Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \underline{~~~~}.\]$

Answers

Answer 1

Answer:

[tex]$\[x^2 + 22x + 121\]$[/tex]

Step-by-step explanation:

Given

[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]

Required

Fill in the gap

Represent the blank with k

[tex]$\[x^2 + 22x + k\]$[/tex]

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

Divide the coefficient by 2

[tex]Result = 22/2[/tex]

[tex]Result = 11[/tex]

Take the square of this result, to give k

[tex]k= 11^2[/tex]

[tex]k= 121[/tex]

Substitute 121 for k

[tex]$\[x^2 + 22x + 121\]$[/tex]

The expression can be factorized as follows;

[tex]x^2 + 11x + 11x + 121[/tex]

[tex]x(x + 11)+11(x+11)[/tex]

[tex](x+11)(x+11)[/tex]

[tex](x+11)^2[/tex]

Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]

Answer 2
The answer would be x^2+22x+121

Related Questions

PLS PLEASE HELP!!!!!!
Evaluate 18 + 4 ÷ 2 − 8. (5 points) 2 8 12 3

Answers

18 + 4 ÷ 2 − 8

Following PEDMAS, divide first:

18 + 2 -8

Now add and subtract to get the final answer:

18+2 = 20

20-8 = 12

The answer is 12

Answer:

12

Step-by-step explanation:

Which of the following are exterior angles? Check all that apply.
6
52
3
O A. 21
O B. 25
O c. 24
O D. 23
E. 22
O F. 26

Answers

Using it's concept, it is found that the exterior angles of the triangle are given as follows:

B. <5

C. <4

What are the exterior angles of a triangle?

The exterior angles of a triangle are the angles that are outside the triangle.

In this problem, the angles are 4 and 5, which means that options B and C are correct.

More can be learned about the exterior angles of a triangle at https://brainly.com/question/2546141

#SPJ1

Draw a net of the triangular prism and label each face with its surface area. Use the net of the three-dimensional triangular prism to find the surface area of the solid. 13 points

Answers

Answer:

300 yards squared

Step-by-step explanation:

Triangle area = 12 x 5 / 2 = 30

2 Triangles (because there are two of them) = 60

Big rectangle = 8 x 13 = 104

Small Rectangle = 8 x 5 = 40

Medium Rectangle = 96

Add all up = 300

Hope that helped!!! k

300 yards squared,, I need to answer questions to be able to ask some more

Find RS. A. 5 B. 10 C. 9 D. 12

Answers

Answer:

x=9

Step-by-step explanation:

PQ + QR + RS = PS

2x-6 + 1 + x-4 = 18

Combine like terms

3x -9 = 18

Add 9 to each side

3x-9+9= 18-9

3x = 27

Divide by 3

3x/3 = 27/3

x = 9

Answer:

RS=5

Step-by-step explanation:

solve for x:

2x-6+1+x-4 = 18

combine like terms

3x-9=18

subtract both sides to make x isolated

3x=27

divide by 3 to get x

x=9

RS=x-4

RS=9-4

RS=5

A doctor asks a nurse to give a
patient 250 mg (milligrams) of the
drug Simethicone. The drug is
available only in a solution whose
concentration is 40 mg Simethicone
per 0.6 ml (milliliter) of solution.
How many milliliters of solution
should the nurse give the patient?

Answers

Answer:

Hey there!

For this question, we write a proportion.

[tex]\frac{40}{0.6}=\frac{250}{x}[/tex]

[tex]40x=150[/tex]

[tex]x=3.75[/tex]

Thus, the nurse to give the patient exactly 3.75 ml of the solution.

Let me know if this helps :)

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

Given:

Doctor asks a nurse to give a  patient 250 milligrams of the  drug Simethicone.The concentration of a drug is 40 mg of Simethicone per 0.6 mL.

To find:

The milliliters of a solution to be given to the patient by a nurse.

Solution:

Mass of simethicone drug to be given = 250 mg

Let the volume of the solution with 250 mg of simethicone be x.

The concentration of simethicone in solution = 40 mg/0.6 mL

Mass of simethicone in 1 mL of solution:

[tex]40 mg/0.6 mL=\frac{40 mg}{0.6 mL}\\\\=\frac{400 mg}{6 mL}[/tex]

The mass of simethicone in 'x' mL of solution:

[tex]250 mg=x\times \frac{400 mg}{6 mL}\\\\x=\frac{250 mg\times 6 mL}{400 mg}\\\\x=3.75 mL[/tex]

The volume of the simethicone solution given by a nurse is 3.75 milliliters.

Learn more about the unitary method here:

brainly.com/question/20065206?referrer=searchResults

brainly.com/question/19359186

Vertex Form y=a(x-h)^2+k what does each variable represent if they were in a problem.

Answers

a represents the step pattern

h represents the x coordinate of the vertex (don’t forget that the - sign changes weather the number is + or -)

k represents the y coordinate of the vertex

A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. What is the probability that a customer will choose vegetable soup as part of the chosen combination? A. 1/4 B.1/3 C.1/2 D.1/6

Answers

Answer:

1/2

Step-by-step explanation:

answer: 1/2

explaination:
there’s two choices of soup

if alan had bought a figure at a discount of 5%, he would pay $20 less. How much would he pay if he had bought it at a discount of 20%

Answers

Answer:

80

Step-by-step explanation:

5%-->20% is increased by x4, therefore you multiply 20 by 4 which is 80 or you can set an proportion

5/20=20/x5x=400x=80
He would pay $320 at a discount of 20%.
The first step in solving this is hidden in the sentence “discount of 5%, he would pay $20 less”. This informs us that 5% of the price and $20 are the same
Our next step is to find how much 100% of the price is
Multiplying 5 and 20 gets us 100, so multiplying 5% by 20 will get us 100%
We already know that 5% is $20, so we can multiply $20 by 20 to get to 100% percent of the price
(20*20=400)
Now that we know the total price, we can find a discount of any percent. Since we know that a five percent discount will give you $20 dollars off, we can deduce that a 20% discount will give us $80 off.
(20/5=4)
(4*20=80)
(400-80=320!)
Hopefully this helps, if you need me to explain anything again I’ll try my best!

Find the measure of a A. 44 B. 88 C. 46 D. 90

Answers

Answer: Choice A. 44

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

Explanation:

Since we have a circle, the segments extending from the center outward to the edge of the circle are radius segments. Any two radii of the same circle are the same length. The triangle on the left with the 92 degree angle is isosceles. Any isosceles triangle has exactly two side lengths that are the same, which leads to the base angles being the same as well.

For the triangle on the left with angles a,b,92, the base angles are 'a' and 'b'. So a = b.

For any triangle, the angles add to 180

a+b+92 = 180

a+a+92 = 180 ... Replace b with 'a'

2a+92 = 180

2a = 180-92

2a = 88

a = 88/2

a = 44

angle b is also 44 as well

a+b+92 = 44+44+92 = 180

Answer for this question is A. 44

PLS HELP ME I NEED THIS FOR HOMEWORK!!!!

Answers

Answer:

36 degrees

Step-by-step explanation:

Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.

(3x+30)+(6x-12)=90

9x+18=90

9x=72

x=8

AOB = 6x-12, so substituting

8 in for x gives us 48-12=36

The answer is 36 degrees

What is - 15 +6f = 5

Answers

Answer:

f = 10/3

Step-by-step explanation:

-15 + 6f = 5

-15 + 15 + 6f = 5 + 15

6f = 20

6f/6 = 20/6

f = 20/6 = 10/3 = 3.333...

Answer:

10/3

Step-by-step explanation:

-15+6f=5

6f=5-(-15)

6f=5+15

6f=20

f=20/6

simplify

f=10/3

Which fraction is equivalent to -0.12? A. -3/25 B. -7/50 C. 4/25 D. -6/25 Please show ALL work! <3

Answers

Answer:

[tex]\huge\boxed{-\frac{3}{25} }[/tex]

Step-by-step explanation:

-0.12 in fraction form can be written as:

=> - 12/100

=> - 6 / 50

=> - 3/25

Answer:

[tex]\large \boxed{\mathrm{A. \ -3/25}}[/tex]

Step-by-step explanation:

Convert the decimal to a fraction.

-(0.12) = -(12/100)

Simplify the fraction.

-(12/100) = -(6/50) = -(3/25)

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36

Answers

Step-by-step explanation:

of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. x 2 + 13x + 36

Answer:

you change your mind, drag the item to the trashcan. Click the trashiecan to clear all your answers. Factor completely and then place the factors in the proper location on the grid.

Step-by-step explanation:

Thanks!

help meplz i want help i bad

Answers

Answer:

.00002

Step-by-step explanation:

2 * 10 ^-5

Move the decimal 5 places to the left since the exponent is negative

2.

We will need to add zeros on the left  Add 4 zeros since we can move it one place already

.00002

Answer:

(D) 0.00002

Step-by-step explanation:

Let's first forget about the 2 in the expression and focus on [tex]10^{-5}[/tex].

If we have 10 to a positive number, that many times the decimal place will move to the right. It's the opposite for 10 to the power of a negative number.

The decimal place will move 5 places to the LEFT.

So:

[tex]0000010\\\\0.00001[/tex]

Now we remember the two, and multiply this by two to get 0.00002.

Hope this helped!

I don't understand this question, somebody help

Answers

Answer:

H. 50 sq cm

Step-by-step explanation:

Triangle PSU is an equilateral triangle because each side of it is a radius of semicircle TRP. Also, the radius of semicircle TRP is the short side of the rectangle. So, if the total perimeter of the triangle is 15, each side is 5 cm. So, the short side of the rectangle is 5cm and the long side is 5*2 = 10 cm.

5 * 10 = 50 sq cm

i need points really bad so yea

A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 4x − 3 and EC = 2x + 6, find the distance between the top and bottom of the bridge, in feet.

Answers

Answer:

Total distance = 30 m

Step-by-step explanation:

Given:

AC : EC = 1:1

AC = 4x − 3 and EC = 2x + 6

Find:

Total distance

Computation:

AC = EC

So,

4x - 3 = 2x + 6

2x = 9

x = 4.5

AC = 4(4.5) - 3 = 15 m

EC = 2(4.5) + 6 = 15 m

Total distance = AC + EC

Total distance = 15 m + 15 m

Total distance = 30 m

The distance between the top and bottom of the bridge, in feet, is 15 + 15 = 30m

Given that a new bridge structure requires triangles that are in a ratio of 1:1 with the following parameters

AC = 4x - 3

EC = 2x + 6

Since the measure are in the same ratio, henec;

AC = EC

4x - 3 = 2x + 6

4x - 2x = 6 + 3

2x = 9

x = 4.5

Get the

AC = EC = 4x - 3

AC = EC = 4(4.5) - 3 = 15feet

The distance between the top and bottom of the bridge, in feet, is 15 + 15 = 30m\

Learn more here: https://brainly.com/question/17247176

plz help me i need help

Answers

4 x 10^-7 x 2 = 8 x 10^-7
Therefore, 2 times as long.
Answer = 2 times as longer

Explanation:

8 x 10^-7 = (2)4 x 10^-7

A power line stretches down a 400-foot country road. A pole is to be put at each end of the road, and 1 in the midpoint of the wire. How far apart is the center pole from the left-most pole?

Answers

Answer:

200 ft

Step-by-step explanation:

Since the road is 400 ft, the midpoint of the road is 200 ft from each end of the road.

Since the road is 400ft the midpoint of the road is 200ft from each end of the road

Please help On this question

Answers

Answer:

202.5 cm^2

Step-by-step explanation:

We can calculate the area of the shape by completing it

to a full rectangle or dividing it to a rectangle and triangle.

The second way seems easier

The area of the rectangle is calculated by multiplying length to width

20 × 9 = 180 cm^2

The area of a triangle is calculated by multiplying height to the base and that divided by two

5 × 9 ÷ 2 = 22.5 cm^2

Now add these two 180 + 22.5 = 202.5 cm^2

Answer:

202.5 cm squared

Step-by-step explanation:

To find the area of this figure easier, you can cut the figure like I showed in the attachment below.

The rectangle (purple): 20 times 9 is 180.

The right triangle (light blue): 9 times 5 times 1/2 is 22.5.

All together: 180 plus 22.5 is 202.5 cm squared!

Hope that helps and maybe earns a brainliest!

Have a great day! :)


Easy question
I need the answers only for (d) and (e) parts.
plz help
will give the brainliest
Need explanation.
Please answer correctly.​

Answers

Answer:

d)33

e)80

Step-by-step explanation:

I'm sorry I don't really know how to explain this.

If for [tex] x[/tex] cumulative frequency the marks are $y$ (as given on the graph), we have $x$ students with marks equal to or less than $y$

d)

Total students are $140$. Hence three-fifths of that is $140\times \frac{3}{5}=84$. Find the marks at $84$ in the graph for the passing marks.

e)

From the graph we have $60$ students having less than or equal to $30$ marks. Total students are $140$.

Subtracting, $140-60=80$ we get the numbee of students achieving more than 30 marks.

What is the value of the expression in the image? A. 216 B. 224 C. 666 D. 678

Answers

Answer:

C. 666

Step-by-step explanation:

USING PEMDAS we can solve this problem.

[tex]675-(15-12)^3 / 3\\15-12=3\\675-(3)^3/3\\675-27/3\\675-9=666[/tex]

Answer:

666

Step-by-step explanation:

Following Order of Operations rules (PEMDAS), we must do first any operations that appear inside parentheses.  Here (15 - 12) = (3).

Next we must perform any exponentiation.  Here we have 3^3 = 27.

Then we have 675 - 27 / 3, or 666 (Answer C)

Simplify
-
12 – 81 – 9
5.12
- 451

Answers

Answer:

-615.12

Step-by-step explanation:

hope this helps

plz mark as brainliest!!

Answer: -615.12
Can check using a calculator

Please help me with this geometry question:((

Answers

Answer:

x = 13

Arc RQ = 180°

Step-by-step explanation:

PEQ is an inscribed angle and the measure of an inscribed angle in a circle is equal to half of the arc it sees.

The perimeter of a circle is always 360° therefore

2 × (5x + 15) + 9x + 17 + 6x - 12 = 25x + 35 = 360°

25x = 360 - 35

25x = 325

x = 13

Since arc RQ is equal to 10x + 30 we replace x with the value we just got

10×13 + 30 = 160°

The answer is 160 fare in height but you need to work out work firstly

Find the distance between the points P and Q shown. Question 6 options: A. 73−−√ B. 13−−√ C. 5–√ D. 65−−√

Answers

Answer:

[tex]d=\sqrt{73}[/tex]

Step-by-step explanation:

[tex]Q(5, -1)[/tex]

[tex]P(-3, 2)[/tex]

Using the distance formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_2+y_1)^2}[/tex]

[tex]d=\sqrt{(-3-5)^2+(2-(-1))^2}[/tex]

[tex]d=\sqrt{(-8)^2+(3)^2}[/tex]

[tex]d=\sqrt{64+9}[/tex]

[tex]d=\sqrt{64+9}[/tex]

[tex]d=\sqrt{73}[/tex]

[tex]d\approx 8.5[/tex]

answer is d = square root 73 bro

simplify (45) - (+14)​

Answers

Answer:

31

Step-by-step explanation:

(45) - (+14)

45 - 14 (Negative sign is distributed)

=31

Is 31
Cause 45 -14 =31

How is 30% equivalent to 1.3?

Answers

Answer:

30% = 30/100 = 0.3

1.3 would be 130%

I hope this helps you!

30% is equivalent to 0.30 or 3/10, but not 1.3.

There seems to be an error in the statement that 30% is equivalent to 1.3. That is not correct.

To clarify, 30% is equivalent to the decimal value 0.30 or the fraction 3/10.

To convert a percentage to a decimal, we divide the percentage value by 100. In this case, 30 divided by 100 equals 0.30.

If you were looking for a value that represents a 30% increase or an amount including a 30% addition, you would multiply the original value by 1.3, not 30%. For example, if you have a value of $100 and want to increase it by 30%, you would multiply $100 by 1.3, resulting in $130.

So, 30% is equivalent to 0.30 or 3/10, but not 1.3.

Learn more about percentage here

https://brainly.com/question/29014288

#SPJ2

A is plotted on a coordinate grid at start bracket 3 and 1 over 2, negative 1 end bracket.. Choose the correct grid that best shows the location of the point. A coordinate grid that shows a point located 4 units to the left and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit down from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the left and 1 unit up from the origin. A coordinate grid that shows a point located halfway between 3 and 4 units to the right and 1 unit up from the origin.

Answers

Answer:

im so sorry for the other answer i reported it and im gonna help with this question because i have the same question on my test.

ok so i got C it makes the most sense to me but if im wrong then ill delete this.

If im correct please mark me as brainliest

Step-by-step explanation:

yes this is wrong but i cant delete it so just ignore it

Answer:

B  3 1/2 to the right and one unit down

Step-by-step explanation:

Jason’s budget is shown in the circle graph below. His total monthly budget is $3,000. How much does Jason spend on groceries? A. $25 B. $150 C.$450 D.$750

Answers

Answer:

D.$750

Step-by-step explanation:

3000 x 0.25 = 750

Answer:

$750

Step-by-step explanation:

First you have to find 2% of the total of $300. To do this you multiply 3000 by .25 to get 750, this is your answer.

Which is a Qualitative graph?

Answers

Answer:

No qualitative graph shown here.

Step-by-step explanation:

No qualititative graph is shown here.  The given graph is quantitative, as it involves numerical measures.

Answer:

qualitative graph are graph that are used to represent situation that do not necessarily have numerial value it repressent the essential elements of a situation in a graphical form

Which of the following represents continuous data? A. Amount of coins in your pocket B. Time it takes to count the coins in your pocket C. Number of collector coins you own D. Value of the coins in your pocket

Answers

Answer:

Time it takes to count the coins in your pocket

Step-by-step explanation:

answer is b. time it takes to count coins in your pocket
Other Questions
PLease help me and thank you How many moles of NaF must be dissolved in 1.00 liter of a saturated solution of PbF 2 at 25C to reduce the [Pb 2+] to 1.0 10 6 M? The K sp for PbF 2 at 25 C is 4.0 10 8. Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express coordinates as fractions, using the slash mark (/) for the fraction bar. (-12, -3) (3, -8) The base of a triangle is two times its height. If the area of the triangle is 36, then what is the height of the triangle? The assets, liabilities, and equity account of a business, which are interrelated and interact with each other, represent:______A. the benchmark of the businessB. the surplus value of the businessC. the financial structure of the businessD. the profit realization rate of the business Calculating the Direct Labor Rate Variance and the Direct Labor Efficiency VarianceGuillermo's Oil and Lube Company is a service company that offers oil changes and lubrication for automobiles and light trucks. On average, Guillermo has found that a typical oil change takes 18 minutes and 6.2 quarts of oil are used. In June, Guillermo's Oil and Lube had 990 oil changes.Guillermo's Oil and Lube Company provided the following information for the production of oil changes during the month of June:Actual number of oil changes performed: 990Actual number of direct labor hours worked: 291 hoursActual rate paid per direct labor hour: $16.00Standard rate per direct labor hour: $15.00Required:a. Calculate the direct labor rate variance (LRV) and the direct labor efficiency variance (LEV) for June using the formula approach.b. Calculate the direct labor rate variance (LRV) and the direct labor efficiency variance (LEV) for June.c. Calculate the total direct labor variance for oil changes for June.d. What if the actual wage rate paid in June was $14.00? What impact would that have had on the direct labor rate variance (LRV)? On the direct labor efficiency variance (LEV)? Indicate what the new variances would be below. If required, round your answers to the nearest cent. 32x 42is equal to how much When Jim goes on his shore adventure in chapter thirteen he is separated from Dr. Livesey. As a result chapters 16-18 are told from Dr. Livesey's point of view to fill the reader in on what happened while Jim was gone. However when Jim goes on his sea adventure, he is separated from Dr. Livesey from chapters 22-33, and we don't know what exactly happens to Dr. Livesey during these chapters. Write at least a five paragraph narrative from Dr. Livesey's point of view that shows what he was doing during these chapters. Make sure you include all the events that Dr. Livesey does throughout these chapters. Factorise: 5 x cube + 10 x square + 15 x . A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential model for the population. If x1 and x2 are the roots of the equation x^2 +5x-3=0, determine the value of x1^2 + x2^2. I know that I have to use vietas formula, but I am stuck :( any help would be appreciated Which of the following recognizes the intellectual property licensing of copyrights by all the signatory nations to the act?a. The Madrid Conventionb. The Export Administration Act of 1985c. The Berne Convention Implementation Act of 1988d. The International Emergency Economic Powers Act of 1977 On a map, two locations are 0.75 centimeter apart. Their actual distance is 15 kilometers apart. What scale could beshown on the map? Select three options. prove tan(theta/2)=sin theta/1+cos theta for theta in quadrant 1 by filling in the calculations and reasons. PLEASE HELP!!!! Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework? Translate the following phrase into an algebraic expression using the variable m. Do not simplify,the cost of renting a car for one day and driving m miles if the rate is $39 per day plus 45 cents per mile In a reversible reaction, the endothermic reaction absorbs ____________ the exothermic reaction releases. A. less energy than B. None of these, endothermic reactions release energy C. the same amount of energy as D. more energy than AWARDING BRAINLIESTWe are one nation today, and 13 tomorrow. Who will treat with us on such terms? -George WashingtonHow does this image reflect George Washingtons views on government?A.)He believed in the importance of state sovereignty B.)He had a foreign policy that favored Great Britain.C.)He did not believe presidents ought to have a third term.D.)He believed the federal government needed more power. In the given figure if p||q what is the value of b? Suppose that four students, Stephanie, Charles, Tim, and Rachel, are all preparing to take standardized exam that contains three subjects, math, reading, and science. Four tutors are available to help the students prepare for the exam. Each tutor is able to help in any of the three subjects. How many different ways can the students, tutors, and subjects be uniquely combined?