In the function f(x) = (x^2 -6x + ___) + 20, what number belongs in the blank to complete the square?

Answers

Answer 1

Answer:

blank = -11

Step-by-step explanation:

The given function is :

[tex]f(x) = (x^2 -6x+x)+20[/tex]

We need to find the number x such that it forms the complete square.

If x = -11, then it will becomes,

[tex]f(x) = (x^2 -6x+(-11))+20\\\\f(x)=x^2-6x+9[/tex]

We can write it as follows :

[tex]f(x)=x^2-2(1)(3x)+(3)^2[/tex] ..(1)

We know that,

[tex](a-b)^2=a^2-2ab+b^2[/tex] ...(2)

Comparing (1) and (2).

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

So, if we put the blank equals -11, then it will become the perfect square.


Related Questions

5.02 Which equation does the graph below represents?

1. y = -1/2x
2. y = -2x
3. y = 1/2x
4. y = 2x

Answers

y= 2x because it’s 8/4 which can be divided by 4 and it equals 2x

Answer:

2. y= -2x

Step-by-step explanation:

When the line is on an exact point like it is on (-4, 8), we can simplify it by going rise/run

Rise is the same as y (8), and your run is x (-4)

When you divide 8/-4, your answer will be -2

Therefore, the answer is y= -2x

helpppppppppppppppp i dont know this

Answers

Answer:

f(- 3) = - 16

Step-by-step explanation:

To evaluate f(- 3) with x = - 3 in the interval x ≤ - 2, then

f(- 3) = 5x - 1 = 5(- 3) - 1 = - 15 - 1 = - 16

5 6 costs $150 to rent a party room at Pizza-n-Games, plus $6 per person for pizza and $5 per person for game ckets. The expression shown gives the total cost for n people. 150+60+5n Evaluate the expression to find the cost for a party of 15 people, A $161 B. $165 C. $315 Click to add speaker note​

Answers

Answer:

315

Step-by-step explanation:

2, 8, 7, 8, 6, 15, 6, 3, 8
What is the range of the data?
A. 2
B. 6
C. 8
D. 13
E. 15

Answers

Answer:

13 or d

Step-by-step explanation:

The range of the data is D. 13

Given that,

The sequence is 2, 8, 7, 8, 6, 15, 6, 3, 8

Calculation:

The range is

= Highest number - lowest number

= 15 -2

= 13

Learn more about the range here: https://brainly.com/question/4135956?referrer=searchResults

c) Which of these numbers is a square number?
А. 4 x 10^5
B. 9 x 10^4
C. 4 x 10^3
D. 9 x 10^3

Answers

Answer:

i think b

Step-by-step explanation:

9=3^2 and 10^4=(10^2)2

The number 9 x 10⁴ is a square number. which the correct answer would be an option (B).

What is the number system?

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

As per option (A),

4 x 10⁵

This number is not a square number.

As per option (B),

9 x 10⁴  = (3² x 10²)²

This number is a square number.

As per option (C),

4 x 10³

This number is not a square number.

As per option (D),

9 x 10³

This number is not a square number.

Thus, the number 9 x 10⁴ is a square number.

Hence, the correct answer would be option (B).

Learn more about the number system here:

https://brainly.com/question/21751836

#SPJ2

Sachi takes 10 rounds of a rectangular park, 50 m long and 20 m wide. Find the total distance covered by him.

Answers

Answer:

700 meters

Step-by-step explanation:

A model rocket was launched from a podium 5 meters above are

an initial velocity of 98 m/s. The function that models height in me

with respect to time (in seconds) is h(t) = 5 + 987-4.9t2

meters above ground at

meters)

Answers

Answer:

See solution below

Step-by-step explanation:

Find the complete question below;

Given the height modeled by the function;

h(t) = 5 + 98t-4.9t²

when t = 0

h(0) = 5 + 98(0)-4.9(0)²

h(0) = 5

when t = 5

h(5) = 5 + 98(5)-4.9(5)²

h(5) = 5 + 490 - 122.5

h(5) = 372.5

when t = 10

h(10) = 5 + 98(10)-4.9(10)²

h(10) = 5 + 980 - 490

h(10) = 495

when t = 15

h(15) = 5 + 98(15)-4.9(15)²

h(15) = 5 + 1470 - 1,102.5

h(15) = 372.5

when t = 20

h(10) = 5 + 98(20)-4.9(20)²

h(10) = 5 + 1960 - 4.9(400)

h(10) = 1965- 1960

h(10) = 5

Find the graph attached

pls anwer fast is due in 5min

Answers

Answer:

Taking my points

Step-by-step explanation:

You spammed my own question

is this a domain or range?

please help :(

Answers

Step-by-step explanation:

it's a function.

the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

the domain is (1,3,7,8)

the range is (2,4,6,9)

Which number would make this number sentence true? (3 + 2) x ? = 5 x 8

Answers

Answer:

8

Step-by-step explanation:

3+2=5

5 x 8 = 5 x 8

Answer:

8

Step-by-step explanation:

2 numbers are in perenticies so do them first 3+2 = 5 Then wait dont do nothing with that do 5x8 to get what to need to get 5 x? to witch is

40 so 8 would be the correct answer

If the triangles are similar, find the value of x.

Answers

Answer:

x=25

Step-by-step explanation:

the triangles are similar

so as we know

when two triangles are similar the rotio of triangles is equal

now let's solve it

to understand the solving stepsyou need to know aboutequation with fractionPEMDAS

according to the question

[tex] \frac{24}{30 } = \frac{x + 7}{2x - 10} [/tex]

[tex] \frac{4}{5} = \frac{x + 7}{2x - 10} [/tex]

[tex]4(2x - 10) = 5(x + 7) \: (cross \: multiplication)[/tex]

[tex]8x - 40 = 5x + 35[/tex]

[tex]8x - 5x = 35 + 40[/tex]

[tex]3x = 75[/tex]

[tex]x = 25[/tex]

Olivia wants to know the proportion of students at her school who use a

certain social media app. She interviews a random sample of students at

her school. She finds that 30% of the students in the sample use the app.

What conclusion can she draw from the sample?

А

It is likely that about 30% of the students at her school use the app.

B Exactly 30% of the students at her school use the app.

Every random sample would find that 30% of the students use

the app

It is likely that 30% of the students at her school were selected for

the sample.

Answers

Answer:

A

Step-by-step explanation:

Random sampling is a sampling method where each sample has an equal chance of being chosen. The random sample chosen is meant to be an unbiased representation of the population.

If 30% of the sample uses the app, it means that 30% of the population are likely to use the app

What is the slope of the line y=8?

Answers

Answer:

undefined or 0

Step-by-step explanation:

Answer:

The answer is 0 because undefined is straight up or vertical

Solve the proportion: 1/4 = x/20

Answers

Answer:

5x?

Step-by-step explanation:

Answer:

= 5

Step-by-step explanation:

Multiply all terms by the same value to eliminate fraction denominators

1/4 = x/20

20 ⋅ 1/4 = 20 ⋅ /20

Simplify

= 5

Does anyone know this if you could help me I would appreciate it

Answers

Answer:

C, B

Step-by-step explanation:

Basically to find the slope you take the rise over run. How many squares does the line go up, over how many does it go left or right. As you can see in the diagram, it goes up 2 squares and goes left 1 square, giving the slope 2/1, which is 2.

The slope of a horizontal line is straight, which means it goes up 0, so automatically your answer is zero, because dividing anything by 0 is 0.

3. A computer is priced at $65,000 plus value added tax at 15%. What amount does the computer actually cost the customer?

Answers

Answer:

$74,750

Step-by-step explanation:

Given that,

The cost of a computer = $65,000 + value added tax at 15%

We need to find the amount the computer actually cost the customer.

Total cost = Cost of computer + VAT at 15%

[tex]=65000+65000\times \dfrac{15}{100}\\\\=\$74,750[/tex]

So, the computer actually cost the customer is $74,750.

can i plz get some help

Answers

1. 1 and 6, 2 and 5, 3 and 8, 4 and 7, 9 and 11, 10 and 12
2. 1 and 5, 2 and 6, 3 and 7, 4 and 8
3. Alternate interior angles
4. Not sure about this one
5. Alternate exterior angles
6. Vertically opposite angles
7. Interior opposite angles
8. Alternate interior angles
9. Corresponding angles
10.alternate exterior angles

Pls Help Step by step look at picture

Answers

Answer:

-6(x-y)

Step-by-step explanation:

Combine the same terms together

; (-3x+2x-5x) + (y+7y-2y)

Use parentheses to make thinking easier.

Combine ; -6x + 6y

Factoring polynomials ; -6(x-y)

hope it helps ☺️

Colin buys a tv for £800. It depreciates at a rate of 1% per year. How much will it be worth in 2 years? Give your answer to the nearest penny where appropriate

Answers

Answer:

708

Step-by-step explanation:

Answer

1.7/5

1

bhagyashreechowdhury

Ace

2.4K answers

4.9M people helped

Given:

The cost of the T.V. for Colin = £ 800.

The rate of depreciation per year = 4%

Time period = 3 years

To find:

How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.

Solution:

To solve the above-given problem, we will use the following formula:

where

A = the final value after depreciation

P = the present value

R = rate of depreciation

n = time period

Now, on substituting the given values in the formula, we get

we will round the above answer to its nearest penny where appropriate

≈ £ 708

Thus, the worth of the t.v. in 3 years will be £ 708.

brianna caught 4 fish . gabi caught 8 times as many fish as brianna. which expression shows how many fish gabi caught

Answers

Answer:

multiplication

Step-by-step explanation:

brianna=4

gabi=8 x brianna

I need help please help me with this question because I don’t know it

Answers

I think its b i hope it helps

4 to 7 equals 21 to what ​

Answers

can you show the whole question

Answer:

Step-by-step explanation:

I dunno wether addition or multiplication, if it's multiplication, it would be 36.75 if it's addition, then it's 24

1. What is 8 turbo jets raised to the power of 4?*

Answers

Answer:

4096

Step-by-step explanation:

Hey there!!!!

8  raised to the power of 4 = [tex]8^{4}[/tex]

[tex]8^{4}[/tex] = 8*8*8*8

if we multiply:

8*8=16

16*8= 128

128*8 = 4096

hope this helps :)

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x – 6y = 54

Answers

y = 4/3x - 9
Hiiiiiiiiii

Need correct answer only PLS
Which option identifies the sectors of the economy involved in the following scenario?
Joe owns a family farm in central Illinois. He goes to the bank for a loan for a new combine.

agriculture and services

services and industry

agribusiness and industry

agriculture and industry

Answers

Answer:

Step-by-step explanation:

A and c

Answer:

a

Step-by-step explanation:

Hope this helps:)

Which two represent 10 cube? *

Answers

Answer:

5 cube and 5 cube = 10 cube..??

Step-by-step explanation: ok so can i have brainiest plaease::)

Which value of k makes 5 – k + 12 = 16 a true statement?
Choose 1 answer:

Answers

Answer:

k =4

Step-by-step explanation:

you ask your self what + 12 = 16

Answer:

K=4

Step-by-step explanation:

Answer: ? + 12 = 16

What is the value of y

Answers

I did something like this but I forgot:(

What operation would you use to solve: x+7=10

Answers

Answer:

x=3

Step-by-step explanation:

x+7=10

x+7-7=10-7

x=3

Answer:

You would use subtraction

Step-by-step explanation:

To get 7 away, you need to subtract it

Please help. I don't understand this.​

Answers

Answer:

radius=6

Step-by-step explanation:

arc ACB=6xPi

Pi=3.14159

arc ACB=18.85 (rounded to 2 places)

ACB is a half circle so a full circle would be 18.85x2 or 37.7

circumference (whole circle)=2 x Pi x radius

37.7=2 x 3.14159 x radius

radius= 37.7/(2 x 3.14159)

radius=6

Other Questions
20 points. describe the actions taken by native americans and british forces against americans west of the appalachians. Contrast Mark 6:4 and Luke 4:24. Why is the lack of honor by the family eliminated by Luke? What kind of information does the speaker provide about the deceased?Upon the Burning of Our HouseIn silent night when rest I took, For sorrow near I did not look, I waken'd was with thund'ring noise And piteous shrieks of dreadful voice. That fearful sound of fire and fire, 5Let no man know is my desire. I, starting up, the light did spy, And to my God my heart did cry To strengthen me in my distress And not to leave me succorless. 10Then coming out beheld a space, The flame consume my dwelling place. And, when I could no longer look, I blest his Name that gave and took, That laid my goods now in the dust: 15Yea so it was, and so 'twas just. It was his own: it was not mine; Far be it that I should repine. He might of all justly bereft, But yet sufficient for us left. 20When by the ruins oft I past, My sorrowing eyes aside did cast, And here and there the places spy Where oft I sat, and long did lie. Here stood that trunk, and there that chest; 25There lay that store I counted best: My pleasant things in ashes lie, And them behold no more shall I Under thy roof no guest shall sit, Nor at thy table eat a bit. 30No pleasant tale shall e'er be told Nor things recounted done of old. No candle e'er shall shine in thee Nor bridegroom's voice ere heard shall be. In silence ever shalt thou lie; 35Adieu, adieu; all's vanity. Then straight I gin my heart to chide, And did thy wealth on earth abide? Didst fix thy hope on mould'ring dust, The arm of flesh didst make thy trust? 40Raise up thy thoughts above the sky That dunghill mists away may fly. Thou hast an house on high erect, Fram'd by that mighty Architect, With glory richly furnished, 45Stands permanent tho' this be fled. It's purchased, and paid for too By him who hath enough to do. A prize so vast as is unknown, Yet, by his gift, is made thine own. 50There's wealth enough, I need no more; Farewell my pelf, farewell my store.The world no longer let me love, My hope and treasure lies above. Anne Bradstreet Write a program that will perform a few different String operations. The program must prompt for a name, and then tell the user how many letters are in the name, what the first letter of the name is, and what the last letter of the name is. It should then end with a goodbye message. A sample transcript of what your program should do is below: Enter your name: Jeremy Hello Jeremy! Your name is 6 letters long. Your name starts with a J. Your name ends with a y.Goodbye! (Another one! just for fun!) if you answer all of them and if the answers are correct I will mark you as brainliest! good luck! and lets say if I got one wrong and this other person got none wrong then the other person got the brainliest or mark as brainliest. so yea good luck and thanks for participating! I will also be checking the answers so be patient!! Pls Help Step by step look at picture Harriet Beecher Stowe's family was mostly made up of?ministerslawyerssenatorsprofessors What is the slope of the line y=8? Ill give brainliest, a thankyou, 5 points, and 5 stars if correct.In the mid-1800s, Democrats believed that a policy of Manifest DestinyA. would prevent a war with nations that claimed territory in North America.B. was less important than developing existing territory in the United States.C. would boost the American economy and open up economic opportunities.D. would prevent hostilities with American Indian tribes that lived in the West. Jason is making pumpkin bread. He needs 4 cups of pumpkin for every 3 cups of sugar. What is the ratio of cups of sugar to cups of pumpkin that Jason will need?A. 3 to 4B. 4 to 3C. 4 to 7D. 7 to 3 Solve the proportion: 1/4 = x/20 WHAT INFORMATION DOES THE CORRELATION COEFFICIENT TELL YOU ABOUT A SCATTERPLOT To prepare for the class debate about the importance of space exploration, Kyle creates an agenda and a list of rules to share before the debate begins.Based on his actions, what will be Kyles role in the debate?teacherlistenermoderatorparticipant Of the three theories of learning, which one do you think most influences your own learning? Why? Was Karas reaction of hitting Jake justified? What would you do if you were at Karas place? Give reasons for your answer. A model rocket was launched from a podium 5 meters above arean initial velocity of 98 m/s. The function that models height in mewith respect to time (in seconds) is h(t) = 5 + 987-4.9t2meters above ground atmeters) The liquid inside the cell is called For the word below, click on the drop-down arrows to select the prefix and its meaning. advocate prefix: meaning: Because of Italys long coastlines, Italian city-states became wealthy througha.farming.c.fishing.b.shipbuilding.d. Why does Jim cry when the captain dies but not when his father passed away?