URGENT!! The quotient of the rational expressions

Answer:

Choice C. [tex]84\, x + C[/tex].

Step-by-step explanation:

Consider the power rule for integration. Let [tex]n[/tex] be a real number that is not equal to [tex](-1)[/tex]. The power rule for integration states that:

[tex]\displaystyle \int x^{n}\, d x = \frac{1}{n + 1}\, x^{n+ 1} + C[/tex],

How could this rule apply to this question, since there's apparently no [tex]x[/tex] (or its powers) in the integrand? Keep in mind that [tex]x^{0} = 1[/tex] for all real (and particularly non-zero) values of [tex]x[/tex]. In other words, the integrand [tex]84[/tex] is equal to [tex]84\, x^0[/tex]. The integral becomes:

[tex]\displaystyle \int 84\, x^{0}\, dx[/tex].

The constant can be moved outside the integral sign. Therefore:

[tex]\displaystyle \int 84\, x^{0}\, dx= 84 \int x^{0}\, dx[/tex].

Now that resembles the power rule. In particular, [tex]n = 0[/tex], such that [tex]n + 1 = 1[/tex]. By the power rule:

[tex]\begin{aligned}84 \int x^{0}\, dx = 84\, \left(\frac{1}{1}\, x^{1} + C\right) = 84\, x + 84\, C\end{aligned}[/tex].

The non-zero constant in front of [tex]C[/tex] can be ignored (where [tex]C[/tex] represents the constant of integration.) Therefore:

[tex]\displaystyle \int 84\, dx = 84\, x + C[/tex].

If a is a constant then it's inetgration is

[tex]\boxed{\sf \displaystyel\int adx=ax+C}[/tex]

[tex]\\ \rm\Rrightarrow \displaystyle\int 84dx[/tex]

[tex]\\ \rm\Rrightarrow 84x+C[/tex]

Option C

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D

Answer:

1. a = -31/9

2. -3/4

3. Different degree polynomials

4. Yes, of a degree 2n

5. a. Even-degree variables

b. Odd- degree variables

Step-by-step explanation:

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a?

Plugging in 3 for x:

f(3)= 3^4 - 2*3^3 + a*3^2 + 3 + 3= 81 - 54 + 6 + 9a = 33 + 9a and f(3)= 2

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2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

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3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g?

If the sum of monic polynomials f(x) + g(x) is also monic, then f(x) and g(x) are of different degree and their sum only change the one with the lower degree, leaving the higher degree variable unchanged.

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4. If f(x) is a polynomial, is f(x^2) also a polynomial?

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5. Consider the polynomial function g(x) = x^4-3x^2+9

a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial?

b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial?

Answer:

32

Step-by-step explanation:

8(3 + 4) = 24 + ?

8(3)+8(4)= 24 + ?

24+32= 24 + ?

24-24+32=?

32=?

Answer:

? = 32

Step-by-step explanation:

Let's assume a = 8 , b = 3 , c = 4

[tex] \sf \: So :- \: \: a(b + c) = 8(3 + 4)[/tex]

[tex]8 \times 3 + 8 \times 4[/tex]

[tex]24 + 32[/tex]

Hence, The required value of ? = 32 .

Answer:

Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is  ( 0.541 , 0.683)

Step-by-step explanation:

The sample proportion is = p = 112/181 = 0.61878= 0.612

q = 1-p = 1- 0.612= 0.388

The degree of confidence is 98 % so z₀.₀₂₅= 1.96  taking α = 5 at 95 %

The interval X~± 0.98  is a random variable because X does not have a particular value but takes different values in different samples.

In repeated samples of size 16 from a normal distribution with standard deviation 2 the interval X~± 0.98 will contain true unknown value of mean about 95 percent of the time .

p ± z ( base alpha by 2) √pq/n

Substituting the values

0.612 ± 1.96√0.612*0.388/181

Multiplying p and q

= 0.612 ± 1.96 √0.237456/181

Solving the square root

=0.612 ± 1.96( 0.03622)

Multiplying  value of z with the value of square root

=0.612 ±  0.07099

Adding or subtracting will give   0.683, 0.541

Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is  ( 0.541 , 0.683)

Answer:

Hello There!!

Step-by-step explanation:

Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...

Answer:

It should be 1/3d+4=28, but i dont see that option

Step-by-step explanation:

All the other ones are wrong. Its plus 4 because it states that its 4 years greater not lesser. Greater in the context means that its addition of 4.

idk if theres a typo or something but yeah.

Answer:

The graph of g is the graph of f shifted up by 3 units.

Step-by-step explanation:

Consider the graph of a function r with real numbers k and h.

Transformation Effect

r(x) + k shifts the graph up k units

r(x) - k shifts the graph down k units

r(x + h) shifts the graph to the left h units

r(x - h) shifts the graph to the right h units

It is given that g(x) = f(x) + 3. Therefore, the graph of g is the graph of f shifted up by 3 units.

Answer:

[tex]\boxed{x = 7}[/tex]

Step-by-step explanation:

75 = 11x-2 (Corresponding angles are equal)

11x -2 = 75

Adding 2 to both sides

11x = 75+2

11x = 77

Dividing both sides by 11

x = 7

Answer:

[tex]\left[\begin{array}{ccc}\\x = 7\\\end{array}\right][/tex]

Step-by-step explanation:

Well to find x we can set up the following equation,

11x - 2 = 75

So we have to single out x.

+2 to both sides

11x = 77

Divide 11 by both sides

x = 7

Thus,

x = 7.

Hope this helps :)

Answer:

  5/18

Step-by-step explanation:

There are a couple of ways to look at this.

1) If you make a matrix of all possibilities, you find there are 36 possible outcomes from the roll of a die twice. (That is the same number as for rolling two dice once.) Of those 36 outcomes, 10 are outcomes in which a 5 shows exactly once: (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5).

The probability of obtaining exactly one 5 is 10/36 = 5/18.

__

2) As listed above, there are two ways to get exactly one 5 in two rolls:

  (5 on the first, non-5 on the second) or (non-5 on the first, 5 on the second)

When the rolls are independent, as we assume here, the probability of a certain sequence is the product of the probabilities of the events in that sequence.

  P(5, non-5) = (1/6)(5/6) = 5/36

  P(non-5, 5) = (5/6)(1/6) = 5/36

The probability of obtaining either event is the sum of their individual probabilities:

  P({5, 5'} or {5', 5}) = 5/36 +5/36 = 10/36 = 5/18

__

The probability of obtaining exactly one 5 in two rolls of a die is 5/18.

Answer:

S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

    (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

    (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

    (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

    (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

    (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:

(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)

And then the probability would be:

[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]

Step-by-step explanation:

For this case w ehave the following sample space:

S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

    (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

    (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

    (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

    (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

    (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:

(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)

And then the probability would be:

[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]

Answer:

ln [2^4 * 5^3]

Step-by-step explanation:

Rewrite 4 ln 2 as ln 2^4 and 3 ln 5 as ln 5^3.

Then 4 In 2+3 In 5 = ln 2^4 + ln 5^3, which in turn becomes

ln [2^4 * 5^3]

Answer:

[tex]6-8cos2x+2cos4x[/tex]

Step-by-step explanation:

We are given that

[tex]16sin^4 x[/tex]

We can write the given expression as

[tex]16(sin^2x \times sin^2 x)[/tex]

[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]

By using the formula

[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]

[tex]4(1-cos2x)^2[/tex]

[tex]4(1-2cos2x+cos^2(2x)[/tex]

Using the identity

[tex](a-b)^2=a^2+b^2-2ab[/tex]

[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]

[tex]4-8cos2x+2+2cos4x[/tex]

[tex]6-8cos2x+2cos4x[/tex]

This is required expression.

Answer:

9.06×10 to the power of 8(8 is superscript above 10)

Answer:

9.06 x 10^8

Step-by-step explanation:

906000000 = 9.06 x 10^8

8 decimal places in

Answer:

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.

Step-by-step explanation:

The solution to the system of equations is at the point where they intercept each other.

y1 = y2

For the given equation;

y=x^2-2x and y=-2x-1

To get the where they intercept, we will equal both equations;

y=x^2-2x = -2x-1

x^2 - 2x = -2x - 1

x^2 - 2x + 2x + 1 =0

x^2 +1 = 0

x^2 = -1

x = √(-1) = i

Since the value of √(-1) is not real.

The system has no real solution.

Answer:

work shown and pictured

Answer:

x= -1  y = 1

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

At this point you can guess and try. And it seems that x = -1/2, lets check:

So, this is correct: x= -1/2

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

3x/8 - 41/5

Step-by-step explanation:

Simplify each term.

3x/8 − 9+4/5

To write −9 as a fraction with a common denominator, multiply by 5/5

3x/8−9 x 5/5 + 4/5

Combine −9 and 5/5

Combine the numerators over the common denominator.

3x/8 + −41/5

Move the negative in front of the fraction

3x/8 - 41/5

Hope this helps you

Answer:

(2x^2+1)(4x+3)

Step-by-step explanation:

8x^3 + 6x^2 + 4x+3

Split into two groups

8x^3 + 6x^2       + 4x+3

Factor out 2x^2 from the first group and 1 from the second group

2x^2( 4x+3)  +1( 4x+3)

Factor out (4x+3) from each group

(4x+3) (2x^2+1)

Rearranging the order

(2x^2+1)(4x+3)

Answer:

(2x²+1)(4x+3)

Step-by-step explanation:

Correct choice is the second one

Answer:

The probability is  [tex]P(\= X > x ) = 0.78814[/tex]

Step-by-step explanation:

From the question we are given that

     The population  mean is  [tex]\mu = 149[/tex]

     The standard deviation is  [tex]\sigma = 14[/tex]

     The random number    [tex]x = 147.81[/tex]

      The sample  size is  [tex]n = 88[/tex]

The probability that  the sample mean would be greater than [tex]P(\= X > x ) = P( \frac{ \= x - \mu }{\sigma_{\= x} } > \frac{ x - \mu }{\sigma_{\= x} } )[/tex]

Generally the z- score of this normal distribution is mathematically represented as

       [tex]Z = \frac{ \= x - \mu }{\sigma_{\= x} }[/tex]

Now

        [tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]\sigma_{\= x } = \frac{14 }{\sqrt{88} }[/tex]

         [tex]\sigma_{\= x } = 1.492[/tex]

Which implies that

         [tex]P(\= X > x ) = P( Z > \frac{ 147.81 - 149 }{ 1.492} )[/tex]

        [tex]P(\= X > x ) = P( Z > -0.80 )[/tex]

Now from the z-table  the  probability is  found to be

        [tex]P(\= X > x ) = 0.78814[/tex]

Answer:

1 2/3

Step-by-step explanation:

Well we divide 75 by 45 which is 1.6 repeating and that as a fraction is 1 2/3.

Thus,

the scale factor that relates the 2 triangles is 1 2/3.

Hope this helps :)

Step-by-step explanation:

Hi, there!!..

The format of report writing are given in points;

and start your body,

and write conclusion,

You may add comments on it.

Hope it helps....

The correct answers are Part 1: 7x + 12y  50, x,y 0; Part 2: 7; Part 3: 0: Part 4: 2 old and 3 new video games.

Step-by-step explanation:

Penny's parents gave her $50 to buy new video games.

Price of used games are $7 and new games are $12.

Let Penny buy x number of old video games and y number of new video games.

Part 1:

Total price she spent on buying the video games are 7x + 12y.

This amount should be less than or equal to the amount of money she possess. therefore 7x + 12y  50, x, y  0.

Part 2:

Maximum number of used game she can buy can be given when she spends all her money just on used games. Therefore y = 0. This implies x .

Thus the maximum number of used game she can buy is 7 where she does not buy any new game and has $1 left with her after the purchase.

Part 3:

Minimum number of new games that Penny can buy is zero. She can not buy any new games and spent all her money purchasing old games.

Part 4:

The possible combination in which she can purchase both the video games is 2 old games and 3 new games.

hope this helps

Answer:

x = {-3, -2, -1, 0}

Step-by-step explanation:

x ≤ 0

x > -4

then

x {-3, -2, -1, 0}

Answer:

CI = ( μ  -  1,64 * σ /√n ;  μ  +  1,64 * σ /√n )

Step-by-step explanation:

We assume Normal Distribution

For Confidence Interval, CI = 90 %     and  α = 10 %

α = 0,1  and  α/2  =  0,05

So  we will look for z score reciprocate to these values, at the two tails of the bell

z(α/2) = 1,64 at th right tail  and -1,64 at the left

CI = ( μ  ±  1,64 * σ /√n  )

CI = ( μ  -  1,64 * σ /√n ;  μ  +  1,64 * σ /√n )

Answer:

P(A︱B) =0.50

Step-by-step explanation:

That's the answer

Answer:

Rs. 32,000

Step-by-step explanation:

height = 4m

let length = x m

breadth = x/3 m

Area of the 4 walls = 2(length × height) + 2(breadth × height)

Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3

Area = (32x)/3 m²

1 m² = Rs. 5

The cost for an area that is (32x)/3 m²=  (32x)/3  × 5 Rs.

The cost of plastering 4 walls at Rs.5 per m² = 640

(32x)/3  × 5  = 640

(160x)/3 = 640

x = length = 12

Area =  (32x)/3 m² = (32×12)/3 = 128m²

The cost of carpeting its floor at the rate of Rs. 250/m²:

= 128m² × Rs. 250/m² = 32,000

The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000

Answer:

Dang shes rich, but what is the question?

Step-by-step explanation:

Answer: d. 83

Step-by-step explanation: 59+ 24 = 83

Answer:

D. 83 degrees

Step-by-step explanation:

Angle WXY is made up of two angles, angle WXD and angle YXD.

Therefore, angle WXY will be equal to the sum of angle WXD and YXD.

So, we can add angles WXD and YXD together to find out what the measure of angle WXY is.

<WXY= <WXD + <YXD

We know that angle WXD is 24 degrees and angle YXD is 59 degrees.

<WXD= 24

<YXD= 59

<WXY= 24+59

Add 24 and 59

<WXY=83

The measure of angle WXY is 83 degrees, so choice D is correct.

Answer:

25 students

Step-by-step explanation:

Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.

[tex] y = 0.677(35) + 1.77 [/tex]

[tex] y = 23.695 + 1.77 [/tex]

[tex] y = 25.465 [/tex]

The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.

Answer:25 students

Step-by-step explanation: