Mathematics High School

What number would u add to complete the square ? x^2+22x=9

Answers

Answer 1
To complete the square, take half of the coefficient of x, 22, square it, then add it to both sides of the equation.

[tex]x^2 + 22x = 9[/tex]

22 / 2 = 11
[tex]11^2[/tex] = 121

[tex]x^2 + 22x + 121 = 9 + 121[/tex]
[tex]x^2 + 22x + 121 = 130[/tex]

Then you can go from there.

Related Questions

rewrite the standard form equation below into slope-intercept form. x-2y=3 A. y=x+3 By=-3/2x-1/2 C.y=3/2x-1/2 D.y=1/2x-3/2

Answers

Let us start converting!

[tex]x-2y=3 \ \textgreater \ \mathrm{Subtract\:}x\mathrm{\:from\:both\:sides} \ \textgreater \ x-2y-x=3-x [/tex]

[tex]-2y=3-x \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-2 \ \textgreater \ \frac{-2y}{-2}=\frac{3}{-2}-\frac{x}{-2}[/tex]

[tex]\frac{-2y}{-2} \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}:\ \frac{-a}{-b}=\frac{a}{b} \ \textgreater \ \frac{2y}{2}[/tex]

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1 \ \textgreater \ y[/tex]

[tex]\frac{3}{-2}-\frac{x}{-2} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{3-x}{-2} [/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\ \textgreater \ -\frac{-x+3}{2} \ \textgreater \ y = -\frac{3-x}{2}[/tex]

[tex]Therefore... y=\frac{1}{2}x-\frac{3}{2} (Note: m=\frac{1}{2},\:b=-\frac{3}{2}) [/tex]

M is the slope and b is the y intercept.

Hope this helps!



4747​% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answers

Given:
p = 47% = 0.47, the probability that a man considers himself a professional baseball fan.
q = 1 - p = 0.53, the probability that a man does not consider himself a professional baseball fan.
n = 10, the number of men surveyed.

(a) Calculate the probability that exactly 5 of 10 men surveyed consider themselves as professional baseball fans.
P(5 of 10) = ₁₀C₅ p⁵q⁵ = 252*0.47⁵*0.53⁵ = 0.242

Answer: 0.242 or 24.2%

(b) Calculate the probability of at least 6 out of 10.
P(at least 6 of 10)
= ₁₀C₆ p⁶q⁴ + ₁₀C₇ p⁷q³ + ₁₀C₈ p⁸q² + ₁₀C₉ p⁹q + ₁₀C₁₀ p¹⁰ q⁰
= 0.1786 + 0.0905 + 0.0301 + 0.0059 + 0.0
= 0.3057

Answer: 0.3057 or 30.6%
 
(c) Calculate the probability of less than 4 of 10.
P(less than 4 of 10)
= ₁₀C₁ pq⁹ + ₁₀C₂ p²q⁸ + ₁₀C₃ p³q⁷
= 0.0155 + 0.0619 + 0.1464
= 0.2238

Answer: 0.2238 or 22.4%

The situation represents a binomial probabilty with the probability of success (p) = 47% or 0.47 and the number of trials (n) = 10.

The probability of a binomial distribution is given by:

[tex]P(X)=\left(^n_x)p^x(1-p)^{n-x}[/tex]


Part A:

The probability that the number who consider themselves baseball fans is​ exactly​ five is given by:

[tex]P(5)=\left(^{10}_{\,5}\right)(0.47)^5(1-0.47)^{10-5} \\ \\ =252(0.022935)(0.041820)=\bold{0.2417}[/tex]



Part B:

The probability that the number who consider themselves baseball fans is​ at least​ six is given by:

[tex]P(X\geq6)=P(6)+P(7)+P(8)+P(9)+p(10) \\ \\ =\left(^{10}_{\,6}\right)(0.47)^6(1-0.47)^{10-6}+\left(^{10}_{\,7}\right)(0.47)^7(1-0.47)^{10-7} \\ +\left(^{10}_{\,8}\right)(0.47)^8(1-0.47)^{10-8}+\left(^{10}_{\,9}\right)(0.47)^9(1-0.47)^{10-9} \\ +\left(^{10}_{10}\right)(0.47)^{10}(1-0.47)^{10-10} \\ \\ =210(0.010779)(0.078905)+120(0.005066)(0.148877) \\ +45(0.002381)(0.2809)+10(0.001119)(0.53)+1(0.000526)(1) \\ \\ =0.1786+0.0905+0.0301+0.0059+0.0005=\bold{0.3056}[/tex]

This can be approximated using normal distribution as I will illustrate in part c.



Part C:

The probability that the number who consider themselves baseball fans is​ less than four is given by:

[tex]P(X\ \textless \ 4)=P(0)+P(1)+P(2)+P(3)[/tex]

We can approximate this using normal distribution by subtracting 0.5 from the least value and adding 0.5 to the greatest value.

This gives [tex]P(0-0.5\ \textless \ X\ \textless \ 3+0.5)=P(-0.5\ \textless \ X\ \textless \ 3.5)[/tex]

The mean of a binomial distribution is given by [tex]\mu=np[/tex], while the standard deviation is given by [tex]\sigma= \sqrt{np(1-p)} [/tex].

Thus,

[tex]\mu=10(0.47)=4.7 \ and \ \sigma=\sqrt{10(0.47)(0.53)}=1.578[/tex]

The probability of a nomal distribution between two values (a, b) is given by:

[tex]P(a\ \textless \ X\ \textless \ b)=P\left( \frac{b-\mu}{\sigma} \right)-P\left( \frac{a-\mu}{\sigma} \right)[/tex]

Thus,

[tex]P(-0.5\ \textless \ X\ \textless \ 3.5)=P\left( \frac{3.5-4.7}{1.578} \right)-P\left( \frac{-0.5-4.7}{1.578} \right) \\ \\ =P(-0.7605)-P(-3.295)=0.2235-0.0005=\bold{0.223}[/tex]

Which is best definition of contrapposto?
a. an active pose
b.an s-shaped pose
c. a block-shaped pose

Answers

The answer is an s shaped pose.  Contrapposto is an Italian word that means counterpose. It is practiced in visual arts to depict a human figure standing with the majority of its heaviness on one foot so that its shoulders and arms curl off in an axis from the hips and legs forming a letter s.

I just finished the quiz the answer is B. an S-shaped pose

I'm stuck on trying to get X

Answers

They must be equal, since they are alternate interior angles, (3x-50)=(2x-5)
This will simplify to x=45.
I am assuming the two lines are parallel.

In this case, these two angles are Alternate Interior Angles, which we know are congruent.

Because they are congruent, they will be the same angle. In other words, they will equal each other.

So we can set this problem up as an equation and solve for x:

3x-50 = 2x-5
3x-50+50 = 2x -5 + 50
3x = 2x + 45
3x - 2x = 2x -2x + 45
x = 45

ANSWER:
X= 45

Now find the angles accordingly.
3(45) - 50 = 85
2(45) - 5 = 85✔️
Everything checks out.

Determine f(2) where f(x)= x+1/4x-2

Answers

F(2)= (2)+1/4(2)-2
F(2)=3/6
F(2)= 1/2

How many solutions does the equation have?y+7=y–3many solutions1 solutionno solutions?

Answers

No solution
Subtract y on both sides, giving you...
7= -3
Which is false

What number gives a result of -5 when 11 is subtracted from the quotient of the number and 6?

Answers

This word equation is equivalent x/6-11=-5. Simplifying this will get you x=36.

Final answer:

The answer explains how to find a number from an equation involving subtraction and division, providing step-by-step instructions.

Explanation:

To find the number that gives a result of -5 when 11 is subtracted from the quotient of the number and 6, we can create an equation:

Let the number be x.

The equation becomes: x/6 - 11 = -5

Solve for x:

Add 11 to both sides: x/6 = 6

Multiply both sides by 6: x = 36

Therefore, the number is 36.

I need the answer for 9

Answers

The sum of the measures of the angles of a polygon of n sides is 180(n - 2).

Set that expression equal to 1800 and solve for n, the number of sides.

180(n - 2) = 1800

Divide both sides by 180

n - 2 = 10

Add 2 to both sides

n = 12

The polygon has 10 sides.
Sum of Interior Angles = (n-2) × 180°
so you can use this to find out how many sides of this polygon

 (n-2) × 180° = 1800
 n - 2 = 10
      n = 12

this polygon has 12 sides

Find the missing term of the following sequence. . . . –45, __, –12, . . .

Answers

(-45 + (-12) / 2 = -28.5 
So the answer is -28.5

53 plz help me with this

Answers

3 large beads cost 2.50 * 3 = 7.50

30-7.50 = 22.50

20-7.50 = 12.50

 so they can spend between 12.50 and 22.50 on small beads

12.50 / 1.25 = 10

22.50/1.25 = 18

can buy between 10 and 18 small beads

1.25x >=12.50 and 1.25x<=22.50

The ratio of red pens to black pens is 3:2. What fraction of the pens are red

Answers

im not sure but i think 1/4

Answer:

1/4

Step-by-step explanation:

3/12 simplified is 1/4.

An investment doubles in value every 9 years. What was the starting value of the investment if it is worth $4800 after 27 years.

Answers

The starting was $1600

If cos70 = 0.342, give another angle whose cosine is 0.343

Answers

The another angle whose cosine is 0.343 is  -70.789 degrees.

Given that,

cos(70) = 0.342

We can use the fact that cos(x) = cos(-x) to find another angle whose cosine is 0.343.

Now

⇒ cos(x) = 0.343

⇒cos(-x) = cos(x)

              = 0.343

Now, we need to find -x.

⇒ cos(-x) = 0.343

Taking inverse cosine on both sides, we get:

⇒ -x = arcos(0.343)  we get,

⇒ -x = 70.789

Therefore, x = -70.789

Hence, another angle whose cosine is 0.343 is -70.789 degrees.

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What is the term for the point where angle bisectors of a triangle meet?

Answers

The three perpendicular bisectors of the sides of a triangle meet in a single point,called the circumcenter . A point where three or more lines intersect is called a pointof concurrency. So, the circumcenter is the point of concurrency of perpendicular bisectors of a triangle.
I think the answer is circumcentre

The amount of money it takes to fill up a gas tank varies directly with the number of gallons bought. It cost $21.87 to fill up a car with gasoline with 9 gallons of gasoline. What is the constant of variation?

Answers

no that much 2 or 3 gallons
9 because it is constantly changing

Determine the value of r so the line passing through each pair of points has the given slope
(6,3) (r,2), m=1/2

Answers

We can use the slope formula to solve this one:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{1}{2}=\frac{2-3}{r-6}[/tex]
[tex](r-6)=2(-1)[/tex]
[tex]r-6=-2[/tex]
[tex]r=4[/tex]

That is the screen shot for questions 5.

Answers

It's choice C as the root overhead bar goes over all of (x-7) and not just the x. So you have the correct answer. 

f(x) = x^4+7
y = x^4+7
x = y^4+7
y^4 = x-7
y = FourthRoot(x-7)

[tex]y = \sqrt[4]{x-7}[/tex]

y=10x+16 looks like what on a graph

Answers

Here is my graph. Hope it helps

There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day. Which linear equation represents the total amount of quarters in the jar after x days? A. 6y = 2x B. y = 6x + 2 C. y=16x+2 D. y = 2x + 6

Answers

Given: Say 6Q = 6 quarters in a jar 2Q is added everyday After X days, Amount of quarters = 6Q + (2Q * X) So answer would be: D) which is y = 2x + 6

Answer:

D. y = 2x + 6

Step-by-step explanation:

The amount of quarters that there´s in the jar is expressed by the letter "Y".

We know the jar had already 6 quarters.

Jill adds 2 quarters to the jar everyday, the number of days Jill does this will be represented by the letter "X", because it´s our variable.

What remains constant is that we started with 6 quarters and Jill deposits 2 more every day

Number of quarters in the jar "Y"= (Number of quarters deposited) 2*(number of days)X + (Number of quarters already in the jar) 6.

Y= 2x+6

Your company gives you a cell phone plan which allows you 600 minutes to talk per month. So far this month, you have used 330 minutes and you have 10 days left on this month's plan. Which inequality could you use to determine how many minutes at most you can use per day so that you don't go over your monthly plan minutes?

A.)10x+330≥600

B.)10x+330>600

C.)10x+330≤600

D.)10x+330<600

Answers

The answer is C) 10x + 330 ≤ 600. 
We use the ≤ since you are allowed to use the 600th minute.
When we subtract 330 from both sides, it makes a bit more sense
10x ≤ 270
270 is the number of minutes left your plan since you've already used 330, and you have 10 days left in the month. 

Find the sum of each group of numbers. You may add the numbers in any order. Then, check your work by adding the numbers again in a different order. a. 110, 83, and 328 b. 92, 37, 14, and 66 c. 432, 11, 157, and 30

Answers

The sum of each group of numbers are as follows:
1. 110 + 83 + 328 = 521
2. 92 + 37 + 14  + 66 = 209
3. 432 + 11 + 157 + 30 = 630
It does not matter how much you re-arrange the numbers in each group, you will keep arriving at the same answers, this is because the sum of a particular set of numbers will always remain the same.

Answer:

1. 110 + 83 + 328 = 521

2. 92 + 37 + 14  + 66 = 209

3. 432 + 11 + 157 + 30 = 630


Find the “missing terms” in the polynomial problems. Answers will have multiple terms.

1. (c^3 + c^2 - 5) + ( ) = c^2 + 2c - 7

2. (2d^2 + d) - ( ) = - d^3 + 3d - 1

3. ( ) - (2x^4 - 2x^2 - 3) = x^4 + x^3 - 2x^2 + x

Answers

1. (c^3 + c^2 - 5) + (-c^3 + 2c - 2 )= c^2 + 2c - 7 

2. (2d^2 + d) - (d^3 + 2d^2 - 2d + 1) = - d^3 + 3d - 1 

3. ( 3x^4 + x^3 - 4x^2 + x - 3) - (2x^4 - 2x^2 - 3) = x^4 + x^3 - 2x^2 + x

which of the following is a factor of 15x2-14x-8

Answers

It can be 1 1/3 or -(2/5)
26x-8 i think is it i am not sure

Which logical form represents this statement?
Either it is not cold today or i am wearing woolen coat.
p: It is cold today.
q: I am wearing woolen coat.

~p ∧~q
~p ∧ q
~p ∨ q
~(p∨ q)

Answers

The third choice.
That's what I put for my answer.

Answer:

The correct answer is:

~p ∨ q

Step-by-step explanation:

p: It is cold today.

q: I am wearing woolen coat

~p: It is not cold today

V represents either...or...

Hence, ~p V q represents:  

Either it is not cold today or i am wearing woolen coat.

Hence, the correct option is:

~p ∨ q

Write 5 3/8 as an improper fraction.
15/8
43/8
23/8
53/8




Answers

I hope this helps you!
To change to an improper fraction, multiply the denominator by the whole number, add the numerator to what you get and write it over the denominator. That will be;
8 x 5=40
Add 3 to 40 that will be 43
So you have 43/8
The answer is 43/8
Hope that helped. Have a nice day

Bonnie filled her car’s tank. She put in 10 1/2 gallons and paid $15.26. Determine the cost of gasoline per gallon.

Answers

So, it starts off with 10 half gallons. 10*1/2 is 5, so in other words she put in 5 gallons and paid 15.26. As an equation it can be represented by 5x=15.26 where x is the cost of the gallons which is what we're trying to find. We can solve by using the division property of equality and divide both sides by 5. This gets us x=3.052. So, it costs $3.052 exactly for a gallon of gasoline.

If Jeremy walks 2 miles in 74 minutes, then how far will Jeremy walk in 84 minutes?

Answers

2.27miles in 84 minutes

To find how far Jeremy will walk in 84 minutes, set up a proportion relating time and distance covered.

To find the distance he walks in 84 minutes, you can set up a proportion: 2 miles / 74 minutes = x miles / 84 minutes.

Solving for x, Jeremy will walk approximately 2.27 miles in 84 minutes. Jeremy walks at a speed of 2 miles in 74 minutes.

((Use the graph shown below to fill in the blank.))

If (4, y) is an ordered pair of the function, then y = a0.

Answers

The point (4,y) has a known x coordinate of x = 4. The y coordinate is unknown right now so we'll just call it y.

Draw a vertical line (see side note below) through 4 on the x axis. I've done so in red (see attached image). The red line crosses the graph at the point (4,1) so this tells us that y = 1

Answer: y = 1

Side Note: you don't have to draw a vertical red line but it's handy to see how it works out. After you get used to these types of problems, you can visually be able to see the answer without these extra lines. 

If (4, y) is an ordered pair of the function, then value of y = 1.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

(4, y) is an ordered pair of the function.

Now, The point (4, y) has a known x coordinate of x = 4.

For the value of y at x = 4,

Draw a vertical line through 4 on the x axis.

Then, The vertical line crosses the graph at the point (4, 1).

Thus, The value of y is 1.

Thus, If (4, y) is an ordered pair of the function, then value of y = 1.

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△EFG≅△JKL. What is m∠K?

Answers

Download the app Photomath that will help you

Answer:

62

Step-by-step explanation:

Determine the slope of the graph of x3 = ln(xy) at the point (1, e).

Answers

Final answer:

The slope of the graph of x^3 = ln(xy) at the point (1, e) is 2e. This is found by taking the derivative of the equation to find a formula for the slope at any point, and then substitifying the given point into that formula.

Explanation:

To determine the slope of a graph of the equation x3 = ln(xy) at a specific point, we need to take the derivative of the equation, which gives us the slope at any point. Given the equation x^3 = ln(xy) and the point (1, e), first we can take the derivative implicitly.

Using the chain rule and the fact that the derivative of ln(x) is 1/x, we have 3x2dx = (1/y + x/y')dx. Simplifying this gives y' = (3x2y - 1)/x, which is the derivative of the equation and represents the slope at any given point.

Substituting x = 1 and y = e into the equation of the derivative, we get y' = (3.1e - 1)/1 = 2e, so the slope at the point (1, e) is 2e.

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