Kevin bought a desk on sale for $280.80. This price was 36% of the original price.
What was the original price?

The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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The price that yields maximum revenue is equal to $99. Also, the maximum revenue is equal to $490,050.

In order to determine the price that would yield the maximum revenue, we have to find the derivative of the revenue function R(p) by applying the Power Rule.

Mathematically, the revenue function, R(p) is given by this mathematical expression:

Revenue function, R(p) = NP

Where:

Let the variable n represent the number of reductions in the price. Therefore, we have:

N = 3,400 + 50n    ....equation 1.

P = 130 - n

n = 130 - P

From equation 1, we have:

N = 3,400 + 50(130 - P)

N = 3,400 + 6,500 - 50P

Next, we would re-write the revenue function R(p) as follows:

Revenue function, R(p) = (3,400 + 6,500 - 50P)P

Revenue function, R(p) = 3,400P + 6,500P - 50P²

Revenue function, R(p) = 9,900P - 50P²

Taking the derivative of R(p), we have:

R'(p) = 9,900 - 100P

100P = 9,900

Price, P = 9,900/100

Price, P = $99

For the the maximum revenue, we have:

Maximum revenue, R(p) = 9,900P - 50P²

Maximum revenue, R(p) = 9,900(99) - 50(99)²

Maximum revenue, R(p) = 980,100 - 490,050

Maximum revenue, R(p) = $490,050.

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Complete Question:

A cable TV company has 3400 customers paying $130 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.

The value of P=2 and Q=8 as in AP, The difference in two terms is equal between all the terms.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. Sn = n/2[2a + (n 1) d] is the formula to determine the sum of an arithmetic progression. where an is the first term in the arithmetic progression, n is the total number of terms, and d is the common difference. If there is always the same difference between any two consecutive terms in a series of numbers, that progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series.

Here,

18--12=30/3=10

P=-12+10

=-2

Q=-2+10

=8

P=2 and Q=8 as in AP, the difference between the two terms is equal for all terms.

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Answer:

162.4$

Step-by-step explanation:

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By the concept of polynomial, first second and third option are correct.\

What is polynomial?

At first it is important to know about algebraic expression

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

An algebraic expression of the form [tex]a_0+a_1x+a_2x^2 + ....+a_nx^n[/tex] is called a polynomial of degree n

For the First Option

5 - 2a is in the form of [tex]b_0 + a_1a[/tex]

So the first option is a polynomial

For the second option

[tex]4 - 8^2 -16\\4 -64 -16\\-76[/tex]

which is a constant

And all constants are polynomial

So the second option is a polynomial

For the third option

[tex]5x^3 +4x^13x +1\\5x^3 + 12x^2 +1[/tex]

which is of the form [tex]a_0+a_1x + a_2x^2 + a_3x^3, a_1 = 0[/tex]

So the third option is a polynomial

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Answer:

[tex]y=12[/tex]

Step-by-step explanation:

The [tex]y[/tex]-axis has equation [tex]x=0[/tex], so the equation of a line perpendicular to the [tex]y[/tex]-axis would be of the form [tex]y=c[/tex].

The equation of this line given the point [tex](3,12)[/tex] is [tex]y=12[/tex].

a.

The ratio of the number of students in 2006-2007 to the number of students in 2005-2006 is = 12,256 : 11,937

b.

Growth factor = (12256-11937)/11937

= 0.02672.

c.

Increase in percent = 100* (12256 - 11937)/11937

=  100 * 0.02672

= 2.672%

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Answer:  x = 8   y = 21

Step-by-step explanation:

7x + 12 = 12x - 28

40 = 5x

x = 8

180 = 12(8-28) + 9y - 77

180 = 96 - 28 - 77 + 9y

180 = -9 + 9y

189 = 9y

y = 21

Answer:

x=8

y=21

Step-by-step explanation:

9y-77+12x-28=180

9y+12x=285

7x+12=12x-28

5x=40

x=8

9y+96=285

9y=189

y=21

Answer:

1/2a (4a+7)

Step-by-step explanation:

First You Divide:7/2a+ 2a^2

Rearrange Terms: 2a^2+ 7/2a

Find the Common Factor: 1/2(4a^2+7a)

Rewrite in the Fraction Form: 1/2a (4a+7)

I know this is the right answer because I learned this in 5th grade.

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Answer:

D, 2/3

Step-by-step explanation:

Using the Slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find the slope of the line.

Input values:

[tex]m=\frac{6-4}{5-2}=\frac{2}{3}[/tex]

[tex]m=\frac{2}{3}[/tex]

The value of the algebraic expression is:

a^2*b = -15 + 20i

Here we have the following expression:

a^2*b

And we want to use the values:

a = -1 + 2i

b = 5

Replacing these values in the expression we will get:

(-1 + 2i)^2*5

Expanding the  first part we get:

(-1 + 2i)*(-1 + 2i) = (-1)*(-1) + (-1)*(2i) + (2i)*(-1) + (2i)*(2i)

                        = 1 - 2i - 2i - 4

                        = -3 + 4i

Replacing that in the expression we get:

(-1 + 2i)^2*5 = (-3 + 4i)*5 = -3*5 + 4i*5 = -15 + 20i

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Answer:

4/15

Step-by-step explanation:

[tex]\frac{3}{5}=\frac{9}{15} \\ \\ \frac{1}{3}=\frac{5}{15} \\ \\ \frac{3}{5}-\frac{1}{3}=\frac{9}{15}-\frac{5}{15}=\frac{4}{15}[/tex]

Basically,  Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers. GCF/HCF ( Greatest/Highest Common Factor) is the highest number that divides exactly into two or more numbers.

Answers:

9) LCM of 36, 3, 12 = 36

   GCF of 36, 3, 12 = 3

10) LCM of 6, 54, 12 = 108

     GCF of 6, 54, 12 = 6

11) LCM of 16, 8, 12 = 48

   GCF of 16, 8, 12 = 4

The expression (2/3)² when simplified by repeated multiplication is 4/9

From the question. the expression is given as

(2/3)²

We start by rewriting the expression using repeated multiplication

This in other words means that:

We rewrite the (2/3)² as repeated multiplication

To do this, we apply the exponent rule of indices

This rule states that:

a^m = a * a * a .... in m places

So, we have

(2/3)² = (2/3) x (2/3)

Evaluate the products

(2/3)² = 4/9

Hence, the equivalent expression is 4/9

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The solution is 1/(x+1)

From the question, we have

(x^2+4)/(x^3+x^2+4x+4)

=(x^2+4)/(x^2 (x^3/x^2 +x^2/x^2 )+2^2 ((2^2⋅x)/2^2 +2^2/2^2 ) )

=(x^2+4)/(x^2 (x^(3-2)+1)+2^2 (x+1))

=(x^2+4)/(x^2 (x+1)+2^2 (x+1))

=(x^2+4)/((x+1)((x^2 (x+1))/(x+1)+(2^2 (x+1))/(x+1)) )

=(x^2+4)/((x+1)(x^2+2^2 ) )

=(x^2+4)/((x+1)(x^2+4) )

=1/(x+1)

The solution is 1/(x+1)

Divide:

Split is to divide into two or more equal sections, places, groupings, or divisions in its most basic form. To divide something simply means to provide it to a group in equal quantities or to cut it up into equal pieces. Let's imagine a diagonal divides a square into two triangles with equal areas. An integer may or may not be the result of a division operation. Sometimes the result will be expressed as decimal numbers.

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The operating income of Division B will increase by $640,000

Given that: Division B incurs variable costs of $10 per unit and  a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A

This cost of production by division B is:

cost = $10 × 80,000 = $800,000

Division B uses a transfer price of $18 per unit. That is:

Selling price = $18  × 80,000 = $1,440,000

Operating income increase = Selling price - cost

Operating income increase = $1,440,000 - $800,000 = $640,000

Therefore, Division B's operating income increase will be $640,000

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The mean value is 7.6. Option (D) is the correct answer.

The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.

The mean value of a binomial distribution is,

[tex]\mu =np\\=38*0.2\\=7.6[/tex]

Multiplication:

In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.

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Answer:

Step-by-step explanation:

Solutionx% of 199 is 761 is  382.41206…% Answer 

Convert x% into a decimal and multiply by 199

In order to convert a percent to a ratio, divide it by 100:     

a%=a100 

a=x

x% =x100 

Convert to decimal form=0.01x

Multiply 0.01x by 199

=0.01x· 199=1.99x

Solve 1.99x=761  

1.99x=761  

x=761/1.99

x=382.41206%

Answer:

[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

Slope = m

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

m = [tex]\frac{7-3}{9-2}[/tex] = [tex]\frac{4}{7}[/tex]

If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.

What is distributive property?

The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.

A × (B + C) = AB + AC

A (B - C) = AB - AC

Here,

we can write 6 × 9 as,

           =  6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property

Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.

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The value of the x is 60 km and the value of the y is 70 km.

Given that a man travels x km at 60 km/h and y km at 40 km/h and the total time traveled is 11/4 i.e 2.75 h.

Let's suppose that the time traveled for the x km is t1, time traveled for the y km is t2 and total time is T ,so by using the speed distance formula t1 & t2 will be :

t1 = x/60 and t2 = y/40 ;

T = t1 + t2;

i.e 2.75 = x/60 + y/40 ;

Multiply both sides with 120,

330 = 2x + 3y ............i

Now given that man traveled 5x km at 40 km/h and 3y km at 50 km/h in total time of 11. 7 hours. Similarly the equation for this situation will be :

T = t1 + t2;

x/8 + 3y/50 = 11.7 ;

Multiply both sides with 200, we will get

25x + 12y = 2340 .........ii

Now by simplifying the equation i and ii we will get the value of x and y which are 60 and 70 respectively.

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Answer:IT WOULD BE 60.00

Step-by-step explanation:

BC 40 = 60

The area of the given figure is 25cm².

Area of rectangle

Area = length x width

Perimeter of rectangle

Perimeter = length + length + width + width

Hence, we have

length = 5cm

width = 5cm

then, by applying the Area of the rectangle, we get

Area = length x width

Area = 5 x 5

      = 25cm²

Hence, The area of the given figure is 25cm².

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The average hourly pay of person making 4500 per year is 21.63 per hour.

Given that,

we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.

To calculate this

The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.

We have to multiply 52-week year and a 40-hour work week.

40×52

2080

Now, divide 45000 by 2080

45000/2080

21.63

Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.

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A Linear equation in standard form is

2x + y = -4

slope of the function = -2

the perpendicular line equation in standard form -x + 2y = -6

A standard equation is of the form Ax + By = C

A = 2

B = 1

C = -4

Rearranging the equation to the slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Ax + By = C

By = -Ax + C

y = -Ax/B + C

calculation of slope

m = -A/B

substituting the values of A and B

m = - 2/1

m = -2

a new perpendicular slope, m' is given by

m' = -1/m

plug in the value of m

m' = -(1/-2)

m' = 1/2

new equation passing through point (8, 1)

(y - y₁) = m'  (x - x₁)

y - 1 = 1/2(x -8)

y - 1 = x/2 - 4

y = x/2 - 3

writing in standard form

y = x/2 - 3

2y = x - 6

-x + 2y = -6

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Answer:

Can't be written as fraction

Step-by-step explanation:

Irrational Numbers are Real Numbers which are not rational , which means that it can't be written as fraction

The required expression is 3h(150) + h(270) which is the correct answer would be an option (D).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Since each house will have 3 smaller bedrooms that required 150 square feet of carpet

⇒ 3 × 150

Each house will have 1 larger bedroom that requires 270 square feet of carpet.

⇒ 270

So, (3 × 150 + 270) × h

⇒ 3h(150) + h(270)

Thus, The required expression is 3h(150) + h(270).

Hence, the correct answer would be an option (D).

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