (1 + 0.008333) ^ 60 = X

700 x 1.64530 = X

1,151.71 = X

Therefore, in 5 years I will have $ 1,151.71.

Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ≥ 500 and solved it to find the solution x ≥ 55.25.

1.Explain how you know Elena made a mistake based on her solution.

2.Fix Elena’s inequality and explain what each part of the inequality means.

Answers

Answer:

x is 69.75

Step-by-step explanation:

8x+58>500

500-58

8x/8>558/8

x>

All squares are rectangles but not all rectangles are squares. Prove wheater this statement is true or false with an explanation

Answers

~All squares are rectangles, but not all rectangles are squares.
~All squares are rhombuses, but not all rhombuses are squares.
This statement is ✨True✨

A bicycle has a cash price of $319.95. It can be bought on hire purchase with a deposit of $69 and ten monthly installments of $28.50 each.​

a. what is the total hire purchase price of the bicycle?

b. Find the difference between the hire purchase price and the cost price of the bicycle.

Answers

Answer:

a. $354

b.$34.05p

Step-by-step explanation:

10 monthly instalments

10x28.5=280

plus the deposit 280+69=354

The difference between 354 and 319.95 is 34.05  

a. The total hire purchase price of the bicycle is $354.

b. The difference between the hire purchase price and the cost price of the bicycle is $34.05.

a. Total hire purchase price:

Total hire purchase price=(10 months×$28.5)+$69

Total hire purchase price=$285+$69

Total hire purchase price=$354

b. Hire purchase price and cost price:

Difference=$354-$319.95

Difference=$34.05  

Inconclusion the total hire purchase price of the bicycle is $354 and the difference between the hire purchase price and the cost price of the bicycle is $34.05.

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Craig threw a handful of identically shaped buttons into the air then collected 14 bottoms that landed on the carpet. Is this sample of the buttons likely to be biased yes or no

Answers

Answer:

possible?? but I think that there is a typo, and that there would not be a bias

Step-by-step explanation:

can we assume that there are no typos in the question

he threw BUTTONS in the air, and look at buttons that landed with the BOTTOMS facing up ??? in that case the weight might bias the orientation of the landing... I think that you have a typo and it just says that he collected 14 BUTTONS, in that case given that they are "IDENTICAL" we most likely can assume that there would be no bias (size color, texture are all the same)

A rectangular prism has a height of 10 inches, breadth of 19 inches and length twice the height. What is the volume of the prism?

Answers

Answer:

3800

Step-by-step explanation:

Volume= Length x width x height

v=20x19x10

v=3800 inches²

Brainliest please

Which of the following is a quadratic function?

Answers

Answer:

A

Step-by-step explanation:

A

when multiplied out

the highest exponent of x is 2

y = 2x² + x - 6

Answer:

option A

Step-by-step explanation:

A quadratic equation is a single variable polynomial of degree 2.

[tex]A ) y = ( x + 2)(2x-3) = 2x^2 -3x +4x - 6 =2x^2 + x - 6 \ - Yes \\\\B) y = 3(x - 4) \ - No\\\\C) y = \frac{1}{x^2} \ - No\\\\D) y = x(x-4)(x+3) = x(x^2 -x - 12) = x^3 -x^2 - 12x \ - No[/tex]

find the outer perimeter of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate π.​

Answers

Answer:

19.42 ft.

Step-by-step explanation:

The diameter of the semicircle is 6, so 3.14 x 6 = 18.84. Since it is a semicircle, we divide that by 2 to get 9.42.

The hypotenuse of the right triangles only matter for the perimeter. 5 + 5 = 10, and 9.42 + 10 = 19.42 ft.

The outer perimeter is 19.42 ft.

What is perimeter?

Perimeter is the distance around the edge of a shape.

Given:

radius= 3 ft

height= 4 ft

slant height= 5 ft

diameter of the semicircle is 6 feet.

So,

= 3.14 x 6 = 18.84.

Since it is a semicircle,

=18.84/2

=9.42 feet

Now, the perimeter.

= 5 + 5 +9.42

= 19.42 ft.

Hence, the perimeter is 19.42 feet.

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There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

Answers

Answer: 7 red marbles.

Step-by-step explanation:

Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.

Then the number of red marbles will be:

= 1/9 × 63

= 7

There are 7 red marbles

The number if blue marbles will be:

= 63 - 7

= 56 blue marbles

Solve the absolute value inequalty ⎜3x + 5⎟≤ - 2 a No Solution b - 2 ≤ x ≤ - 7 c All real numbers d -7/3 ≤ x ≤ -3/7

Answers

Answer:

Step-by-step explanation:

First, absolute value is always POSITIVE ⇒ the given inequality has No Solution!!

Just to show you how to solve this kind of problems:

1). If (3x + 5) ≥ 0, then 3x + 5 ≤ - 2

3x ≤ - 5 - 2

3x ≤ - 7

x ≤ - [tex]\frac{7}{3}[/tex]

2). If (3x + 5) < 0, then - (3x + 5) ≤ - 2

3x + 5 ≥ 2

3x ≥ - 3

x ≥ - 1

x ∈ ∅

HELPPPPPPPPPP!!!! IF ITS RIGHT I WILL MARK

Solve 3t + 2 = 5t - 4
Options:

t = 3
t = -1
t = 2

Answers

Answer:

t=3

Step-by-step explanation:

Heres why i think t=3

Replace the T in 3t+2

3x3+2

9+2=11

11=5t-4

Now Replace the t again by 3

5x3-4

15-4

11

11=11

T=3

Answer:

t = 3

Step-by-step explanation:

3t + 2 = 5t - 4

2 + 4 = 5t - 3t

6 = 2t

6/2 = 2/2t

t = 3

if this helps you, please mark brainliest!

Point P (a, b), where neither a orbis equal to 0, is subject to the following operations, one after the other in any order:
reflection about the x-axis, reflection about the y-axis, reflection about the origin.
What will be the final position of point P?

Answers

Answer:

(a, b)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.

Reflection is the flipping of an object about a point. If a point A(x, y) is reflected over x axis, the new point is at A'(x, -y). If the a point A(x, y) is reflected over y axis, the new point is at A'(-x, y). If a point A(x, y) is reflected over origin, the new point is at A'(-x, -y).

Given point P(a, b). It reflection about the x-axis gives P'(a, -b), then the reflection about the y-axis gives P"(-a, -b). Lastly, reflection about the origin gives P"'(a, b)

The area of a rectangular field is 7626m2. If the length of the field is 93m, what is its width?

Answers

Answer:

The width is [tex]82m[/tex]

Step-by-step explanation:

------------------------------>>>>

The formula to find the area of a rectangle is [tex]A=lw[/tex]

We already know the area of the rectangular field which is [tex]7626m[/tex]

We already know the length is [tex]93m[/tex]

--------------->>>>

Now let's substitute [tex]7626[/tex] for [tex]A[/tex] because that's the area and substitute [tex]93[/tex] for [tex]l[/tex] because that's the length. After that, let's solve to find the width.

[tex]7626=93w[/tex]

Divide both sides by 93 because that's the opposite of multiplication.

[tex]82=w[/tex]

--------------->>>>

This means that the width of the rectangular field is [tex]82m[/tex]

Hope this is helpful

Brainliest, 10 points

You can convert or translate mathematical expressions into verbal statements and verbal statements into mathematical expressions by using the following: (Select all that apply)

question mark
periods
capital letters
commas

Answers

commas and capital letters

period, commas. question marks

Please help I’ll give brainliest

Answers

Answer:

The rules for standard form are

Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative. The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number)

I hope this helps

Answer:

False

Step-by-step explanation:

Please Mark me brainliest

The quartile deviation and coefficient of quartile deviation of a continuous frequency distribution are 2 and 0.25 respectively. Find lower and upper quartiles.

Answers

Answer:

Lower quartile = 6

Uppwr quartile = 10

Step-by-step explanation:

Coefficient of quartile deviation = 0.25

Quartile deviation = 2

Coefficient of quartile deviation = (Q3 - Q1) / (Q3 + Q1)

Quartile deviation = (Q3 - Q1) / 2

Hence;

Quartile deviation = (Q3 - Q1) / 2 = 2

Q3 - Q1 = 2 * 2

Q3 - Q1 = 4 - - - - (1)

Q3 = 4 + Q1 - - - - (2)

(Q3 - Q1) / (Q3 + Q1) = 0.25

Q3 - Q1 = 4

4 = 0.25(Q3 + Q1)

Q3 + Q1 = 4 / 0.25

Q3 + Q1 = 16 - - - - (3)

Put Q3 = 4 + Q1 in (3)

4 + Q1 + Q1 = 16

4 + 2Q1 = 16

2Q1 = 16 - 4

Q1 = 12 / 2

Q1 = 6

Q3 = 4 + Q1

Q3 = 4 + 6

Q3 = 10

5) Last week a Pizza Hut sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. Based on these data, which number is closest to the probability that the next customer will order a cheese pizza?

Answers

Answer:

[tex]P(Cheese) = 0.30[/tex]

Step-by-step explanation:

Given

[tex]Cheese = 36[/tex]

[tex]Pepperoni = 64[/tex]

[tex]Veggie = 20[/tex]

Required

[tex]P(Cheese)[/tex]

This is calculated as:

[tex]P(Cheese) = \frac{Cheese}{Total}[/tex]

[tex]P(Cheese) = \frac{36}{36+64+20}[/tex]

[tex]P(Cheese) = \frac{36}{120}\\[/tex]

[tex]P(Cheese) = 0.30[/tex]

someone plz help me!!

Answers

Answer:

P'=(0,3)

Step-by-step explanation:

P'=(-5+5, 7-4)

will give brainliest !!PLSS HELP fast !! and explain

Answers

Answer:

C

Step-by-step explanation:

Difference means subtraction. That makes B incorrect.

D is wrong because we have no way of knowing if g and h are squares.

A is wrong because the numerical numbers (2 and 6) are not perfect squares. Even if you take out a 2 you are not left with numbers that are prefect squares.

That leaves with C which is the correct answer. The literals are perfect squares and so are the numbers.

Answer:

C

Step-by-step explanation:

has endpoints J(13, 8) and K(–6, –6). Find the coordinates of the midpoint of .

Answers

Answer:

the midpoint of it is 8,-6

Step-by-step explanation:

rhgsr egh

Math help please due today ill give you brainlist if correct !!!

Answers

Answer:

a. Vertical

b. Corresponding

c. Alternate exterior

d. Supplementary

e. 40 degrees

f. 40 degrees

Table

45  45  135

20  70  160

87   3    93

Step-by-step explanation:

a. Vertical angles are congruent and opposite each other.

b. Corresponding angles are congruent and are located in similar positions.

c. Alternate exterior angles are congruent and opposite each other when a line intersects two parallel lines.

d. Supplementary angles are next to each other and add to 180 degrees.

e. Supplementary angles. Subtract 140 from 180 to find <M.

f. Alternate interior angles. <X and <M are congruent.

Table

Complementary angles add to 90 degrees. Supplementary angles add to 180 degrees.

45 + 45 = 90

45 + 135 = 180

etc.

Which of the following is the correct definition of payment shock??

Answers

Answer:

payment shock refers to a dramatic increase in an individual's debts and liabilities that may cause them to default on their financial obligations. Put simply, payment shock occurs when, rather suddenly, someone is obligated to pay more in monthly debt than they can afford from their income

Answer: The new payment after the initial fixed-rate period is much higher

than the homeowner expected.

Step-by-step explanation: took the quiz.

What is the slope and y intercept of the equation?
y=1/2x
m=
b=

Answers

⊹˚ʚ ❑Answer︰slope is 1/2 and y-int. is 0

      ✎Daily reminder: make sure to eat food and stay hydrated, have a good day :D

i need the base and hight

Answers

Answer:

Height = 5 and Base = 10

Step-by-step explanation:

The base of the parallelogram is twice the perpendicular height of the parallelogram. The area of the parallelogram is 50 cm².

Formula for area of parallelogram = base × height

Base = 2h

Height = h

∴ Area = 2h × h = 50

Solution:

2h × h = 50

2h² = 50

[tex]\frac{2h^{2} }{2} = \frac{50}{2}[/tex]

h² = 25

[tex]\sqrt{h^{2} } = \sqrt{25}[/tex]

h = 5

∴ height = 5 and base = 2(5) = 10

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