Expand (x-3)^5 using the vi al theorem and Pascal’s triangle. Show all the steps

Answer:

Step-by-step explanation:

first you need to figure out what your solving for We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

The dimension of minimum paper size would be 18 inches by 9 inches.

Let the paper size be x inches in length and y inches in width.

The length of the printed space would be x-8 inches and width would be y-4 inches.

Print area would thus be (x-8)(y-4)=50.

From this [tex]$y=4+\frac{50}{x-8}=\frac{4 x+18}{x-8}$[/tex]

Also from the same equation on simplifying, it is x y-8 y-4 x+32=50.

Since the area of the paper of size x inches by y inches is xy, let it be denoted as A.

Thus

[tex]$A-8 y-4 x=18$[/tex] Or [tex]$A=8 y+4 x+18$[/tex]

[tex]$A=\frac{32 x+144}{x-8}+4 x+18$[/tex].

For minimum paper size [tex]$\frac{d A}{d x}$[/tex] must be =0, hence,

[tex]$\frac{d A}{d x}=\frac{32(x-8)-(32 x+144)}{(x-8)^2}+4=0$[/tex]

[tex]$\frac{-400}{(x-8)^2}+4=0$[/tex]

(x-8)² = 100

x-8 = 10

[tex]$\mathrm{x}=18$[/tex], hence [tex]$\mathrm{y}=4+\frac{50}{x-8}=9$[/tex]

Dimension of minimum paper size would be 18 inches by 9 inches.

The complete question is:

You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?

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Answer:

mn²

Step-by-step explanation:

the square of n is n² and m multiplied by this is

mn²

Answer:

-4

Step-by-step explanation:

-3(x+3)+11=14

-3·x-3·3+11=14

-3x-9+11=14

-3x+2=14

-3x=14-2

-3x=12

x=12÷(-3)

x=-4

Answer

The values of a that ensures that the system has at least one solution is

a > (21/127)

Explanation

We are told to find the values of a that ensures that the system has at least one solution. The system of equations include

3 (a - 5x) < 1 + x

2 - (x/2) > 3 + 5 (x - a)

To do this, we need to solve the expressions

3 (a - 5x) < 1 + x

3a - 15x < 1 + x

We can rewrite this as

1 + x > 3a - 15x

x + 15x > 3a - 1

16x > 3a - 1

Divide both sides 16

We then solve the second one. But to do this, let's multiply through by 2

2 - (x/2) > 3 + 5 (x - a)

4 - x > 6 + 10 (x - a)

we can rewrite as

6 + 10 (x - a) < 4 - x

6 + 10x - 10a < 4 - x

10x + x < 10a - 6 + 4

11x < 10a - 2

Divide both sides by 11

The two solutions are

x > (3a/16) - (1/16)

x < (10a/11) - (2/11)

To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1

x > (3a/16) - (1/16)

-x < (-3a/16) + (1/16)

So, the system of equations become

-x < (-3a/16) + (1/16)

x < (10a/11) - (2/11)

We can then add the two equations

-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)

0 < (-3a/16) + (10a/11) + (1/16) - (2/11)

0 < -0.1875a + 0.9091a + 0.0625 - 0.1818

0 < 0.7216a - 0.1193

Rewrite

0.7216a - 0.1193 > 0

0.7216a > 0.1193

Divide both sides by 0.7216

(0.7216a/0.7216) > (0.1193/0.7216)

a > 0.1653

a > (21/127)

Hope this Helps!!!

We have the next given information:

-18.5% is the percentage of methyl alcohol

- The bottle contains 1.43 L

Now, we need to convert the percentage into a decimal.

Then 18.5% = 0.185

We need to determinate the volume in millimeters for methyl alcohol:

If 143L of solution contains 18.5% of methyl alcohol. Therefore:

The volume of methyl alcohol = 1.43 * 0.185

= 0.26455 L

Then, we need to convert Liters to milliliters:

1L ---------------------------- 1000ml

0.26455 L ------------------ x

Where x = (0.26455 L*1000ml)/1L

x =264.55ml

Answer:

8

Step-by-step explanation:

To find the perimeter, you must add the lengths of all sides.

In this question the perimeter is given, which is 63.

63 = 12 + 12 + 3x + 2x + 1 + x + 2

1. Add the numbers

63 = 12 + 12 + 3x + 2x + 1 + x + 2

12 + 12 + 1 + 2 = 27

63 = 27 + 3x + 2x + x

2. Combine Like Terms

63 = 27 + 3x + 2x + x

x = 1
3x + 2x + 1x = 6x

63 = 27 + 6x

3. Move Variable to the left

63 = 27 + 6x

63 = 6x + 27

4. Subtract 27 from both sides, the opposite of adding 27

63 = 6x + 27

63 - 27 = 6x + 27 - 27

36 = 6x

5. Divide by the same factor, the opposite of multiplying 6

36 = 6x

36/6 = 6x/6

6. Cancel out the 6s but leave the x

36/6 = 6x/6

x = 6

So, now that we know that x = 6 we can solve the expression, x + 2, to find out the length of the side BC.

6 + 2 = 8

The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]

Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]

[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]

Refine

[tex]m=-\frac{7}{2}$$[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

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The graphs of the hyperbola have zero point of intersection.

The point of intersection is the point where two or more functions meet.

The given parameters;

3x² – 4y² + 4x – 8y +4= 0

3x² + y² + 4x – 3y +4= 0

To find the points of intersection, we simply equate both equations.

So;

3x² – 4y² + 4x – 8y +4= 3x² + y² + 4x – 3y +4

Now Cancel out the common terms

y² - 3y = - 4y² - 8y

Collect like terms;

y² + 4y²=  3y - 8y

5y² = - 5y

Divide through by 5

y² = -y

Divide through by y

y = -1

Hence, the graphs of the hyperbola have zero point of intersection.

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Based on the probability of the macro-economic probabilities and the share returns, the expected share return can be found to be 10%.

The expected share return based on the economic probabilities can be found by the formula:

= (Probability of recession x Share return in recessions) + (Probability of steady state x Share return in steady state) + (Probability of boom x Share return in boom)

Solving for the expected share return gives:

= (20% x 5%) + (60% x 10%) + (20% x 15%)

= 1% + 6% + 3%

= 10%

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Answer:

[tex]1 \div 6 = 0.16 \times 100 = 16.6 percent[/tex]

that's all I know

Note ; We multiplied each of the x-values with their probabilities and obtain the sum of all. This gives the expected value.

Answer:

Straight-line percent change method example

Growth rate = (489 - 402) / 402. Absolute change = 87 (489 - 402) Growth rate = 0.2164 (87 / 402) Percent change = 21.64% (0.2164 x 100)

If the total traveling time is 1 hour 8 minutes f the average speed is 45 km/h.

This is a problem from time and distance. We can solve this equation by following a few steps.

Let's assume the car travel in the city for t minutes and the average speed is v.

According to the question, the car travel outside the city for, (68- t) minutes as 1 hour 8 minutes is equal to 68 minutes.

As per the question, Outside the city, it travels at twice its former speed v.

Now, we can form an equation,  2 (15/t) =  72/(68- t).

Let's simplify the given equation. 30/t = 72/(68- t)

Or, 72t = 30(68- t)                 [cross multiplication]

Or, 72t = 2040 - 30t

Or, 102t = 2040                    [add with +30t both sides]

Or, t = 2040/102    

Or, t = 20                              [dividing by 102 both sides]

Therefore we can conclude that the average speed ( km/h) is (15×60) / 20 = 45 km/h.

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The area of a rectangle is:

where w is the width and l is the length. Plugging the values we have and solving for w:

Therefore the width is 85 meters.

Given that line segment, GC bisects ∠FGH

I made a sketch of the angles, they are not at scale.

That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.

a) ∠FGH=86º

So, in this case, the measure of ∠FGC is 43º.

b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2

Answer:

257 kg

Step-by-step explanation:

Hello!

The mass of the cow is 257 kg.

Answer:

For f(x);

The domain is;

The range is;

Graphing those points for function A, we have;

The domain and range of the given function A is;

Graphing those points for function B, we have;

The domain and range of the given function B is;

Explanation:

Given the function in the attached image;

The function is a square function and can be written as;

The domain is;

The range is;

A.

B.

Graphing the functions;

For A;

Graphing those points for function A, we have;

The domain and range of the given function A is;

For B;

Graphing those points for function B, we have;

The domain and range of the given function B is;

The common differences of arithmetic sequence are;

For a) -3

For b) - 20

For c) - 30

For d) - 10

What is Arithmetic sequence?

An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.

Given that;

The Arithmetic sequence are;

a) 35, 32, 29, 26 ...

b) - 3, -23, - 43, -63

c) -34, -64, -94, - 124

d) - 30, - 40, - 50, -60

Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.

For Arithmetic sequence a;

Common difference = 32 - 35 = -3

And, For Arithmetic sequence b;

Common difference = - 23 - (-3)

                               = - 23 + 3

                               = - 20

For Arithmetic sequence c;

Common difference = - 64 - (-34)

                               = - 64 + 34

                               = - 30

For Arithmetic sequence d;

Common difference = - 40 - (-30)

                               = - 40 + 30

                               = - 10

Thus, The common differences of arithmetic sequence are;

For a) -3

For b) - 20

For c) - 30

For d) - 10

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The distance around a circle is known as the circumference, by definition.

The range of the function is determined as 1 ≤ M ≤ 6.5 kg.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Also we can defined a domain of a function as all the possible values that go into a function.

From the  graph the range of the function of the mass of the bucket is calculated as follows;

The minimum value of the mass of the bucket = 1

The maximum value of the mass of the bucket = 6.5 kg

The range of the function (mass, M of the bucket) = {1, 2, 3, 4, 5, 6.5 kg}

1 ≤ M ≤ 6.5 kg

Thus, the range of the function includes numbers ranging from 1 to 6.5 kg. That is  {1, 2, 3, 4, 5, 6.5 kg}.

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Volume = Area of the base * height

Area of the base = (7 * 6) / 2

Area of the base = 42/2

Area of the base = 21ft^2

Volume of the prism = 21 * 13

Volume of the prism = 273 ft^3 The thi

The circumference of a circle is found using the formula,

Where

C is the circumference

r is the radius

A circle has radius 12 cm, so its circumference is

When the radius (12 cm) is increased by a factor of 7, we mean the radius is 7 times the original, so, the new radius is

So, the circumference of this circle will be >>>>

To find how many times larger this circumference is of the previous one, we divide,

Using the circumference formula, we can find the circumference of this circle,

The original circle had a circumference of 24π

The question basically asks "how many times is the circumference of this circle compared to the circumference of the original circle?"

Of couse, it will be less than 1 since this circle is smaller than the original one.

So,

So, the scale factor is 1/4, or 0.25

Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.

What is Coordinate?

Total coordinates son number line from -7 to +7 =15

Number line ratio that has to be provided = 3:2

Let the coordinate be provided is x.

Therefore, 3x+2x=15

⇒5x=15

⇒x=3

Coordinate X

3x=3(3)=9

9th coordinate from -7 = 1 i.e. D

Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.

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To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.

Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:

We also can use the Law of Sines to solve it:

Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)

Answer:

Distance = 9 ft

Explanation:

We can represent the position of the large fish with the number -13 because it is 13ft below the surface. In the same way, we can represent the position of the smaller fish with the number -4.

Then, the distance between the fish will be the absolute value of the difference between their positions. So, the expressions that are equivalent to the distance between the fish are:

| - 13 - ( - 4) | = | - 13 + 4| = 9

or

| -4 - (- 13) | = | - 4 + 13 | = 9

Therefore the distance between the fish is 9 ft

Answer:

A - 35 copies

B - $4050

Step-by-step explanation:

A-

2300 + 70c = 4750

70c = 4750 - 2300

70c = 2450

c = 35

He sold 35 copies

B-

P = 2300 + 70(25)

P = 2300 + 1750

P = $4050

Total if he sold 25 copies: $4050

Answer:

158,760$

Step-by-step explanation:

120,000$ + 40%=168,000$-5.5%=158,760$

Answer:

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

Step-by-step explanation:

you just put the shape the opisite way