please help please help​

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:2

Step-by-step explanation:

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.

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

A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.

So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.

Answer:

Step-by-step explanation:

Answer:

2(w+3)

Step-by-step explanation:

2(w+3) or 2w+6

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:

obtuse                    

aniuhafjhnfajfnha

Answer:

95%

Step-by-step explanation:

Mean , xbar = 64.3; standard deviation, s= 2.4

Using the empirical formula where ;

68% of the distribution is within 1 standard deviation from the mean ;

95% of the distribution is within 2 standard deviation from the mean

percent of heights that lie between 59.5 inches and 69.1 inches.

Number of standard deviations from the mean /

Z = (x - μ) / σ

(x - μ) / σ < Z < (x - μ) / σ

(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4

-2 < Z < 2

Thia is within 2 standard deviations of the means :

2 standard deviation form the mean = 95% according to the empirical rule.

Answer:

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

Step-by-step explanation:

bxhrrrhi5u44ftj7gttjoy

Answer:

x = (y+1)/y

xy = (y+1)

xy -y = 1

y(x-1)=1

y = 1/(x-1)

Step-by-step explanation:

Answer:

18.05

Step-by-step explanation:

Answer:

a.

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

Answer:

By finding LCM of 9 and 12 the answer is 36

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

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

Answer:

C)slides graph 4 units to the right

Answer:

2.5 or 5/2

Step-by-step explanation:

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other - in other words, separated by the crossing point of the lines and not by the lines themselves.

but that also means they are equal.

8x + 15 = 4x +25

4x = 10

x = 10/4 = 5/2 or 2.5

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:

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:

(-∞,∞) is the domain.

2 is the range

Step-by-step explanation:

Answer:

Step-by-step explanation:

x+y = 67

2x-y = 38

Add the equations together

3x = 108

x = 36

y = 67-x = 31

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:

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:

-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:

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:

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:

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!