Find the real number solution(s) to the polynomial function f(x) = (x + 9)(x − 5)(x + 7).

a
x = −5, 7, 9

b
x = −9, −7, 5

c
x = −280

d
x = 11

1. A fraction whose denominator is 3 more than it's numerator x: x/(x+3)

A. If x =6, then the value of the fraction is 2/3.

B. If the denominator is 8, then the fraction is 5/8.

2. The length of a rectangular garden with an area of 32 square meters and has width w meters: 32/w.

A. The length of the garden if the width 4 meters = 8 meters

B. The width of the garden if the length is 16 meters = 2 meters

3. The rate of a car traveled 240 kilometers in t hours = 240/t km per hour

A. The rate of the car if t= 2.5 hour is 96 km/hour.

B. The rate of the car if the time is doubled is 120/t.

1. Let 'x' be the numerator. Then the denominator is 3 more than its numerator. So the denominator = x +3.

Hence the fraction whose denominator is 3 more than it's numerator x: x/(x+3).

A. If x = 6, then x+3 = 6+3 = 9.

So x/x+3 = 6/9 = 2/3

So the fraction is 2/3

B. Denominator = 8

⇒ x+3 = 8

⇒ x = 8-3 = 5

So the fraction is x/x+3 = 5/8.

2. Area of the rectangular garden = 32 square meters

⇒ length x width = 32

⇒ length x w = 32

⇒ length = 32/w

So the length of a rectangular garden with an area of 32 square meters and has width w meters is 32/w.

A. Width, w = 4 meters

Then, length = 32/w = 32/4 = 8 meters

B. Length = 16 meters

⇒ 32/w = 16

⇒ w = 32/16

⇒ width, w = 2 meters

3. Distance travelled by the car = 240 kilometers

Let 't' be the time taken in hours.

Then, Rate of the car = Distance / Time taken

⇒ Rate of the car in t hours = 240/t kilometers per hour

A. If t = 2.5 hour, then,

Rate of the car = 240/2.5 = 96 kilometers/ hour

B. If the time is doubled, then time = 2t

Rate of the car = 240/2t = 120/t

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Before change

Dimensions: r= 2 ; h=7

Lateral Surface area=  2πrh= 28π sqyd

Total Surface area= 2πr(h+r)=4π(9)= 36π sqyd

After change(trippling radius)

Dimensions: r= 6 (3*2); h=7

Lateral Surface area=  2πrh= 84π sqyd

Total Surface area= 2πr(h+r)=12π(13)= 156π sqyd

What is surface area of a cylinder?

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While traveling to his grandmothers for Christmas, George had been asleep for 50% of the entire journey and this distance is found by reviewing the information given to us.

The length of the entire journey taken to get from one point to another is the distance travelled. Travel distance is not a vector. It has no orientation.

In this question,

Let us take that George had been asleep for x distance.

Then according to question, we can form the equation

3/4 = 1/2x + x

3/4 = 3x/2

x = 1/2

so, the total distance travelled is 50% of the entire journey.

Displacement is the straight path between the initial and final points, whereas distance travelled is the actual length the body covers.

The International System of Units defines a meter as the distance unit.

How can velocity be used to calculate distance travelled?

Finding the area under the velocity, in particular when velocity is positive on an interval, allows us to determine the total distance travelled.

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Answer: 270

Step-by-step explanation: A tip for multiplying a number with any power of 10 is to just "add" a 0 to the end of the number depending on how many 0's there are in the power of 10.

For example, there is one 0 in 10. So I would just add a 0 to the end of 27 to get 270. If I were to multiply 27 by 100, there are two 0's in 100 so it would be 2700. 27 x 1000 would be 27000.

Hope this helped

The equation of the line perpendicular to 12y = 2x + 10 and passing though the point (-2,-1) is  y = -6x -7.

Writing the equation  12y = 2x + 10 in slope intercept form, we get,

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

The slope of the line is 1/6.

We know that,

Product of slope of two lines perpendicular to each other = -1.

Let the slope of the line perpendicular to the given line be m.

Hence, we can write,

m*(1/6) = -1

m = -6

Let the line perpendicular to the given line be y = mx + c.

It is given that the line perpendicular to the given line goes through (-2,-1).

Hence, we can write,

-1 = -6.(-1) + c

-1 = 6 + c

c = -7

Hence, the slope-intercept form of the line perpendicular to the given line is y = -6x -7.

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To answer this question, first of all, we need to find the equation for each of the lines on the graph. To do so, we have to identify two points for each line, and then use the two-point form equation (of the line) to find the equation of each line.

Then, we have:

We identify two points: (1, 1) and (2, 2).

Then we have:

Then if we label both points above:

• (1, 1) ---> x1 = 1, y1 = 1

• (2, 2) ---> x2 = 2, y2 = 2

Therefore:

Therefore, the equation of the line for the solid line is y = x.

We can proceed similarly as we did before. Then we have:

The two points are (2, 4) and (4, 8).

Then we can label them as follows:

• (2, 4) ---> x1 = 2, y1 = 4

• (4, 8) ---> x2 = 4, y2 = 8

Therefore, the equation for the dotted line is y = 2x.

We need to remember that when we have the symbols < or > the inequality is represented by a dotted line. Conversely, when it appears additionally an equal sign in the inequality symbol, ≥ or ≤ the line is represented as a solid line.

If we see the graph, we can say that the graph is represented by the following inequalities:

Since if we represent them graphically, we have - using a graphing calculator:

We can observe that the shaded area is the same as the one represented in the graph given in the question.

We can prove that if we take a point in the solution region as follows:

1. For example, we can test the point (-2, 2). Then we have:

Now, using this we can check if the other system of inequalities is equivalent to this:

We can check the following inequalities:

Which is equivalent to the previous one.

In summary, we have that the systems of linear inequalities are the following:

[Third option]

And

[Fourth option]

[The second and the third options are not answers since both have the symbol, ≥, - and it means that we have two solid lines representing the inequality system.]

[In the first option we have that the first inequality represents a solid line, and this is not the case. The dotted line is represented by y > 2x.]

The number of stocks that went up yesterday given the stocks that went down yesterday is 618.

Ratio is used compare two or values together. It shows the number of times that one value is contained in another value or values. According to the information provided in the question,  the ratio of stocks that go up and the stock that goes down is 6 : 7.

The number of stocks that went up yesterday = (ratio of stocks that went up x number of stocks that went down yesterday) / ratio of stocks that went down yesterday

The number of stocks that went up yesterday =(6 x 721) / 7 = 618

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The probability mass function for this is given by the table that is attached below.

Probability is defined as the proper fraction which signifies the likelihood of an event to occur.

Total number of possible arrangements of 6 people are 6! = 720

Here X can take value 0, 1, 2, 3, or4.

For the probability function : When X= 0 , it means there is no child between mother and father. Taking mother and father as one , number of possible arrangements of 5 people are 5!.

And mother and father can arranged themselves is 2! ways. So for X=0, possible ways are 5! *2 = 240.

Therefore the require probability at X=0 is given by:

P(X=0) = 240 /720 = 0.3333

For the probability function : When X = 1 , then there is one child between mother and father. Number of ways of selecting one child is C(4,1) = 4.

Mother and father can be arrange themselves in 2 ways so possible number of arrangements are 4 * 2 * 4! = 192

Therefore the require probability at X=1 is given by:

P(X=1) = 192 /720 = 0.2667

For the probability function :When X=2 , then there are two children between mother and father. Number of ways of selecting two children is C(4,2) = 6.

Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 2 ways so possible number of arrangements are 6 * 2 * 2* 3! = 144

Therefore the require probability at X=2 is given by:

P(X=2) = 144 /720 = 0.2

For the probability function : When X=3 , then there are three children between mother and father. Number of ways of selecting three children is C(4,3) = 4.

Mother and father can arrange themselves in 2 ways, children between mother and father can arranged themselves in 3! ways so possible number of arrangements are 4 * 2 * 3!* 2! = 96

Therefore the require probability at X=3 is given by:

P(X=3) = 96 /720 = 0.1333

For the probability function: When X=4 , then there are 4 children between mother and father. Number of ways of selecting 4 children is C(4,4) = 1.

Mother and father can arranged themselves in 2 ways, children between mother and father can arranged themselves in 4! ways so possible number of arrangements are 1 * 2 * 4! = 48

Therefore the require probability at X=0 is given by:

P(X=4) = 48 /720 = 0.0667

Hence the probability mass function can be represented by a table below.

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Answer:

  C. It is not proportional. y/x ratios are not equivalent

Step-by-step explanation:

Given a rental charge of $25 for the first hour and $20 for each additional hour, you want to know if the charges are proportional to the time.

In this situation, if the relationship were proportional, the charge per hour (constant of proportionality) would be the same for every hour. Here, the first hour costs more, so the hourly charge is not constant.

Here, we have, for x=hours, y=dollars, ...

  (1, 25)   ⇒   y/x = 25

  (2, 45)   ⇒   y/x = 22.5

  (3, 65)   ⇒   y/x ≈ 21.67

The y/x values are not constant (because the charge per hour is not constant). The relationship is not proportional.

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By using the method of interest, principle is 2777.7.

An expense associated with borrowing money or other assets is interest. The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time. The expense of borrowing money is interest. It equates to a fee or additional charge the borrower pays the lender for the loaned amount, and is sometimes stated as a percentage. When you make a payment on a loan with simple interest, the money first goes toward the interest for that month and the rest is applied to the principal. S.I. = P R T, where P = Principal, R = Rate of Interest in% per annum, and T = Time, typically calculated as the number of years, is the formula used to compute simple interest.

Given that,

S.I= PTR

Simple interest= 50

Time= 9/12= 0.75

Rate of interest= 2.4

Principle amount=?

S.I= PTR

50= P x 0.75 x 2.4

50= P x 1.8

P = 50X1.8

P= 2777.7

Therefore, principle is 2777.7

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Answer:

Step-by-step explanation : devise ----> divide496 = 2*2*2*2*31The 2's can be used in 5 ways, that is, not take anytake 1take 2take 3take all 4the 31 can be used in 2 ways, either take or not take itnumber of factors = 5*2 = 10but that includes taking all or noneif we correspond to none as the factor 1 and if we take all we would get 496the factors would be1, 2, 4, 8, 16, 31, 62, 124, 248, and 496

the equation of the line will be:

then

and we obtain

and making the subtraction, we have

which is the same as

When f(x) > 0, it means that on a graph, the line is above the x-axis.

Out of all the options, only in -2 < x < -1 is the graph above the x-axis.

For the other two intervals, the graph is below the x-axis.

-2 < x < -1

The equation that represents the possible tables that may be used to seat 200 people at the wedding is 8x + 10y = 200.

The combination will be 10 round tables and 12 rectangular tables; 15 round tables and 8 rectangular tables.

Based on the information, there can be round tables that sit 8 people and rectangular tables that sit 10 people and the total number will be 200.

Therefore, the equation that represents the possible tables is 8x + 10y = 200

where x = number of round table

y = number of rectangular tables

The possible combinations of table types that your sister can use at her wedding reception will be 10 round tables and 12 rectangular tables. This will be:

8x + 10y = 8(10) + 10(12) = 200

Another combination will be 15 round tables and 8 rectangular tables

8x + 10y = 8(15) + 10(8) = 200

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A polynomial of degree 4 in factored form with zeros 1, -4, 0, and 6 is

f(x) = x(x - 1)(x + 4)(x - 6).

Given:

x₁ = 1

x₂ = -4

x₃ = 0

x₄ = 6

Utilize the fact that x - b is a factor of the polynomial if b is a root.

Simply take each zero, modify its sign, and add an x in front of it to obtain the four factors.

The polynomial is,

f(x) = (x - x₁)(x - x₂)(x - x₃)(x - x₄)

f(x) =  (x - 1)(x - (-4))(x - 0)(x - 6)

     = (x - 1)(x + 4(x)(x - 6)

Therefore,a 4 degree polynomial in factored form with zeros 1, -4, 0,and 6 is x(x - 1)(x + 4)(x - 6).

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Answer:800

Step-by-step explanation:

x + 4x = 1000

   5x     = 1000

    x     = 1000/5 = 200 dollars.

[tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

In the given question we have to find the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

Firstly we learn about terms used in this question,

The return needed by either a business or an individual to justify an investment in equity is known as the cost of equity.

The relationship between systemic risk, or the general dangers of investing, and expected return for assets, particularly equities, is described by the Capital Asset Pricing Model.

Since we have to find the cost of equity using the capital asset pricing model. So the formula is

Cost of equity = Risk free rate + Beta * Equity Risk Premium

Risk free rate = 4.5%

Beta = 1.75

Equity Risk Premium = 4.25%

Now putting the value in the formula

Cost of equity [tex]=4.5\%+1.75\times4.25\%[/tex]

Simplifying

Cost of equity [tex]=4.5\%+7.4375\%[/tex]

Cost of equity [tex]=11.9375\%[/tex]

Hence, [tex]11.9375\%[/tex] is the cost of equity using the capital asset pricing model if the risk free rate is 4.5%, the beta is 1.75 and the equity risk premium is 4.25%.

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Given:

The formula is

Required:

Make h the subject of the formula.

Explanation:

We will put formula in terms of h as:

Answer:

Hence, above is the answer.

1) I'll calculate the hypotenuse

hyp = squared root [(16)^2 + (12)^2]

= squared root [ 256 + 144]

2) the answer is letter C. 5/7

3) calculate the hypotenuse

hyp = squared root [(2^2 + (-3)^2]

= squared root [ 4 + 9]

= squared root [13]

sin 0 = -3/squared root 13

= -3squared root (13) / 13

The answer for number three = letter B

Answer:

g

<

−

7

Step-by-step explanation:

If the gondola is filled with 25 randomly selected skiers, the probability that it will be overloaded is; 50%

The formula to find the maximum mean weight of passengers is;

Maximum mean weight = Load limit ÷ number of passengers

We are given;

Load limit = 5000 lb

Maximum number of passengers = 25

Thus;

Maximum mean weight of passengers = 5000 ÷ 25 = 200lb

Let us find the z-score:

z = (max value - mean) / st. dev

z = (200 - 200)/40

z  = 0

From online p-value from z-score calculator, the p-value = 0.5 and so that is the probability that it will be overloaded.

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Answer:

Step-by-step explanation:

A) 5x+3x

5x+3x

= 8x

B) 9s-3s+4s

9s-3s+4s

6s+4s

=10s

Answer: see answers below

Step-by-step explanation:

F(x) is bascially the y

the absolute value means any numbers that you use for x when substituted into x-2 will always be a positive number even if x-2 is negative as with any number 3 or greater, or any number -3 or less.  

for the values that are 0, 1, 2, 3, 4 or 0, -1, -2  the answer for f(x) will be a negative number.  All other numbers positive or negative for x will result in a positive answer.  

So you need to graph your line with an arrow on each end to show it goes to infinity.  in your chart you choose a number for x, and the f(x) number (which is equivalent to the y number for purposes of graphing.

I cannot draw on her a graph for you because I don't have that ability without an app for that.  

here are some sample points for your chart.  THe first number in each parenthesis is x and the second is f(x)

(-1, -2),  (-2, -1), (0, -3), (-3, 0), (1, -4), (2, -5), (3-4), (4,-3), (5-2), (6, -1)  All other numbers positive or negative for x will result in f(x) being positive.

You only need two sets of points to put on the graph to draw the line through.  

So negative values for f(x) can only be -1, -2, -3, -4, -5.   x can include all negative numbers through infinity.

Positive will include all positive numbers through infinity for x  and f(x).

F(x) cannot decrease beyond -5.   x can decrease all numbers  through infinity.

Answer:

A)Linear angles

B) they have a sum of 180

C)25x+5+4+32x=180

57x+9=180

57x=171

x=3

D)25(9)+5=

75+5=80

32(3)+4=

96+4=100

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

You need to take -112 and subtract it by -80 to get 32

Hope this helped! :)

Answer:

C -7

Step-by-step explanation:

the numbers keep on decreasing by 7

Answer:

true

Step-by-step explanation:

the answer of both the smaller squares added is the same as the andwer of the bigger square