4
If f(x)=x-4 and g(x) = -2x² + 3, which polynomial is equivalent to g(f(x))?
A -2x² + 16x - 29
C-2x² - 1
B -2x²-16x +35
D -2x³ +8x² + 3x - 12

The complex number with polar coordinates (3, StartFraction 5 pi Over 6 EndFraction) is:

z = 2.598 - 1.5i

What is the complex number?

Complex numbers are the numbers that are expressed in the form of a+ib where, a, and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

This can be found by using the polar form of a complex number, which is:

z = r (cos θ + i sin θ)

where r is the magnitude or modulus of the complex number, θ is the angle in radians, and i is the imaginary unit.

In this case, we have r = 3, and θ = StartFraction 5 pi Over 6 EndFraction. Plugging these values into the equation above gives:

z = 3 (cos (StartFraction 5 pi Over 6 EndFraction) + i sin (StartFraction 5 pi Over 6 EndFraction))

z = 2.598 - 1.5i

we can round the coefficients to the nearest thousandth.

The complex number with polar coordinates (3, StartFraction 5 pi Over 6 EndFraction) is z = 2.598 - 1.5i.

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The model estimates an increase, on average of 0.86 cent per year in the price of the stamp.

What is meant by average?

Equation of best fit line is y =  -0.71 + 0.86x

y = predicted price in cents of a stamp.

x = represents the number of years since 1958.

Slope = 0.86 means rate of chance of price in cent per year slope is positive mean increase in price .

The model estimates an increase, on average of 0.86 cent per year in the price of the stamp.

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Answer:He used 6 plots of land.

explanation:

total no. of plots =10 (land was divided in 10 equal parts)

used plots = 3/5 of 10 =3/5*10 =6

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

6(x+1)=24

6x + 6 = 24

6x = 18

x = 3

Let's check

6(3 + 1) = 24

6(4) = 24

24 = 24

So, x = 3 is the correct answer.

Answer: 3

Step-by-step explanation:

Expand:

6x + 6 = 24

6x = 18

x = 3

Put the value into the equation:

6(3+1) = 24

6 * 4 = 24

24 = 24

Correct! :>

The total price of the shoes, including tax is $39.944.

Given is that a pair of shoes usually sells for $56. The shoes are 40% off, and sales tax is 6%.

We can write the total cost of shoes as -

{x} = 56 - {40% of 56} + 6% of {40% of 56}

{x} = 56 - {40/100 x 56} + 6/100 x {40/100 x 56}

{x} = 56 - 22.4 + 1.344

{x} = 56 - 21.056

{x} = 34.944

Therefore, the total price of the shoes, including tax is $39.944.

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Answer:

Alternate interior angles

Step-by-step explanation:

The two angles are in the interior of the two parallel lines on the opposite sides of the line making them alternate

Therefore, the name for these angles are:

Alternate interior angles

Answer:

2:36pm

Step-by-step explanation:

Let's say it takes x hours after leaving the station when the trains are 400 miles apart

Let's refer to the two trains using the letters A and B for easier reference

A is the train that travels on a straight track due East
B is the train that travels on a track 130° relative to the path of train A

A travels at a speed of 95 mph
B travels at a speed of 75 mph

Let the distance between the two trains be 400 miles after they have traveled an unknown [tex]x[/tex]  hours. We have to determine [tex]x[/tex]

After [tex]x[/tex] hours, train A would be [tex]95x[/tex] miles from the railroad station and train B would be [tex]75x[/tex] miles from the station

We can visualize this situation as given in the attached image.

You can see that A = 95x, B = 75x and the longest side is 400 miles

We will use the law of cosines to determine x

The Law of Cosines (also called the Cosine Rule) says:

[tex]c^2 = a^2 + b^2 - 2ab\cos (\theta)[/tex]

where [tex]\theta[/tex] is the angle opposite c i.e. the angle bounded by a and b which are the other two sides

Using the diagram as a reference we see

c = 400, a = 95x, b= 75x, [tex]\theta =[/tex] 130°

Using this information and plugging values into the cosine rule formula we get

[tex]c^2 = a^2 + b^2 -2ab \cos(\theta)\\\\c^2 = (95x)^2 + (75x)^2 - 2(95x)(75x)\cos(130^\circ)\\\\c^2 = 9025x^2 + 5625x ^2 - 14250x^2\cdot \cos(130^\circ)\\\\[/tex]

[tex]c^2 = x^2(9025 + 5625 -14250 \cdot \cos130^\circ)\\\\\\c^2 = x^2(14650 - (14250 \times -0.64278))\\[/tex]

[tex]c^2 = (14650 - (-9159.72343))x^2\\\\c^2 = (14650 + 9159.72343)x^2 \\\\c^2 \approx 23809.7234x^2\\\\[/tex]

But we know that c = 400 since that's what the question says
So we get

[tex]23809.7234x^2 = 400^2\\\\23809.7234x^2 = 160000\\\\x^2 = \dfrac{160000}{23809.7234} \approx 6.71994\\\\\\x = \sqrt{6.71994} = 2.59228\\\\\textrm{Rounding to nearest tenth}\\x = 2.6 \textrm{ hours}\\\\[/tex]

So the two trains will be 400 miles apart 2.6 hours after they have left the station.

2.6 hours = 2 hours and 36 minutes

So the trains will be 400 miles 2 hours and 36 minutes after they have left the station

Since they have left at noon, they are 400 miles apart at 2:36pm

On solving the provided question, we can say that we can form equation 2x - 4 = 120 => x = 58

What is equation?

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here, we can form equation

2x - 4 = 120

2x = 116

x = 58

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The solution to the given statement "75 less than a number x is greater than or equal to 420" is written as 75 - x ≥ 420 where x ≤ -345

75 less than a number x is greater than or equal to 420

75 - x ≥ 420

Subtract 75 from both sides

- x ≥ 420 - 75

- x ≥ 345

divide both sides by -1

x ≤ 345/-1

x ≤ -345

Therefore, the expression is given by 75 - x ≥ 420 where, x ≤ -345

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If cosine of x degrees equals three-fifths, the value of b is 7.

What is cosine ?

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. The most common trigonometric functions are sine, cosine, and tangent. The reciprocal functions are cosecant, secant, and cotangent.

In this case, we are given that cos(x) = 3/5. From this, we can use the inverse cosine function (arccos) to find the value of x in degrees. However, this alone is not enough to determine the value of b.

In the given triangle LNM, we know that angle M measures 90 degrees and angle L measures x degrees. We also know that side LM measures 3b units and LN measures 20 units.

Using the Pythagorean theorem, we know that the length of MN, which is the hypotenuse, can be found by:

MN^2 = LM^2 + LN^2

We also know that

cos(x) = LM / MN

Therefore, we have:

3/5 = (3b) / (sqrt(3b^2 + 20^2))

b = 7

So , If cosine of x degrees equals three-fifths, the value of b is 7.

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The increase in price represents linear growth and the constant growth rate or growth factor per minute = 0.65 per min.

A linear growth is defined as the type of growth that is always at the same rate while exponential growth is the type of growth that increases with time.

From the data recorded by the student, the amount collected every 10 minutes by the driver = $6.5

If 10 minutes = 6.5

1 minute = X

Make X the subject of formula;

X = 6.5/10

X = 0.65

Therefore, the growth rate per minute = 0.65/min

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Answer:

2a(3a + 8)

Step-by-step explanation:

Combine like terms

6a2 + 15 + a

6a2 + 16a

interest rate- 4%, monthly payment- $275.96, total payment- $16,556.51

interest rate- 6%, monthly payment- $292.65, total payment- $17,359.22

interest rate- 8%, monthly payment- $310.74, total payment- $18,244.54

interest rate- 10%, monthly payment- $329.51, total payment- $19,370.40

What does money interest mean?

You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.

To calculate the monthly payment and total payment, you can use the following formulas:

Monthly Payment: (loan amount * interest rate) / (1 - (1 + interest rate)^-n)

Total Payment: Monthly Payment * number of payments

Where the loan amount is 14450, the interest rate is the percentage given, n is the number of payments (12*5) and the interest is compounded monthly.

Keep in mind that all the values are approximate, and these calculations are based on the assumption that all payments are made on time and there are no additional charges or fees. It's important to check with the lender to get exact numbers and terms of the loan.

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The equivalent expression for given complex number i^55 is -i.

What are complex numbers?

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

An imaginary number is usually represented by ‘i’ or ‘j’, which is equal to √-1. Therefore, the square of the imaginary number gives a negative value.

Since, i = √-1, so, i^2 = -1

Now,

complex number i^55=(i^4)^13(i^2*i)

=1^13(i^2*i)     (i^4=1)

=1(-1*i)             (i^2=-1)

Hence,

i^55=-i

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Answer:

22.48 km/h

Step-by-step explanation:

it took James 45 minutes to cycle 15 km, sInce he was traveling at 20 km/h, which was worked out by dividing 50 by 2.5.

since Peter left 5 minutes later, it took 5 minutes less, so 40 minutes. 40 minutes as a fraction is 0.667.

15 divided by 0.667 is 22.48 km/h

Answer:22

Step-by-step explanation:

what the guy before said

The major difference between asymmetrical model and symmetrical model  is that one deal with the public with help of organization and other with interacting with people directly.

The asymmetrical model offers a more "scientifically convincing" method of reaching out to important audiences. Here, content makers carry out research to better comprehend the attitudes and actions of the target audience. It is still asymmetrical or unbalanced because this paradigm uses persuasive communication to the organization's advantage rather than the audiences. 

According to the symmetrical model, a public relations professional should function more as a bridge between an organization and its target audiences than as a persuasive force. Practitioners operate as negotiators in this situation and use communication to make sure that everyone involved, not just the company they work for, benefits.

Asymmetric Digital Subscriber Line (ADSL) is an example of asymmetric communications and when a company uses surveying as an IMC tool, it is initiating two-way symmetrical communication with its audiences.

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The sum of the areas of the room will be → S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}.

Given are the area of each separate room.

Assume the sum of the areas of the room will be {S}. Let the dimensions of the room be -

[tex]$L_{i},\; B_{i},\; H_{i}[/tex]

where {i} is the room number.

Then we can write the sum of the areas of the room as -

S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}

Therefore, the sum of the areas of the room will be -

S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}

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If the points be, A(3, 2), B(-2, -3) and C(2, 3) then the given triangle is a right angled triangle.

The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two arms of the right angle.

By their angles, triangles can also be categorized. There are three sharp angles in a triangle (less than 90 degrees). There is a right angle and two acute angles in a right triangle. In addition, an acute triangle has two angles that are equal in size to the obtuse angle (which is more than 90 degrees).

Let the given points be, A(3, 2), B(-2, -3) and C(2, 3).

Therefore,

[tex]$& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2} \text { units } \\[/tex]

[tex]$& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13} \text { units } \\[/tex]

[tex]$& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2} \text { units }[/tex]

Now, we can see that,}

[tex]$& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]$& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

The complete question is:

Do the points (3, 2), (-2, -3) and (2, 3) form a triangle? If so, name the type.

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Answer:

43.70%

Step-by-step explanation:

Expressions that are equivalent to 7(2 - 3n) are 14 - 21n and (2 - 3n). 7

1. 14 - 21n is equivalent to 7(2 - 3n) because we can distribute the 7 to the 2 and -3n in the expression, 7(2 - 3n) = 72 - 73n = 14 - 21n.

2. (2 - 3n). 7 is equivalent to 7(2 - 3n) because it can be changed by the distributive property, (2 - 3n). 7 = 2. 7 - 3n. 7 = 14 - 21n

All the other expressions are not equivalent to 7(2 - 3n) because they don't follow the distributive property and some of them don't have the same coefficients.The distributive property is a mathematical property that states that for any two numbers a and b, and for any third number c, the following equation holds true: a(b + c) = ab + ac. This property is also known as the distributive law of multiplication over addition. The distributive property is used to simplify expressions by breaking them down into smaller parts that can be calculated separately and then combined again.

Therefore, Expressions that are equivalent to 7(2 - 3n) are 14 - 21n and (2 - 3n). 7

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A jar of cleaning fluid weights 24 ounces , remaining,The jar weigh is 1/2 kg ounces.

To subtract is to take something away from a group or several different items. The number of items in the group decreases or gets less as we subtract. A subtraction issue has three components: the minuend, subtrahend, and difference.

A jar of cleaning fluid weights 24 ounces (oz.). When one half of the cleaning fluid is used up the jar and remaining fluid weigh 17 ounces.

The jar weigh

24 ounces

17 ounces

so,

24 ounces - 17 ounces = 7  ounces

A jar of cleaning fluid weights 24 ounces , remaining,The jar weigh is 1/2 ounces.

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Answer:x>12

Step-by-step explanation:

The sum of angles in a hexagon is 720⁰. The missing interior angles in Noah's list is 110⁰  

The sum of interior angles of a triangle is equal to 180⁰. The sum of interior angles of a polygon is equal to:

sum of interior angles of a polygon = number of triangles x 180⁰

A hexagon consists of 4 triangles, hence, the sum of interior angles in a hexagon = 4 x 180⁰ = 720⁰

In general, we can find the sum of interior angles in a polygon using the formula:

(n - 2) x 180⁰

Where n = number of sides

In the given problem, let's denote the missing interior angle as q. The sum of interior angles are:

80⁰ + 85⁰ + 95⁰ + 105⁰ + 120⁰ + 125⁰ + q = 720⁰

610⁰ + q = 720⁰

q = 720⁰ - 610⁰ =  110⁰  

The picture in your question is missing. Most likely it was like on the attached picture.

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Answer:

20 goals

Step-by-step explanation:

The percentage 125 is over 100. So it's going to be 125/100 ×16. so the answer is 20

To find the distance between two points in a coordinate plane, we can use the Pythagorean theorem.

The distance between (2, 4) and (5, -2) can be found using the following steps:

Find the difference in the x-coordinates: 5 - 2 = 3

Find the difference in the y-coordinates: -2 - 4 = -6

Use the Pythagorean theorem to find the distance: d = √(3^2 + (-6)^2) = √(9 + 36) = √45

So the distance between (2, 4) and (5, -2) is √45.

Answer:

Step-by-step explanation:

kk gworl

This depends on the mode of transport. If travelling by car, it could take 3 to 4 hours. If travelling by bus, it could take 5 to 6 hours. If travelling by train, it could take 4 to 5 hours.

1. Determine the mode of transport.

2. Calculate the average speed of the transport.

3. Calculate the total time by dividing the total distance by the average speed.

4. Determine the estimated time for the journey.

The time it takes to travel 250km depends on the mode of transport being used. For example, travelling by car would require an average speed of around 80km/h and would take approximately 3 to 4 hours. Travelling by bus would require an average speed of around 50km/h and would take 5 to 6 hours. Travelling by train would require an average speed of around 70km/h and would take around 4 to 5 hours. Calculating the total time for the journey is as simple as dividing the total distance by the average speed. Once the average speed and total distance are known, the total time for the journey can easily be determined.

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The probability of A having more heads than B depends on the number of coins each has, and which is P(A>B) = ∑i=0,n2 (n1 choose i)[tex]1/2^{n1+n2}[/tex]

If both players have the same number of coins, the probability of A having more heads than B is 0.5. If A has more coins than B, then the probability of A having more heads than B is greater than 0.5.

Conversely, if B has more coins than A, then the probability of A having more heads than B is less than 0.5. The exact probability can be calculated with binomial coefficients.

Let n1 be the number of coins A has and n2 be the number of coins B has. The probability of A having more heads than B is then given by: P(A>B) = ∑i=0,n2 (n1 choose i)[tex]1/2^{n1+n2}[/tex]

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