For the function N(t)=4|t+5|+3, evaluate N(2).

Perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]

What do you mean by perimeter of polygon?

A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface.

The total of a polygon's sides is referred to as the polygon's perimeter. A regular polygon's perimeter is provided by if it is one.

Regular polygon perimeter equals (number of sides) x (length of polygon's sides) units.

Given sides of the polygon are 4y , [tex]y^{2} , 4x^{2} -y^{2},3x,x^{2} +y^{2}[/tex]

Perimeter of the polygon is the sum of all sides of the polygon

Perimeter of the polygon = [tex]4y+4x^{2} -y^{2}+3x+x^{2} +y^{2} +y^{2}[/tex]

                                          = [tex]5x^{2} +y^{2}+3x+4y[/tex]

Therefore, perimeter of the polygon is [tex]5x^{2} +y^{2}+3x+4y[/tex]

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For the given expression -21 is not a irrational number.

What is irrational number?

In mathematics, all real numbers that are not rational are referred to as irrational numbers. Irrational numbers can't be expressed as the ratio of two integers, in other words.

Any real number that cannot be expressed as the ratio of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, there is no integer or fraction that equals the square root of 2.

Consider the given expression,

(-14) + (-7)

Solving this, we get

(-14) + (-7) = -14 - 7 = -21

Here 21 can be written in the form p/q.

⇒ -21 = -21/1

So, -21 is a rational number.

Hence, -21 is not a irrational number.

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Answer:

8

Step-by-step explanation:

72 ÷ 9 = 8

Answer:

8

Step-by-step explanation:

72 divided by 9 is 8

Answer: the correct anserw is A.!

Step-by-step explanation:

Answer:

15/8

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

The area of the parallelogram will be equal to 28 units squared. Hence, option B is correct.

The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.

As per the data obtained from the given values,

Length of base (b) of parallelogram = 7

Length of height (h) of parallelogram = 4

Use the formula of area (A) of a parallelogram,

[tex]Area = Base*Height[/tex]

A = 7 × 4

A = 28 units squared.

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Answer: i think it's 942,480

Step-by-step explanation:

i just multiplied all of the numbers but i'm probably wrong srry

Answer:

7986m^2

Step-by-step explanation:

140-102=38

area of triangle:

(38*66)/2=1254m^2

area of rectangle:

66*102=6732m^2

total area:

1254+6732=7986m^2

$92000 is the James’s current equity in the home.

Equity, also known as shareholders' equity or owners' equity for privately held businesses, is the sum of money that, in the event of a company's liquidation, would be distributed to its shareholders after all of the company's assets have been sold and its debt has been fully repaid.

In an acquisition scenario, it is equal to the sum of the company's sales less any liabilities that were not transferred to the new owner.

A company's book value can also be represented by shareholder equity. A payment-in-kind arrangement may occasionally include equity. Furthermore, it represents the proportionate ownership of a company's shares.

James’s current equity =  (180000 × 1.25) - ((180000 × 0.8) -11000)

                                       = 92000

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The predicted height for someone with a femur length of 55 cm is of:

175 cm.

The linear function in this problem is obtained using the point-slope format, which is given as follows:

y - y' = m(x - x').

In which:

From the image given at the end of the answer, two points on the line are given as follows:

(35, 139) and (40, 151).

Given two points the slope is calculated as the change in y divided by the change in x, hence:

m = (151 - 139)/(40 - 35) = 2.4.

Considering the first point, the definition of the line is given as follows:

y - 139 = 2.4(x - 40).

The predicted height for someone with a femur length of 55 cm is y when x = 55, hence:

y - 139 = 2.4(x - 40).

y - 139 = 2.4(55 - 40)

y = 175 cm.

The graph of the linear function is given by the image shown at the end of the answer.

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1) The annual decay rate of the exponential function is given as follows: 12.94%.

2) The number of people who started the rumor is of 10.

3) The number of people who will have heard the rumor after 3 days is given as follows: 96 people.

For item 1, the format of the exponential function is given as follows:

A(t) = A(0)(1 - r)^t.

In which r represents the annual decay rate.

The half-life of Radium-228 is 5.75 years, hence:

A(5.75) = 0.5A(0).

Thus the annual decay rate of the exponential function is given as follows:

0.5A(0) = A(0)(1 - r)^5.

(1 - r)^5 = 0.5

Applying the fifth root to both sides:

1 - r = (0.5)^(1/5)

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294 = 12.94%.

Then for items 2 and 3 we just obtain the numeric values.

The number of people who started the rumor is N(0), hence:

N(0) = 600/(1 + 59e^(-0.7 x 0)) = 600/60 = 10 people.

The number of people who heart the rumor after three days is N(3), hence:

N(3) = 700/(1 + 69e^(-0.8 x 3)) = 96 people.

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Jack spend $15 on sweets

Jack spend $35 on magazines

Jack saves $50

Given,

Jack spends 15 % of his pocket money on sweets and 35 % on magazines.

Jack save the rest ; 100 - (15 + 35) = 100 - 50 = 50%

Here,

If Jack has a pocket money of $100

The money he spends on sweets = 15% of 100 = $15

The money he spends on magazines = 35% of 100 = $35

Then,

The money he saves = 50% of 100 = $50

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Answer:

3 cats are orange and The other 1 is not

Because

the slope of the line is zero, as change in y cordintae is 0.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

In the given line in the graph, the change in y coordinate is 0.

We know that slope = change in y / change in x

As the change in y coordinate is 0.

The slope of the line will be zero.

Hence, the slope of the line is zero.

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[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

What do you mean by integration?

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a collection of little data that cannot be measured separately, the integral is calculated.

The idea of integration has evolved to address the following issues:

once the derivatives of the problem function have been determined.

to determine the region enclosed by a function's graph under specific restrictions.

Given function f(x) = [tex]\frac{4}{x^2+2}[/tex]

[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex]

Substitute u = [tex]\frac{x}{\sqrt{2} }[/tex]

⇒ [tex]\frac{du}{dx} =\frac{1}{\sqrt{2} }[/tex]

⇒ dx = [tex]\sqrt{2}[/tex] du

= [tex]\frac{2^{\frac{5}{2}} }{2u^2+2}du[/tex]

On simplifying

= [tex]2^{\frac{3}{2} }[/tex][tex]\int\limits\frac{1}{u^2+1} \, du[/tex] .........(1)

Now  [tex]\int\limits\frac{1}{u^2+1} \, du[/tex] = [tex]tan^{-1} (u)[/tex]

Substitute this value in equation (1)

= [tex]2^{\frac{3}{2} }tan^{-1}(u)[/tex]

Substitute the value of u here

= [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex]

Therefore, [tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] =  [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.

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Answer:

20

Step-by-step explanation:

A parallelogram has 4 sides.

Each pair of opposite sides is congruent.

To find the perimeter, find the length of 2 adjacent sides and multiply by 2.

Length of side (0, 0) to (5, 0) is 5.

Length of side (5, 0) to (8, 4) is the hypotenuse of a right triangle with legs of lengths 3 and 4.

a² + b² = c²

3² + 4² = c²

c² = 9 + 16

c² = 25

c = √25

c = 5

The hypotenuse measures 5 units.

perimeter = 2(5 + 5)

perimeter = 2(10)

perimeter = 20

the breadth of the river is [tex]20\sqrt{3} m[/tex] or 34.614 m

as per given in the question ,

the length of the tower (l) = 20m

the angle of elevation of the top of the tower from the opposite bank

[tex]\theta[/tex] = [tex]30^{0}[/tex]

the breadth of the river should be found

let the breadth of the river be x,

to find breadth,

[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}[/tex]                        ----(1)

the opposite side will be the length of the pole i.e, 20m

the adjacent side will be the breadth of the river i.e, x

now substitute all the values in equation (1)

[tex]tan\theta=\frac{20}{x}[/tex]

=> [tex]tan 30^0= \frac{20}{x}[/tex]             ( the value of [tex]tan30^0 =\frac{1}{\sqrt{3} }[/tex] )

=> [tex]\frac{1}{\sqrt{3} } =\frac{20}{x}[/tex]

=> [tex]x=20\sqrt{3}m[/tex]

so,  

     the breadth of the river is [tex]20\sqrt{3} m[/tex] or we can write 34.614m

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Answer:

s = 9

Step-by-step explanation:

calculate the slope m through the 2 points using the slope formula and equate to - 5

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )

m = [tex]\frac{-7-3}{s-7}[/tex] = [tex]\frac{-10}{s-7}[/tex]

equate m to slope of - 5

[tex]\frac{-10}{s-7}[/tex] = - 5 ← multiply both sides by s - 7

- 10 = - 5(s - 7) ← divide both sides by - 5

2 = s - 7 ( add 7 to both sides )

9 = s

Answer: the slope of the line is 2 or 2/1

Step-by-step explanation:

Answer:

A reflection over the x axis

Step-by-step explanation:

x is the horizontal line we are reflecting one across it to get the other

Answer:

[tex]\dfrac{2(x+4)}{x}[/tex]    or     [tex]2 + \dfrac{8}{x}[/tex]

Step-by-step explanation:

Rewrite the problem as a fraction.

[tex]\dfrac{6(x+4)^2}{3x(x+4)}[/tex]

Then, represent the squared term on the top as two values to make it easier to cancel.

[tex]\dfrac{6(x+4)(x+4)}{3x(x+4)}[/tex]

Now, cancel an x+4 from the top and bottom.

[tex]\dfrac{6(x+4)}{3x}[/tex]

Finally, divide the numerator and denominator by 3.

[tex]\dfrac{2(x+4)}{x}[/tex]     or     [tex]2 + \dfrac{8}{x}[/tex]

[tex]\bf{\dfrac{6(x+4)2}{3x(x+4)} \iff \ Eliminate \ (x+4).}\\ \\ \bf{That\:is, isolating\:the \ common \ factor \ \dfrac{\not{6}\times2 }{\not{3}x} \ \--\to\dfrac{2\times2}{x}=\dfrac{4}{x} } \\ \\ \boldsymbol{\sf{\dfrac{4}{x} }}\bf{\iff}\boxed{\boxed{\bf{Answer}}}[/tex]

The answer to the Question based on Federal Income Tax return is Yes

What is Federal Income Tax Returm?

It is a kind of tax that people have to pay to government.

Federal Income tax has some of its special conditions also and so is suggested by its name

Solution:

As MJF husband is aged 66 and his Gross income is 25200$ and this amount of money is not very less but infact very high hence there is fixed percentage of tax decided by government per fixed amount of money and MJF husband has to pay that amount of tax to government

Hence answer to the Question is Yes

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The equations that represent a line passing through the point (–2, 5) with a slope of 4 are:

Equation of the line of slope = 4 passing through point (-2, 5) is calculated using the point slope formula which is

(y - y') = m(x - x')

y' = 5

slope, m = 4

x' = -2

substituting the known variables and solving

(y - 5) = 4(x - ( -2 ) )

y -5 = 4( x + 2)

y - 5 = 4x + 8

y = 4x + 8 + 5

y = 4x + 13

the equation of the line with a slope of 4 and passing through point (-2, 5) is  y = 4x + 13

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Answer:

Step-by-step explanation:

0.15625

Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

The equation of a line with slope [tex]m[/tex] and [tex]y[/tex]-intercept [tex](0,b)[/tex] is [tex]y=mx+b[/tex].

Answer:

Step-by-step explanation:

First question. Answer is

Equivalent expression to the given expression [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to

Option d. ( 7 /5)² ( 1/3)³.

As given in the question,

Given expression is equal to :

[ ( 5/7)² ( 1/3)⁻³]⁻¹

Apply law of exponent power to power we get,

( mᵃ nᵇ )ˣ =  (m)ᵃˣ × (n )ᵇˣ

( x /y)⁻ᵃ = ( y /x)ᵃ

Here m = 5/ 7, n = 1/3 , a = 2 , b = -3 and x = -1

Equivalent expression of the given expression is:

[ ( 5/7)² ( 1/3)⁻³]⁻¹

= ( 5 / 7 )^(2 × -1) ( 1 / 3)^(-3 × -1)

= ( 5 / 7 )⁻² ( 1 / 3)³

= ( 7 / 5 )²× ( 1 / 3)³

Therefore , equivalent expression of [ ( 5/7)² ( 1/3)⁻³]⁻¹  is equal to the

option d.( 7 /5)² ( 1/3)³.

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Answer:

14 gallons

Step-by-step explanation:

456 - 28.5g = 5

28.5g =399

G=14

The age of Lance and Chad are 7 years and 20 years respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let age of Lance's is  = L

Age of Chad's = C

Given that The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age.

The system of equations that represents this situation is;

L + c = 27

C - 6 = 2L

2L - c = -6------ (1)

Therefore,

⇒ ( 2L - c ) + (L + c) = 21

⇒ 3L = 21------- (2)

L = 7

C = 20

Therefore the age of each person;

7 years and 20 years

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The domain of s = 13.5h is (0, 1, 2, 3, 4).

The range of s = 13.5h is (0, 13.5, 27, 40.5, 54).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

s = 13.5h

For h = 0,

s = 0

For h = 1,

s = 13.5

For h = 2,

s = 27

For h = 3,

s = 40.5

For h = 4,

s = 54

Thus,

The domain is (0, 1, 2, 3, 4).

The range is (0, 13.5, 27, 40.5, 54).

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