Need help with this math question

Answer:

No of real solutions =1

No of  extraneous solution =2

Real solution: x =3

Step-by-step explanation:

[tex]\frac{3}{x}-\frac{x}{x+6}=\frac{18}{x^2+6x}[/tex]

solving:

Taking LCM of x, x+6 and x^2+6 we get x(x+6)

Multiply the equation with LCM

[tex]\frac{3}{x}*x(x+6)-\frac{x}{x+6}*x(x+6)=\frac{18}{x^2+6x}*x(x+6)\\3(x+6)-x*x=\frac{18}{x(x+6)}*x(x+6)\\3(x+6)-x*x=18\\3x+18-x^2=18\\-x^2+3x+18-18=0\\-x^2+3x=0\\x^2-3x=0\\x(x-3)=0\\x=0 \,\,and\,\, x =3\\[/tex]

Checking for extraneous solution

for extraneous solution we check the points where the solution is undefined

The solution will be undefined. if, x=0 or x=-6 so both are extraneous solutions

Putting x =3

[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(0)}[/tex]

[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(3)}\\1-\frac{3}{9}=\frac{18}{9+18}\\1-\frac{1}{3}=\frac{18}{27}\\\frac{3-1}{3}=\frac{2}{3}\\\frac{2}{3}=\frac{2}{3}[/tex]

So, x=3 is real solution.

Now, Selecting answers from tables

No of real solutions =1

No of  extraneous solution =2

Real solution: x =3

Number of                Number of                         Real solutions

real solution            Extraneous solution

     1                                        1                                     x=3

Extraneous solution--

It is a solution which is obtained on solving the equation but it does not satisfies the equation i.e. after it is put back to the equation it does not occur as a valid solution.

True solution or real solution--

It is the solution which is obtained on solving the equation and is also a valid solution to the equation.

The equation is:

[tex]\dfrac{3}{x}-\dfrac{x}{x+6}=\dfrac{18}{x^2+6x}[/tex]

On taking lcm in the left hand side of the equation we get:

[tex]\dfrac{3\times (x+6)-x\times x}{x(x+6)}=\dfrac{18}{x^2+6x}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}=\dfrac{18}{x(x+6)}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}-\dfrac{18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x+18-x^2-18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x-x^2}{x(x+6)}=0\\\\i.e.\\\\3x-x^2=0\\\\i.e.\\\\x(3-x)=0\\\\i.e.\\\\x=0\ or\ x=3[/tex]

When we put x=0 back to the equation we observe that the first term of the left hand side of the equation becomes undefined.

Hence, x=0 is the extraneous solution.

whereas x=3 is a valid solution to the equation.

Answer:

1/12

Step-by-step explanation:

There are two dices being rolled. A dice has six faces numbered from one to six. A fair dice means that the probability of each number to appear is equal. Thus the probability of any number showing up is:

P(a number appears on the dice) = how much times the number has been displayed on the dice/number of faces of the dice.

Since all numbers appear once, and there are six sides of a dice. therefore:

P(a number appears on the dice) = 1/6. Thus, P(6 appears on a dice) = 1/6.

As far as the odd numbers are concerned, there are three even numbers and three odd numbers on the dice. So P(odd number appears on the dice) = 3/6 = 1/2.

Assuming that the probabilities of both the dices are independent, we can safely multiply both the probabilities. Thus:

P(first dice lands on a 6 and second dice lands on an odd number) = 1/6 * 1/2 = 1/12.

Thus, the final probability is 1/12!!!

Answer:

The solutions are x=8 and x=-4

Step-by-step explanation:

we have

[tex]\left|x-2\right|=6[/tex]

step 1

Find the first solution

case positive

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

[tex]x=6+2=8[/tex]

step 2

Find the second solution

case negative

[tex]-(x-2)=6[/tex]

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

[tex]x=2-6=-4[/tex]

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \\\\ ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{48}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{3.4}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf h(t)=-16t^2+48t+3.4\implies \stackrel{\textit{when it hits the ground}}{\stackrel{h(t)}{0}=-16t^2+48t+3.4}[/tex]

Check the picture below.

1.)

   =(x-8i)(x+8i)

x^2+8ix-8ix-64i^2

x^2-64i^2

x^2-64(-1)

x^2+64

2.)

    =(4x-7i)(4x+7i)

16x^2+28ix-28ix-49i^2

16x^2-49i^2

16x^2-49(-1)

16x^2+49

3.)

    =(x+9i)(x+9i)

x^2+9ix+9ix+81i^2

x^2+18ix+81(-1)

x^2+18ix-81

4.)

    =(x-2i)(x-2i)

x^2-2ix-2ix+4i^2

x^2-4ix+4(-1)

x^2-4ix-4

5.)

    =[x+(3+5i)]^2

(x+5i+3)^2

(x+5i+3)(x+5i+3)

x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9

x^2+6x+10ix+30i+25i^2+9

x^2+6x+10ix+30i+25(-1)+9

x^2+6x+10ix+30i-25+9

x^2+6x+10ix+30i-16

Hope this helps :)

Answer:

a) Yes the events Chocolate and Adults are independent

b) Yes the events Children and Chocolate are independent

c) Yes the events Vanilla and Children are independent

Step-by-step explanation:

* Lets study the meaning independent and dependent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question

# From the table:  

- The probability of chocolate is 0.35

- The probability of vanilla is 0.65

- The probability of adults is 0.60

- The probability of children is 0.40

- The probability of chocolate and adults is 0.21

- The probability of chocolate and children is 0.14

- The probability of vanilla and adult is 0.39

- The probability of vanilla and children is 0.26

a.

∵ P(chocolate) = 0.35

∵ P(Adults) = 0.60

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(chocolate) · P(adults) = (0.35)(0.60) = 0.21

∵ P(chocolate and adults) = 0.21

∴ P(chocolate and adults) = P(chocolate) · P(adults)

∴ The events chocolate and adults are independent

b.

∵ P(chocolate) = 0.35

∵ P(children) = 0.40

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(chocolate) · P(children) = (0.35)(0.40) = 0.14

∵ P(children and chocolate) = 0.14

∴ P(chocolate and children) = P(chocolate) · P(children)

∴ The events chocolate and children are independent

c.

∵ P(vanilla) = 0.65

∵ P(children) = 0.40

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(vanilla) · P(children) = (0.65)(0.40) = 0.26

∵ P(vanilla and children) = 0.26

∴ P(vanilla and children) = P(vanilla) · P(children)

∴ The events vanilla and children are independent

Answer:

C.11.2

Step-by-step explanation:

The distance between 2 points is given by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

   = sqrt( ( -2-0)^2 + (-7-4)^2)

   = sqrt( (-2)^2 + (-11)^2)

  = sqrt( 4 + 121)

  = sqrt(125)

 = 11.18033989

To the nearest tenth

11.2

Answer: Area of 1+Area of 2=Area of 3

I just took the test

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Since the given triangle is a right angle triangle and it has been given that squares 1, 2 and 3 are constructed on its respective sides.

Since the triangle is the right angle triangle so it will follow Pythagoras theorem.

Hypotenuse² = (height )² + (base)²

since hypotenuse is the one side of square 3

so area of square 3 = Hypotenuse²

similarly height² = area of square 1

Base² = area of square 2

so area of 1 + area of 2 = area of 3 will be defined by the Pythagoras theorem.

Therefore, Option D. is the answer.

First of all, for a point to be the solution to the system of equations, it must be located on both lines, since we are calculating the point at which the lines cross. Therefor, we can automatically discount B and D as the answers, which state that the point does not lie on either line. To see whether it is A or C we will have to solve the equations.

1. There are quite a few ways to approach solving the system of equations, however I will show the substitution method as it requires less modification of equations.

What we need to do is to isolate either x or y in one of the equations so that we can then substitute this value into the other equation. So for example if we take the first equation and isolate x:

3y + x = 6

x = 6 - 3y (Subtract 6 from both sides)

2. Now we can substitute this into the second equation (2y - x = 9).

when x = 6 - 3y:

2y - (6 - 3y) = 9

2y - 6 + 3y = 9

5y - 6 = 9 (Add 2y and 3y)

5y = 15 (Add 6 to both sides)

y = 3 (Divide both sides by 5)

From here, we can already see that the answer is C, since A has a y-value of 4, however if we were to completely solve the question we would do the following:

3. Now that we know the value of y, we can substitute this back into our equation of x = 6 - 3y to find x:

x = 6 - 3(3)

x = 6 - 9

x = -3

So, our solution is the point (-3, 3). It also has to lie on both lines to be a solution. Therefor C. It is (-3, 3) and lies on both lines, is the correct answer.

Answer:

The answer is C

(It is (−3, 3) and lies on both lines.)

Step-by-step explanation:

Answer:

Write the equation as n+31=113 and subtract 31 from both sides. The answer is 82.

Step-by-step explanation:

Let

n ----> the number

we have that

The equation is equal to

n+31=113

solve for n

subtract 31 both sides

n+31-31=113-31

n=82

Answer:Write the equation as n+31=113 and subtract 31 from both sides. The answer is 82.

Step-by-step explanation:

Answer:

  all points in the 1st and 3rd quadrants (not including the x- and y-axes).

Step-by-step explanation:

The product of positive numbers will be greater than 0, as will the product of two negative numbers. Both coordinates are positive in the first quadrant; both are negative in the third quadrant.

The quadrant boundaries, x=0, y=0, are excluded from the solution set.

Answer:

A)  x + 2y = 4

3x + 4y -9z = 2

-x + 7z = 1

Step-by-step explanation:

The matrix form is

x y z  

1 2 0    4

3 4 -9   2

-1 0 7    1

Here 0 represents no term in system.

So, the following system represents the above matrix.

x + 2y + 0z = 4  => x + 2y = 4

3x + 4y -9z = 2

-x + 0y + 7z = 1  => -x + 7z = 1

Therefore, the answer is A.

Answer:

Option A is correct.

Step-by-step explanation:

2x+3y=25

4x+2y=22

Option A

2y = 22-4x

y = 11 -2x

Option B

2x = 25 -3y

x = 25/2 -3/2y

Option C

3y = 25 - 2x

y = 25/3 -2/3x

Option D

4x = 22 - 2y

x = 22/4 -2/4y

x = 11/2 -1/2y

In Option B,C and D we have fractions and for substitution the calculations will be complex.

But Option A has no fractions and solving by putting the value of y in equation 1 is easy.

So, Option A is correct.

Answer:

A

Sarita should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.

Step-by-step explanation:

Answer:

190000 is the best answer in my opinion because by 2006 it is more then 160000 but it is less then 200000

Step-by-step explanation:

Answer:

y= 250x + 2175

Step-by-step explanation:

the slope intercept form is y = mx + b so you would put 250 for the M because it depends on each policy he sells which is X so y = 250x + b and B is the fixed price of 2,175 so you would get Y = 250x + 2175 as your answer

Answer:

The required answer is [tex]y = 250x + 2175[/tex].

Step-by-step explanation:

Consider the provided information.

The base salary of Mr. Jensen is 2175.

The commission per policy is 250.

The slope intercept form is:

[tex]y = mx + c[/tex]

Where, m is slope and c is y intercept.

Let "x" be the number of policy Mr. Jensen sells and "y" is the total paycheck including the commission.  

[tex]y = 250x + 2175[/tex]

Therefore, the required answer is [tex]y = 250x + 2175[/tex].

Answer:

Z =7

Step-by-step explanation:

The middle segment theorem of a triangle says that: A middle segment connecting two sides of a triangle is parallel to the third side and is half its length.

In this case, the middle segment connecting two sides of a triangle is Z.

This means that

[tex]Z = 0.5(14)[/tex]

Finally we have that:

[tex]Z =7[/tex]

The length of the middle segment is 7 units

Answer:

it would take 5 seconds for the object to hit the ground after launched.

////////////////////////////////////////////////////////////////////////////////

1st step: (turn the quadratic function to a quadratic equation by setting the equal to zero): 0 = -16t2 + 80t + 0

2nd step: t = 0 & t = 5

(t = 0 is the time of launch. t = 5 represents the 5 seconds it took to hit the ground after the object was launched.)

Answer:

The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds

Answer:

  None

Step-by-step explanation:

It simplifies to -12 = 12, which cannot be made true by any value of m.

Answer:

none

Step-by-step explanation:

Answer:

(7, .5)

Step-by-step explanation:

From the origin, our intersection is 7 units to the right where x is positive, so x = 7.  It appears that we are between y values of 0 and 1 at x = 7, so the coordinate that best represents the solution is (7, .5)

Answer:

B. 2

Step-by-step explanation:

Assuming the term is meant to look like this: -3x², then the answer is B.2. An exponent is a superscript (super means above, script means writing) that tells you to multiply something by itself.

In this case, -3x² means -3·x·x

If it was written as (-3x)², it would mean (-3x)·(-3x)

Answer:

2

Step-by-step explanation:

The exponent is raised to the power of any variable [smaller number].

I am joyous to assist you anytime.

[tex]|\Omega|=20\\|A|=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}=10\%[/tex]

Answer:

1/10.

Step-by-step explanation:

The length of each cycle is 2 + 18 = 20 minutes.

During this time  the train in stationary for 2 minutes.

So the probability of the train being at the station when you arrive is 2/20 = 1/10.

Move all the terms involving the sine to one side, and all the numbers to the other:

[tex]9\sin(c)-2=\sin(c)-7 \iff 8\sin(c) = -5\iff \sin(c)=-\dfrac{5}{8} \iff c = \arcsin\left(-\dfrac{5}{8}\right)\approx 321.3[/tex]

Answer:

I think 8 hours maybe if I wrong sorry

The time taken for  tap to leak a total of 300mL is 2.4 hours.

A tap is leaking water at a rage of 1L every 8 hours.

Since 1L = 1000 mL and it takes 8 hours

So for 300 mL it takes

[tex]= 300 \times 8 \div 1000[/tex]

= 2.4 hours

Learn more about the tap here: https://brainly.com/question/24489593

Answer:

10

Step-by-step explanation:

Each dot represents 1 rock.

There are 10 dots in the plot, so there are 10 rocks in the collection.

Answer:

x^4 - 15x^2 - 38x - 60.

Step-by-step explanation:

Writing it in factor form:

( x - 5)(x + 3) ( x - (-1 + 2i) )(x - (-1 - 2i))

There are 4 parentheses because  complex roots occur in pairs.

( x - (-1 + 2i) )(x - (-1 - 2i))

=  ( x + 1 - 2i) )(x +1 + 2i))

=  x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i  + 4

= x^2 + 2x + 4.

So our polynomial is

( x - 5)(x + 3)( x^2 + 2x + 4)

=  (x^2 - 2x - 15)(x^2 + 2x + 4)

= x^4 + 2x^3 + 4x^2 - 2x^3 - 4x^2 - 8x - 15x^2 - 30x - 60

= x^4 - 15x^2 - 38x - 60.

Answer:

13,506 m

Step-by-step explanation:

Applying the trigonometric relation between  opposite leg and hypotenuse

[tex]sin(\alpha)=\frac{Op}{h}[/tex]

isolating the variable [tex]sin(\alpha)=\frac{Op}{h} \longrightarrow h=\frac{Op}{sin(\alpha)}\longrightarrow h=\frac{5m}{sin(36^o)}=8,506m[/tex]

the total height is the sum to the hypotenuse and the opposite leg

[tex]h_{total}=hypotenuse+h=8,506m+5m=13,505m[/tex]

Answer:

  108 ft²

Step-by-step explanation:

The product of length and width is ...

  (12 ft)(9 ft) = 12·9 ft·ft = 108 ft²

Answer:

360

Step-by-step explanation:

n=?

1800° = sum of interior angles

Pentagon = 5 sides

n = 1800° ÷ 5

n = 360

Answer: [tex]n=12[/tex]

Step-by-step explanation:

You can observe that the formula for the sum of the interior angles of a polygon is:

[tex]sum=(n-2)180[/tex]

Where "n" is the number of sides of the polygon.

You know that the sum of the interior angles of  this polygon is 1,800 degrees. Therefore, you can find the number of sides by substituting this sum into the formula and then solving for "n".

Then:

[tex]1,800=(n-2)180\\\\\frac{1,800}{180}=n-2\\\\10=n-2\\\\10+2=n\\\\n=12[/tex]