someone help me with number 8

I assume [tex]m,n[/tex] are integers to avoid (ir)rational powers of -1.

If [tex]m,n[/tex] are both even, or if [tex]m=n[/tex], then

[tex]\displaystyle \lim_{n\to-1} \frac{x^m+1}{x^n+1} = \frac{1+1}{1+1} = 1[/tex]

If [tex]m,n[/tex] are both odd and [tex]m\neq n[/tex], then we can factorize

[tex]\dfrac{x^m+1}{x^n+1} = \dfrac{(x+1)(x^{m-1} - x^{m-2} + \cdots - x + 1)}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)}[/tex]

Note that there are [tex]m[/tex] terms in the numerator and [tex]n[/tex] terms in the denominator.

In the limit, the factors of [tex]x+1[/tex] cancel and

[tex]\displaystyle \lim_{x\to-1} \frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^{m-1} - x^{m-2} + \cdots - x + 1}{x^{n-1}-x^{n-2}+\cdots-x+1} \\\\ ~~~~~~~~~~~~~~~~~~= \dfrac{1-(-1)+1-(-1)+\cdots-(-1)+1}{1-(-1)+1-(-1)+\cdots-(-1)+1} \\\\ ~~~~~~~~~~~~~~~~~~=\frac{1+1+\cdots+1}{1+1+\cdots+1} = \dfrac mn[/tex]

If [tex]m[/tex] is even and [tex]n[/tex] is odd, then we can only factorize the denominator and the discontinuity at [tex]x=-1[/tex] is nonremovable, so

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^m+1}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)} \\\\ ~~~~~~~~~~~~~~~~~~= \frac2m \lim_{x\to-1} \frac1{x+1}[/tex]

which does not exist.

If [tex]m[/tex] is odd and [tex]n[/tex] is even, then we can factorize the numerator so that

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{(x+1)(x^{m-1}-x^{m-2} +\cdots -x+1)}{x^n+1} \\\\ ~~~~~~~~~~~~~~~~~~= \frac{0m}2 = 0[/tex]

Answer:

$1317.14

Step-by-step explanation:

compounded continuously formula is A=Pe^rt

given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.

plugging everything in...

1500=P (e)^2x0.065

P=1500/1.139

P=1317.14

Area

Answer:

1725 ft²

Step-by-step explanation:

The formula to find the area of a trapezoid is :

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Let us solve it now.

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30

Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30

Area = [tex]\frac{1}{2}[/tex] × 3450

Area = 1725 ft²

Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

For a similar question on slope-intercept form, do check out the following!

The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.

If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to

[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]

Expand the right side and collect all the coefficients.

[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]

From the z and constant terms, we have

[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]

From the second equation, we get

[tex]B^2 = 16[/tex]

B = ± 4

Then 4+(A+1)i = ± 8

(A + 1)i = 4 or (A + 1)i = -12

Since [tex]$\frac{1}{i} = -i[/tex], we have

[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]

A+1 = -4i or A+1 = 12i

A = -1-4i or A = -1+12i

Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.

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In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.

In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.

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Answer:

the answer is 46.47937775048613

The solution to the given polynomial in their degree are:

2a + 4a³ - 5a² - 1

= 4a³ - 5a² + 2a - 1

The leading coefficient is 4a³

4z - 2z² - 5z⁴

= -5z⁴ - 2z² + 4z

The leading coefficient is -5z⁴

(-3d² - 8 + 2d) + (4d - 12 + d²)

= -3d² - 8 + 2d + 4d - 12 + d²

= -2d² + 6d - 20

(y + 5) + (2y + 4y² - 2)

= y + 5 + 2y + 4y² - 2

= 4y² + 3y + 3

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Answer:

Step-by-step explanation:

8x + 2(x - 7) = 7x + 3x - 14

8x + 2x - 14 = 7x + 3x - 14                 Distributive property.

10x - 14 = 10x - 14                              Combine the like terms.

-14 = -14                                             Subtraction.

0 = 0                                                  Addition.

Since the statement 0 = 0 is true regardless of the value of x, there is infinitely many solutions.

The first ten terms of the sequence are 1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689.

The n-th term of the sequence is aₙ ₊ ₁ = (aₙ + 1) · n.

A sequence is a set of elements generated by at least one condition, usually an equation. In this case, the sequence is generated by a recurrence formula:

a₁ = 1, aₙ ₊ ₁ = (aₙ + 1) · n        (1)

The first ten terms of the sequence are:

n = 1

a₂ = (a₁ + 1) · 1

a₂ = 2

n = 2

a₃ = (a₂ + 2) · 2

a₃ = 4 · 2

a₃ = 8

n = 3

a₄ = (a₃ + 3) · 3

a₄ = 11 · 3

a₄ = 33

n = 4

a₅ = (a₄ + 4) · 4

a₅ = 37 · 4

a₅ = 148

n = 5

a₆ = (a₅ + 5) · 5

a₆ = 153 · 5

a₆ = 765

n = 6

a₇ = (a₆ + 6) · 6

a₇ = (765 + 6) · 6

a₇ = 4626

n = 7

a₈ = (a₇ + 7) · 7

a₈ = 4633 · 7

a₈ = 32431

n = 8

a₉ = (a₈ + 8) · 8

a₉ = 32439 · 8

a₉ = 259512

n = 9

a₁₀ = (a₁₀ + 9) · 9

a₁₀ = 259521 · 9

a₁₀ = 2335689

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Answer:

males = 7

females = 43

Step-by-step explanation:

whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".

You can solve this equation most easily algebraically. For example:

Number of males = x

number of females = y

the question states that the total number of people = 50

therefore we can say that the total number of males (x) + the total number of females (y) = 50 people

therefore: x + y = 50

similarly, the question says that the number of males (x) + 36 = the total number of females (y)

therefore: x + 36 = y

we now have two equations:

x + y = 50

x + 36 = y

whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.

focusing on the second equation: x + 36 = y

we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.

x + 36 + x = y + x

now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.

our two equations:

x + 36 + x = y + x

x + y = 50

therefore:

x + 36 + x = 50

for the sake of clarity, we can combine like terms...

x + x = 2x

therefore:

x + 36 + x = 50

2x + 36 = 50

solve for x by subtracting 36 from both sides, then dividing both sides by 2

2x + 36 - 36 = 50 - 36

2x = 14

2x / 2 = 14 / 2

x = 7

now remember:

Number of males = 7 (we now know x = 7)

now that we've solved for x, we can go back to our original equation:

x + 36 = y

and substitute x...

7 + 36 = y

43 = y

Now remember:

Number of females = 43 (we now know y = 43)

therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.

hope this helps :)

The distance d is 9 ft and the height is 12ft.

Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.

The height is one cathetus and the distance is the other catheti.

Let's define:

We know that the height of the tower is 3 ft larger than the distance, then:

h = d + 3ft

Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Then:

[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]

Now we can solve this equation for d:

[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]

Then the solutions are:

[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]

We only take the positive solution:

d = (-3ft + 21ft)/2 = 9ft

And the height is 3 ft more than that, so:

h = 9ft + 3ft = 12ft

The distance d is 9 ft and the height is 12ft.

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There are 60 questions on the test

Total number of questions = 42

Percentage equivalent= 70%

Let the total number of questions in the test be represented by x

42 = 70% of x

[tex]42=\frac{70}{100} \times x[/tex]

42 = 0.7x

Divide both sides by 0.7

42/0.7  =  0.7x/0.7

x  =  60

Therefore, there are 60 questions on the test

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The roots of the equation is x = 4.56 OR x = 0.44

From the question, we are to determine the roots of the given equation

The given equation is

x² -5x +2 = 0

Using the formula method,

[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

In the given equation,

a = 1, b = -5, c = 2

Putting the values into the formula,

[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]

[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]

[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]

[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]

[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]

x = 4.56 OR x = 0.44

Hence, the roots of the equation is x = 4.56 OR x = 0.44

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h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.

Given,

h(x) = -0.017x² + 1.08x + 5.8

Put h = 24,

h(24) = -0.017(24)² + 1.08(24) + 5.8

h(24) = -9.792 + 25.92 + 5.8

h(24) = 21.93

The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.

Vertical intercept, x = 0

h(0) = -0.017(0)² + 1.08(0) + 5.8

h(0) = 5.8

The height of the shot put above the ground is 5.8 feet at the start.

vertex coordinates,

(h,k) = [(-b/2a),-(b²- 4ac)/4a]

(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]

(h,k) = [(1.08/0.034),(1.5608)/0.068)]

(h,k) = (31.76,22.95)

The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.

Put h(x) = 0,

-0.017x² + 1.08x + 5.8 = 0

Use quadratic formula for solving x,

x = (-b±√b²- 4ac)/2a

Here a = -0.017, b=1.08, c=5.8

x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)

x = [-1.08±√1.5608]/-0.034

x =  [-1.08-1.2493]/-0.034 and x =  [-1.08+1.2493]/-0.034

x = 68.509 and x = - 4.98

Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²

                                                                        = √73.49²

                                                                        = 73.49 feet              

Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.

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I would be better to purchase whole onions at $1.99 per pound, and cut them yourself

Number of bowls = 50

Weight of each bowl = 8

Total weight of the onion soup = 8 x 50 = 400 ounces

Note that:

1 pound = 16 ounces

Total weight in pounds = 400/16

Total weight in pounds = 25 pounds

If you buy the whole onions and purchase at $1.99 per pound

Total cost = 25 x 1.99 = $49.75

If you purchase pre-sliced onions at $2.99 per pound

Total cost = 25 x $2.99 = $74.75

Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice

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Answer:

(3x3+3)*2

Step-by-step explanation:

The additional information needed to calculate ORS are the measures of SPR and PSR

The lines are given as:

Lines a, b, c and d

The special names of the lines are as follows:

The angle is given as:

OPS= 139 degrees

Start by calculating SPR using

SPR = 180- 139

SPR = 41 degrees

So, the additional information needed to calculate ORS are the measures of SPR and PSR

The theorem 65 is not stated.

So, the question cannot be answered

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Answer: 125 pounds

Step-by-step explanation:

Let's first represent the weight of the black rhinoceros and chimpanzee with variables. We will assign r for the rhinoceros and c for the chimpanzee.

In the question, we were given that the weight for a black rhinoceros is 18 times as much as an average-size chimpanzee. This makes 18 times the chimpanzee's weight equal to the rhinoceros' weight.

Let's put this into an equation.

[tex]r=18*c[/tex]

Now, let's put in the values we know to find the weight of the chimpanzee (i.e., c). We know the weight of a rhinoceros (represented by r) is 2250 pounds, so we can replace it for r in the equation.

[tex]2250=18*c[/tex]

To solve this equation, we can divide both sides by 18 to get c by itself and know what it's value is.

[tex]\frac{2250}{18}=\frac{18*c}{18}[/tex]

We can remove the [tex]\frac{18}{18}[/tex] from the right side to be left with c. We can also divide 2250 by 8 to get the weight of an average-size chimpanzee.

[tex]c=\frac{2250}{18}\\ c=125[/tex]

Hence, an average-size chimpanzee weighs 125 pounds.

The conjecture we can use is that the sum of all even numbers is an even number.

We are given the sum of two even numbers as follows;

12 = 4 + 8

26 = 6 + 20

48 = 16 + 32

72 = 24 + 48

88 = 36 x 52

From the above, we see that they are all even numbers and as such the conjecture we can use is that the sum of all even numbers is an even number.

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The two bottom graphs demonstrate translations.

We will have a translation only if:

The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.

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Answer: x>2

Step-by-step explanation:

[tex]8(x-1) > 12-2x\\\\8x-8 > 12-2x\\\\10x-8 > 12\\\\10x > 20\\\\x > 2[/tex]

The answer is d.

Finding area of ABCD :

    2. Apply formula to find area

Finding area of GHIA :

Finding area of DEFG :

Now, let's see whether is true.

∴ Hence, it is proved √

If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.

We are required to find the monthly income in 1996.

We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.

Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month

=2000+175000*1/100+3000

=2000+1750+3000

=Rs.6750

Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

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The dot product of the D⋅n is 32.

According to the statement

We have given the value of n vector and d matrix and we have to find the dot product of these.

So, For this purpose,

The given values:

n = {-2,-1} and D = [−4423].

The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.

So, The d matrix become

[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]

Now solve it with the help of multiplication then the matrix become

D = (-12, -8)

and n = {-2,-1}

Now multiply both terms with the dot product.

So, the dot product of the both terms will become

D.n = 24 +8

Then

The output of the dot product of both terms is 32.

So, The dot product of the D⋅n is 32.

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I assume you're asked to compute

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]

using both of the substitutions provided.

With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

With [tex]u=\sqrt{x-4}[/tex], we have

[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]

and [tex]2u\,du=dx[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du  \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C  \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

Answer:

x=75 degrees

Step-by-step explanation:

since the shape is quadrilateral, all the angles added together should equal 360 degrees so you use 360 to subtract all the given angles on the shape and you can find X

360-131-107-47=75

Answer: [tex](-2, 5)[/tex]

Step-by-step explanation:

The graphs are shown in the attached image.

The solution is where they intersect.

The solution to the system of equations is x = -2 and y = 5.

i.e

The solution is = (-2, 5)

We have,

To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."

So, you'll have:

(-7/2)x - 2 = -2x + 1

Now, let's solve for x:

Step 1:

Get rid of the fractions by multiplying both sides by 2:

2 * ((-7/2)x - 2) = 2 * (-2x + 1)

This simplifies to:

-7x - 4 = -4x + 2

Step 2:

Isolate the x terms on one side of the equation.

Let's move the -4x to the left side by adding 4x to both sides:

-7x - 4 + 4x = -4x + 4x + 2

This simplifies to:

-3x - 4 = 2

Step 3:

Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:

-3x - 4 + 4 = 2 + 4

This simplifies to:

-3x = 6

Step 4:

Finally, solve for x by dividing both sides by -3:

x = 6 / -3

x = -2

Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.

Let's use the first equation y = (-7/2)x - 2:

y = (-7/2) * (-2) - 2

y = 7 - 2

y = 5

Thus,

The solution to the system of equations is x = -2 and y = 5.

i.e

(-2, 5)

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