1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tcecarenko [31]
3 years ago
14

Which value must be added to the expression x^2+12x to make it a perfect square trinomial a:6 b:36 c:72 d:144

Mathematics
2 answers:
Ksivusya [100]3 years ago
7 0

The answer would be 36. Why?


Because in the equation we would need to do (x + 6)(x + 6) to get a perfect square trinomial.


And 6 * 6 is 36.


So the whole equation would be: x^2 + 12 + 36.


Hope this helped! c:

mariarad [96]3 years ago
4 0

The quadratic expression uses the following formula:


ax^2 + bx + c


The expression is missing the variable of c, and it is a perfect square trinomial.


To find c in a perfect square trinomial, we will use the following formula:


c = (\frac{b}{2}})^2


The value of b in this expression is 12. Plug this value into the formula:


\frac{12}{2} = 6


6^2 = \boxed{36}


36 must be added to make this trinomial a perfect square.

You might be interested in
Consider the following. (A computer algebra system is recommended.) y'' + 3y' = 2t4 + t2e−3t + sin 3t (a) Determine a suitable f
drek231 [11]

First look for the fundamental solutions by solving the homogeneous version of the ODE:

y''+3y'=0

The characteristic equation is

r^2+3r=r(r+3)=0

with roots r=0 and r=-3, giving the two solutions C_1 and C_2e^{-3t}.

For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.

y''+3y'=2t^4

Assume the ansatz solution,

{y_p}=at^5+bt^4+ct^3+dt^2+et

\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e

\implies {y_p}''=20at^3+12bt^2+6ct+2d

(You could include a constant term <em>f</em> here, but it would get absorbed by the first solution C_1 anyway.)

Substitute these into the ODE:

(20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4

15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4

\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}

y''+3y'=t^2e^{-3t}

e^{-3t} is already accounted for, so assume an ansatz of the form

y_p=(at^3+bt^2+ct)e^{-3t}

\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}

\implies {y_p}''=(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}

Substitute into the ODE:

(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}

9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c-9at^3+(9a-9b)t^2+(6b-9c)t+3c=t^2

-9at^2+(6a-6b)t+2b-3c=t^2

\implies\begin{cases}-9a=1\\6a-6b=0\\2b-3c=0\end{cases}\implies a=-\dfrac19,b=-\dfrac19,c=-\dfrac2{27}

y''+3y'=\sin(3t)

Assume an ansatz solution

y_p=a\sin(3t)+b\cos(3t)

\implies {y_p}'=3a\cos(3t)-3b\sin(3t)

\implies {y_p}''=-9a\sin(3t)-9b\cos(3t)

Substitute into the ODE:

(-9a\sin(3t)-9b\cos(3t))+3(3a\cos(3t)-3b\sin(3t))=\sin(3t)

(-9a-9b)\sin(3t)+(9a-9b)\cos(3t)=\sin(3t)

\implies\begin{cases}-9a-9b=1\\9a-9b=0\end{cases}\implies a=-\dfrac1{18},b=-\dfrac1{18}

So, the general solution of the original ODE is

y(t)=\dfrac{54t^5 - 90t^4 + 120t^3 - 120t^2 + 80t}{405}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\dfrac{3t^3+3t^2+2t}{27}e^{-3t}-\dfrac{\sin(3t)+\cos(3t)}{18}

3 0
3 years ago
What is the length of AB?<br> O A. 9<br> O B. 18<br> O C. 48<br> D. 6
insens350 [35]
<h3>Answer:  A.  9</h3>

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

Explanation:

Draw in the segments AO and OC.

Triangle ABO is congruent to triangle CBO. We can prove this through the use of the HL theorem. HL stands for hypotenuse leg.

Since the triangles are congruent, this means the corresponding pieces AB and BC are the same length.

Then we can say:

AB+BC = AC .... segment addition postulate

AB+AB = AC .... plug in BC = AB

2*AB = AC

2*AB = 18

AB = 18/2 .... divide both sides by 2

AB = 9

In short, the chord AC is bisected by the perpendicular radius drawn in the diagram. So all we do is cut AC = 18 in half to get AB = 9.

6 0
2 years ago
Read 2 more answers
Suppose that you plan on investing into a account paying simple interest. The formula for simple interest is I = Prt, where I is
Vedmedyk [2.9K]

Answer:

No

Step-by-step explanation:

No.

i = prt is correct; its result is the simple interest earned.  

If you want to solve for time, t, divide both sides by pr:

i/(pr) = t

3 0
3 years ago
According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mou
Sergio [31]

Using the binomial distribution, it is found that:

a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing.

b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when​ sneezing.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 18, p = 0.267.

Item a:

The probability is P(X = 6), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 6) = C_{18,6}.(0.267)^{6}.(0.733)^{12} = 0.1618

There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing.

Item b:

The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{18,0}.(0.267)^{0}.(0.733)^{18} = 0.0037

P(X = 1) = C_{18,1}.(0.267)^{1}.(0.733)^{17} = 0.0245

P(X = 2) = C_{18,2}.(0.267)^{2}.(0.733)^{16} = 0.0758

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.

There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

item c:

We have to look at the mean and the standard deviation, given, respectively, by:

  • E(X) = np = 18 x 0.267 = 4.81.
  • \sqrt{V(X)} = \sqrt{18(0.267)(0.733)} = 1.88

9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when​ sneezing.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0
2 years ago
What is the answer to 0.55 divided by 100
ratelena [41]
The answer is 0.0055
7 0
3 years ago
Read 2 more answers
Other questions:
  • Carol bought 12 stickers two thirds of the stickers where dogs how many of the stickers were dogs
    11·2 answers
  • Solve this quadratic equation by completing the square.<br><br> x^2+10x=7
    7·1 answer
  • What is the volume of the cylinder?
    12·2 answers
  • Easy question it is due in 10 minutes!!!!
    8·1 answer
  • What is the length, in feet, of the hypotenuse of a right triangle with legs that are 3 feet long and 4 feet long? Question 10 o
    7·1 answer
  • You pay 1.5% interest on your credit card bill every month. This month your
    13·1 answer
  • There are 7 red marbles, 7 blue marbles, 7 yellow marbles, and 7 green marbles in a bag. If a person randomly selects 1 marble f
    14·2 answers
  • n = 40 the mean of population of raw scores is 60 with a standard deviation of 16. your sample mean = 64 and . use the criterion
    9·1 answer
  • -12 x (1/3)? what is this equal to!
    5·2 answers
  • Please help asap, i need this!!!!!​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!