when asked to rewrite 27+45 as a product of the GCF and a sum of two numbers, a student wrote 3(9+15). is the student correct? why or why not?

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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The answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

PRobability formula: P(E) = favourable events/Total events

(A) P(red ball):

P(E) = favorable events/Total events

P(E) = 5/8

(B) P(NOT Yellow)

P(E) = favorable events/Total events

P(E) = 7/8

(C) P(white or yellow)

P(E) = favorable events/Total events

P(E) = 3/8

Therefore, the answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

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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]

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

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

Step-by-step explanation:

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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$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 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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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

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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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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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:

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:

Step-by-step explanation:

0.15625

Answer:

8

Step-by-step explanation:

72 ÷ 9 = 8

Answer:

8

Step-by-step explanation:

72 divided by 9 is 8

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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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: 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

Answer: the correct anserw is A.!

Step-by-step explanation:

Answer:

Step-by-step explanation:

First question. Answer is

The fuel efficiency for the speed of 60 mph is (d) 38.55 mpg

From the question, we have the following least-squares regression line equation that can be used in our computation:

ln(Fuel Efficiency) = 1.437 +0.541 In(Speed)

Also from the question, we have the following parameters:

Speed = 60 mph

This means that we substitute 60 mph for speed in the given equation

ln(Fuel Efficiency) = 1.437 + 0.541 In(Speed)

So, we have the following representation

ln(Fuel Efficiency) = 1.437 + 0.541 In(60)

Take the natural logarithm of 60

This gives

ln(Fuel Efficiency) = 1.437 + 0.541 * 4.09434456222

Evaluate the products

So, we have the following representation

ln(Fuel Efficiency) = 1.437 + 2.21504040816

Evaluate the sum

So, we have the following representation

ln(Fuel Efficiency) = 3.65204040816

Take the exponent of both sides

Fuel Efficiency = e^(3.65204040816)

Evaluate

Fuel Efficiency = 38.5532502162

Approximate

Fuel Efficiency = 38.55 mpg

Hence, the fuel efficiency  is (d) 38.55 mpg

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The points on the rhombus M(?, 0) and H(5, 0), and the location of the point O of the rhombus, indicates that the length of a side of a rhombus is 5 units from which Pythagorean Theorem indicates that the x-coordinate of the point M is 3

Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side of a right triangle.

The shape of the quadrilateral RHOM = A rhombus

The specified coordinates of the vertices of the rhombus are;

Point M = (?, 4)

Point H = (5, 0)

A rhombus is a parallelogram that have all four sides of the same length

The length of side OH, which is on the x-axis  = 5 - 0 = 5

Therefore, the length of OM = 5 (properties of a rhombus)

Let x represent the x-coordinate of the point M

According to Pythagorean Theorem, we get;

x² + 4² = 5²

Where x = The horizontal distance of the point M from the y-axis

x² = 5² - 4² = 9

x = √9 = 3

The x-coordinate of the point M, x = 3

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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:

15/8

Step-by-step explanation:

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:

3 cats are orange and The other 1 is not

Because

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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Answer:

14 gallons

Step-by-step explanation:

456 - 28.5g = 5

28.5g =399

G=14