Factorise the following:
a) x² + 4x + 4
b) x²- 12x + 27
c) x²-x-42
d) x² + 8x-9

Answer: all angles are equal

Step-by-step explanation:

in a equilateral triangle all angles will be 60°

The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).

The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.

Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.

In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.

The union of sets, represented by the symbol ∪, is the operation that gives you the set of all elements that are in at least one of the sets being considered.

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Answer:

To find y'(3), we need to use implicit differentiation to differentiate both sides of the equation with respect to x and then solve for y'.

Differentiating both sides with respect to x, we get:

(2x/25) + (2y/64) * (dy/dx) = 0

Now we can solve for dy/dx:

(2y/64) * (dy/dx) = -(2x/25)

dy/dx = -(2x/25) / (2y/64)

dy/dx = -32x/25y

To find y'(3), we need to substitute x=3 and y=6.4 into the expression for dy/dx:

y'(3) = -32(3)/(25)(6.4)

y'(3) = -0.3

Therefore, the value of y'(3) is -0.3

The value of y'(3) in (2x/25) + (2y/64) = 1, is  - 0.3

Finding the derivative of an implicit function is the process of implicit differentiation.

In other words, this method is utilized to discover the implicit derivative.

To find y'(3), After differentiating both sides of the equation with respect to x using implicit differentiation, we must next solve for y'.

Differentiating both sides with respect to x we get,

(2x/25) + (2y/64)×(dy/dx) = 0

Solving for dy/dx

(2y/64)×(dy/dx) = -(2x/25)

dy/dx = -(2x/25) / (2y/64)

dy/dx = -32x/25y

To find y'(3), Replacing x=3 and y=6.4 into the expression for dy/dx:

y'(3) = -32(3)/(25)(6.4)

y'(3) = -0.3

Therefore, the value of y'(3) is - 0.3

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Answer:

7/3>x

Step-by-step explanation:

-5<9-6x

subtract 9 from both sides

-14<-6x

divide by 6

14/6<x

simplified its 7/3<x

but since we divided by a negative we switch the sign

final answer is 7/3>x

Rounded to the nearest tenth, the area of the region that receives the radio signal is approximately 6,366.2 square miles.

Consider a plane region described by a xy-plane graph. The signed area of the region is defined as the area of the graph on or above the x-axis. The negative area of the graph is defined as the area below the x-axis.

The formula A = πr² gives the area of a circle with radius r. In this case, the radio station broadcasts over a 45-mile radius, so the region that receives the radio signal is:

A = π(45)²

A ≈ 6,366.2 square miles

The area of the region that receives the radio signal is approximately 6,366.2 square miles when rounded to the nearest tenth.

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The product of 4.000329 × 1000 is the second option 4,000.329.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have to find the product of 4.000329 × 1000.

When a number is being multiplied by (10)ⁿ, 'n' number of zeroes will be added to the right of the number.

If the number is decimal number, decimal point is being shifted n digits to the right.

The question here is 4.000329 × 1000.

4.000329 × 1000 = 4.000329 × (10)³

Decimal point is shifted three digits to the right.

4.000329 × (10)³ = 4,000.329

Hence the correct option is B.  4,000.329.

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The slope of line q is equal to 3.

The slope of line q is equal to -1/3.

An equation for line p in point-slope form is y + 5 = -1/3(x - 6).

An equation for line p in slope-intercept form is y = -1/3x - 3.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c   ....equation 1.

Where:

From the information provided, we have the following linear equation in slope-intercept form for line q:

y = 3x + 5  ....equation 2.

By comparing equation 1 and equation 2, we can logically deduce the following:

Slope (m) = 3

Since line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q;

m₁ × m₂ = -1

3 × m₂ = -1

Slope, m₂ of line p = -1/3.

At data point (6, -5), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = -1/3(x - 6)

y + 5 = -1/3(x - 6)

By simplifying further, the slope-intercept form is given by;

y + 5 = -1/3(x - 6)

3y + 15 = -x + 6

3y = -x - 9

y = -1/3x - 3

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Complete Question:

Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.

Find the slope of line q.

Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)

Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)

Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b.

Answer:

-x + 9

Step-by-step explanation:

a)  

 8x + 2 + (-9x + 7) = 8x + 2 - 9x + 7

                             = 8x - 9x + 2 + 7

                             = -x + 9

b) We can combine like terms. Like terms have same variable with same power. Here 8x and (-9x) have same variable 'x'. so, combine the coefficients of the like terms which give (-1).

8x - 9x = -1

Combine the constants. 2 + 7= 9

In the expression, 4x+15x,  variable: x; coeficient: 4, 15; constant: 0

In the expression 6n+25+7n+4, variable: n, coeficient: 6, 7; constant: 25, 4

In the expression 3a+4a+17+a+1, variable: a, coeficient: 3, 4, 1; constant: 17, 1

Generally, in an algebraic expression terms, variables, coefficients, and constants are seen. The parts of an expression that are added by either an addition or a subtraction notation are called the terms. The letter of a term is called a variable, the numerical value written along the variable of a term is called a coefficient, and the term contains only the numerical value called a constant.

Take the expression 4x+15x. The terms are 4x and 15x.

Clearly, the variables of the terms are x, the coefficients of the terms are 4 and 15, and the constant is 0. So, the required answers are obtained.

Take the expression 6n+25+7n+4. The terms are 6n, 25, 7n, and 4.

Clearly, the variables of the terms are n, the coefficients of the terms are 6 and 7, and the constants are 25 and 4. So, the required answers are obtained.

Take the expression 3a+4a+17+a+1. The terms are 3a, 4a, 17, a, and 1.

Clearly, the variables of the terms are a, the coefficients of the terms are 3, 4, and 1, and the constants are 17 and 1. So, the required answers are obtained.

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The height of flagpole c is given as follows:

66 ft.

Similar triangles are triangles that share these two features presented as follows:

For each flagpole, the parameters are given as follow:

The triangles are similar, hence the proportional relationship to obtain the height of flagpole's c is given as follows:

2/10 = 13.2/h

Applying cross multiplication, the height is obtained as follows:

2h = 10 x 13.2.

h = 132/2

h = 66 ft.

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The value of the probabilities are

a. P(x ≥ 12.5) is 6.68%

b. P(x ≤ 9) is 2.28%

c. P(10.88 ≤ x ≤ 15.3) is 61.38%

d. P(4.72 ≤ x ≤ 12.46) is 99.45%

Probability is the measure of the likelihood of an event occurring. It is a way of quantifying uncertainty and predicting the likelihood of an outcome. In this question, we will use the normal distribution to calculate probabilities.

The mean is the center of the distribution, and the standard deviation measures the spread of the distribution.

a. P(x ≥ 12.5):

Using a standard normal distribution table, we find that the area to the right of 12.5 is 0.0668. This means that the probability of x being greater than or equal to 12.5 is 0.0668 or 6.68%.

b. P(x ≤ 9):

Using a standard normal distribution table, we find that the area to the left of 9 is 0.0228. This means that the probability of x being less than or equal to 9 is 0.0228 or 2.28%.

c. P(10.88 ≤ x ≤ 15.3):

Using a standard normal distribution table, we find that the area to the left of 15.3 is 0.9987 and the area to the left of 10.88 is 0.3849. Therefore, the area between 10.88 and 15.3 is

=> 0.9987 - 0.3849 = 0.6138.

This means that the probability of x being between 10.88 and 15.3 is 0.6138 or 61.38%.

d. P(4.72 ≤ x ≤ 12.46):

Using a standard normal distribution table, we find that the area to the left of 12.46 is 0.9946 and the area to the left of 4.72 is 0.0001. Therefore, the area between 4.72 and 12.46 is

=> 0.9946 - 0.0001 = 0.9945.

This the probability of x being between 4.72 and 12.46 is 0.9945 or 99.45%.

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The HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.

The Herfindahl-Hirschman Index (HHI) is a measure of market concentration that is commonly used to assess the degree of competition in a market. The index is calculated as the sum of the squared market shares of all the firms in the market. The HHI can range from 0 to 10,000, with higher values indicating greater market concentration.

To calculate the HHI for the two scenarios given, we need to first calculate the market shares of the teams in each scenario. In the first scenario, there are four teams with the following market shares:

Team A: 8/10 = 0.8

Team B: 2/10 = 0.2

Teams C and D: 0/10 = 0

The HHI for this scenario is calculated as:

HHI = [tex](0.8^2 + 0.2^2 + 0^2 + 0^2) \times10,000[/tex]

= 68,000

In the second scenario, there are eight teams with the following market shares:

Teams A and B: 4/10 = 0.4 each

Teams C and D: 1/10 = 0.1 each

Teams E, F, G, and H: 0/10 = 0 each

The HHI for this scenario is calculated as:

HHI = [tex](0.4^2 + 0.4^2 + 0.1^2 + 0.1^2 + 0^2 + 0^2 + 0^2 + 0^2) \times 10,000[/tex]

= 16,000

In both scenarios, the HHI is less than 1,800, which is considered a low level of market concentration. Therefore, we can conclude that both scenarios represent relatively competitive markets.

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Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].

Derivatives refers to the instantaneous rate of change of a quantity with respect to the other. That is, the amount by which a function is changing at one given point.

Given, [tex]x=b-\sqrt{ap-c}[/tex]

To find [tex]\frac{dx}{dp}[/tex]:

⇒[tex]\frac{dp(b-\sqrt{ap-c)}}{dx}[/tex]

⇒0- [tex]\frac{1}{2} (ap-c)^{-1/ 2} .\frac{d}{dp}(ap-c)[/tex]

⇒[tex]-\frac{ a.dp/dp+\frac{d}{dp}(-c) }{2\sqrt{ap-c} }[/tex]

⇒[tex]-\frac{a}{\sqrt{ap-c} }[/tex]

Hence, [tex]-\frac{a}{\sqrt{ap-c} }[/tex] is the derivative of [tex]x=b-\sqrt{ap-c}[/tex].

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Step-by-step explanation:

a. On Monday, the percentage of large bags sold was 57/(57 + 132) x 100 = 30.22%.

b. On Monday, the percentage of small bags sold was 132/(57 + 132) x 100 = 69.78%.

c. The total number of large and small bags sold on the two days combined was 130/(130 + 154) x 100 = 45.45%.

It is less than 21 so it has to be 19.4.

a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.

b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.

Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52

Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,

a) Number of cards are in the deck that are not one of the designated cards

= 52 - 2 = 50

Number of cards that need to be dealt in order for each player to have 7 cards

= 5× 7 = 35

Thus total possible number of ways

= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.

b) Number of cards are in the deck = 52

Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35

Thus total possible number of ways

= ⁵²C₃₅ = 21945588357420

Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards

= 2250829575120/21945588357420

= 0.10256410256

Hence, required probability is 0.1026.

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The lines are parallel because they have the same slope in the equation of lines

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first equation be 9y - 6x = -18   be equation (1)

Let the second equation be 3y - 2x = 24   be equation (2)

On simplifying the equation , we get

Adding 6x on both sides of the equation , we get

9y = 6x - 18

Divide by 9 on both sides of the equation , we get

y = ( 2/3 )x - 2

So , the slope of line 1 is m = 2/3

And , for the second equation ,

Adding 6x on both sides of the equation , we get

3y = 2x + 24

Divide by 3 on both sides of the equation , we get

y = ( 2/3 )x + 8

So , the slope of line 2 is m = 2/3

Since the slopes of the lines are same , they are parallel lines

Hence , the equation of lines are solved

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The complete question is :

The lines represented by the equations 9y - 6x = -18 and 3y - 2x = 24 are

a) perpendicular

b) parallel

c) none of the above

The value of x for the system of equations will be x=6.7.

What is a system of equations?

A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.

Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.

Multiply the second equation by 2 and subtract from the first equation,

2x+2y=17.

8x-2y=50.

10x=67.

x= 67/10

x = 6.7.

Therefore, the value of x for the system of equations will be x=6.7.

\

Answer:

Step-by-step explanation:

56

Answer:

2 vases of lilacs

3 vases of irises

Step-by-step explanation:

7( lilacs ) × 2( vases) = 14 flowers

5( irises ) × 3( vases) = 15 flowers

14 + 15 = 29 flowers

a) The determination of the dividends per share for the cumulative preferred and common stock for each year is as follows:

           Dividends per share

2011           $3.00

2012           $1.20

2013          $4.80

            Dividends per share

2011              $1.50

2012             $0

2013             $2.10

b) The determination of the amount of current dividends that preferred stock should receive per year is $75,000.

Cumulative preferred stock is a special class of preferred stock that enjoys cumulative dividends.

Cumulative dividends imply that any year when sufficient dividends are not declared, the arrears are carried forward to subsequent years.

It is the opposite of non-cumulative preferred stock.

On the other hand, the common stockholders can only receive dividends after the preferred stockholders have been paid, including their cumulative dividends.

Number of shares = 25,000

Dividend rate = 2%

Par value = $150

Total cumulative preferred stock = $3,750,000 (25,000 x $150)

Annual dividend = $75,000 ($3,750,000 x 2%)

Number of shares = 50,000

Par value = $15

Total common stock = $750,000 (50,000 x $15)

                  Dividends Due   (Dividends per share)

2011             $75,000             $3 ($75,000/25,000)

2012            $30,000             $1.2 ($30,000/25,000)

2013           $120,000             $4.8 ($120,000/25,000)

                  Dividends Available                      (Dividends per share)

2011           $75,000 ($150,000 - $75,000)    $1.50 ($75,000/50,000)

2012          $0 ($30,000 - $30,000)               $0

2013         $105,000 ($225,000 - 120,000)   $2.10 ($105,000/50,000)

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The area of the figure is 596.625 in².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

We will consider the figure to have a rectangle and a circle.

Rectangle:

Length = 28 in

Breadth = 15 in

Area = 28 x 15 = 420 in²

Semicircle:

Diameter = 15 in

Radius = 7.5 in

Area = 1/2 πr²

= 1/2 x 3.14 x 7.5²

Area = 176.625/2

Area = 88.3125

There are two semicircles so,

= 2 x 88.3125

= 176.625 in²

Now,

Area of the figure.

= 420 + 176.625

= 596.625 in²

Thus,

596.625 in² is the area of the figure.

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The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Answer:

x = 9/2

Step-by-step explanation:

As both equations are set equal to "y", we can set the equations equal to each other and solve for the x-value:

[tex]4=2x-5\\9=2x\\x=\frac{9}{2}[/tex]

The hypothesis tested are given as follows:

[tex]H_0: \mu = 3.2, H_a: \mu \neq 3.2[/tex]

The claim for this problem is given as follows:

"The mean salary for the baseball players on the East Coast is different from $3.2 million".

At the null hypothesis, we test if the claim is false, that is, if the mean salary is equals to 3.2 million, hence:

[tex]H_0: \mu = 3.2[/tex]

At the alternative hypothesis, we test if the claim is true, that is, if the mean salary is different of 3.2 million, hence:

[tex]H_a: \mu \neq 3.2[/tex]

The [tex]\mu[/tex] symbol, without the bar, is used, as we are testing for the population mean, not sample mean, hence the first option is the correct option.

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a) The unit rate of Kate's sewing productivity can be found by dividing the number of dresses by the number of days:

Kate sews 100 dresses in 20 days.

The unit rate is 100 dresses / 20 days = 5 dresses per day.

b) The unit rate of Kim's running speed can be found by dividing the distance by the time:

Kim runs 5 km in 30 minutes.

The unit rate is 5 km / 0.5 hour = 10 km/hour.

Therefore, the unit rate for Kate's sewing productivity is 5 dresses per day, and the unit rate for Kim's running speed is 10 km/hour.

The value of the evaluated function f(x) = -3x² + 2x  at  

(i) f(-2) is -16   ;

(ii) f(a) is -3a² + 2a .

The Function is represented as : f(x) = -3x² + 2x  ;

(i) We have to evaluate the above function at f(-2),

So, we substitute x = -2 into the function:

we get ;

⇒ f(-2) = -3(-2)² + 2(-2)

⇒ f(-2) = -12 - 4 = -16  .

So ,  f(-2) = -16  .

(ii) Next we have to evaluate f(a),

So , we substitute x = a into the function:

⇒ f(a) = -3a² + 2a

So , f(a) = -3a² + 2a   .

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The given question is incomplete , the complete question is

For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a)  .

The quantities 6 and 2 are called proportions

From the question, we have the following parameters that can be used in our computation:

In the ratio of yellow marbles to blue marbles, 6:2,

This means that

Yellow : Blue = 6 : 2

Using the above as a guide, we have the following:

For every 6 yellow marbles, there are 2 blue marbles

This means that 6 and 2 are the proportions

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