y is inversely proportional to x when y=9, x=24

Answer:

A

Step-by-step explanation:

in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.

recall this formula :

(a-b)(a+b) = a^2 - b^2

in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of    3 -

after multiplying the denominator by its conjugate, we get:

(3 - [tex]\sqrt{6x}[/tex]) (3 +

at this point there is no need to solve the numerator as there is only one answer with this denominator.

hope this helps  :)

Answer:

Step-by-step explanation:

First simplify the expression into polynomial form,

[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]

[tex]x^4+8x^3-10x^2-104x+105=297[/tex]

[tex]x^4+8x^3-10x^2-104x-192=0[/tex]

Now factor into,

[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]

Which means the solutions are,

[tex]x-4=0\implies\boxed{x_1=4}[/tex]

[tex]x+8=0\implies\boxed{x_2=-8}[/tex]

and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],

[tex]x^2+4x+6=0[/tex]

[tex]x^2+4x+4=-2[/tex]

[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]

Hope this helps :)

Answer:

x=4

Step-by-step explanation:

(4-1)(4-3)(4+5)(4+7)=297

Answer:

x = -8, 1

Step-by-step explanation:

Hi there!

[tex]x^2+7x=8[/tex]

Move 8 to the other side:

[tex]x^2+7x-8=8-8\\x^2+7x-8=0[/tex]

Now, we can ask ourselves: what two factors of -8 add to 7? Those two numbers would be 8 and -1. Knowing this, factor:

[tex](x+8)(x-1)=0[/tex]

Because of the zero product property (that states that if the product of two numbers is 0, then one of the numbers must be equal to 0), we can find the solutions to the quadratic by setting each term equal to 0:

[tex]x+8=0\\x=-8[/tex]    

[tex]x-1=0\\x=1[/tex]

Therefore, the solutions of the quadratic are -8 and 1.

I hope this helps!

Answer:

∠ SPQ = 75°

Step-by-step explanation:

The sum of the 4 angles in a quadrilateral = 360°

Subtract the sum of the 3 angles from 360 for ∠ SPQ

∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°

Answer:

obtuse                    

aniuhafjhnfajfnha

Answer:2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Divide by y

kl/y = f/(p + n) + r/u              Subtract r/u from both sides

kl/y - r/u = f/(p + n)               Multiply both sides by (p + n)

(kl/y - r/u ) (p + n) = f            Divide by (kl/y - r/u)

p + n = f / (kl/y - r/u)             Subtract n from both sides

p  =  f / (kl/y - r/u)  - n

I think I'd leave this as the answer. I don't think you are expected to make it a 2 tier fraction.

Answer:

Step-by-step explanation:

Answer:

C)slides graph 4 units to the right

Answer:

-5/8

Step-by-step explanation:

13/ -56   -x = 11/28

Add 13/56 to each side

13/ -56   + 13/56  -x = 11/28+ 13/56

-x = 11/28 + 13/56

Get a common denominator

-x = 11/28 *2/2 +13/56

-x = 22/56 + 13/56

-x = 35/56

Divide top and bottom by 7

-x = 5/8

Multiply both side by -1

x = -5/8

Answer:

Step-by-step explanation:

x+y = 67

2x-y = 38

Add the equations together

3x = 108

x = 36

y = 67-x = 31

The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.

Given:

Probability of student smoke,

P = 27.7%

  = 0.277

Number of students (n) = 632

[tex]q = 1-p[/tex]

  [tex]=1-0.277[/tex]

  [tex]=0.723[/tex]

(i)

Here,

Number of students (n) = 60

then,

⇒ [tex]n_P=60\times 0.277[/tex]

         [tex]=16.62[/tex]

⇒ [tex]n_q=60\times 0.723[/tex]

        [tex]=43.38[/tex]

We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.

Now,

[tex]\mu = n_P= 16.62[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

  [tex]= \sqrt{60\times 0.277\times 0.723}[/tex]

  [tex]=3.9664[/tex]

Now,

⇒ [tex]P(X<19) = P(X<18.5)[/tex]

                      [tex]=P(Z_{18.5})[/tex]

The Z-score is:

= [tex]\frac{18.5-16.62}{3.4664}[/tex]

= [tex]0.5423[/tex]

hence,

The probability will be:

⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]

or,

⇒ [tex]P(Z<19) = 0.7062[/tex]

(ii)

Here,

Number of students (n) = 75

[tex]\mu = n_P = 75\times 0.277[/tex]

            [tex]=20.775[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

   [tex]=\sqrt{75\times 0.277\times 0.723}[/tex]

   [tex]=3.8756[/tex]

Now,

⇒ [tex]P(X>17) = P(X> 17.5)[/tex]

                      [tex]=1-P(X \leq 17.5)[/tex]

                      [tex]=1-P(Z_{17.5})[/tex]

The Z-score is:

= [tex]\frac{17.5-20.775}{3.8756}[/tex]

= [tex]-0.9740[/tex]

then, [tex]P(Z_{17.5}) = 0.165[/tex]

hence,

The probability will be:

⇒ [tex]P(X>17) = 1-0.165[/tex]

                      [tex]=0.835[/tex]    

Learn more about Probability here:

https://brainly.com/question/9825651

Answer:

(-∞,∞) is the domain.

2 is the range

Step-by-step explanation:

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

Answer:

∠ CAB = 60°

Step-by-step explanation:

∠ CAD and ∠ BCA are alternate angles and congruent , so

∠ CAD = 30°

∠ BAD = 90° ( angle in a rectangle ) , then

∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°

The measure of the angle m∠CAB is 60.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

The rectangle has 90 degrees on all the vertices.

So,

In ΔABC,

The sum of the angles = 180

So,

30 + 90 + m∠CAB = 180

m∠CAB = 180 - 120

m∠CAB = 60

Thus,

The measure of the angle m∠CAB is 60.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

Answer:

six in parenthesis n minus two

Step-by-step explanation:

2 ways could be:

A. N minus two then multiply by six

B. Six times parentheses n minus two end parentheses

Answer:

C) 2

Step-by-step explanation:

From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.

Answer:

a.

[tex] \frac{36}{40} [/tex]

Answer:

The measure of ∠1 and ∠2 is 105° and 75° respectively

Step-by-step explanation:

In the given figure, line a is parallel to line b.

We need to find the measure of angles 1 and 2.

∠2 = 75° (because they form corresponding angles)

We know that, interior angles add up to 180. So,

∠1 +75 = 180

∠1 = 180-75

∠1 = 105°

So, the measure of ∠1 and ∠2 is 105° and 75° respectively.

Answer:

18.05

Step-by-step explanation:

Answer:

Use inequalities.

At certain x values.

Step-by-step explanation:

[tex]3 \leqslant x \leqslant 6[/tex]

[tex] - \infty < x < \infty [/tex]

[tex]x = 6[/tex]

Answer:

The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.

9514 1404 393

Answer:

  (a) The blue line ... solution ... (-6, -2)..

Step-by-step explanation:

The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.

The blue line represents the equation 2x -3y = -6.

The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.

Answer:

A)

Step-by-step explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)

Answer:

[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]

Step-by-step explanation:

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Answer:

x = (y+1)/y

xy = (y+1)

xy -y = 1

y(x-1)=1

y = 1/(x-1)

Step-by-step explanation:

Answer:

5180.56 Dollars...........

Answer:

-33

Step-by-step explanation:

-p/3-8=3

or,(-p-24)/3=3

or,(-p-24)=9

or,-p=33

Therefore, p=-33

Answer:

By finding LCM of 9 and 12 the answer is 36

Step-by-step explanation:

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