1) Form a polynomial whose real zeros and degree are given.
Zeros: -1, 0, 6 Degree: 3
2) Information is given about a polynomial​ f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree​ 4; ​ zeros: 7i, 2, -2

Answer:

  CD = 3/√2 in

Step-by-step explanation:

You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.

All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.

In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...

  CD = BD = CB/√2

  CD = 3/√2 in

__

Additional comment

Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...

  CD = 3/√2 = (3/2)√2 = 1.5√2

<95141404393>

Answer:

The standard form of the equation of a line is:

y = mx + b

Where m is the slope of the line and (x,y) is a point on the line. We know that the line passes through the point (4, -11) and has a slope of 3/4.

We can use the point-slope form to find the equation of the line:

y - y1 = m(x - x1)

Where (x1, y1) is the point on the line and m is the slope.

Substituting in the given information we get:

y - (-11) = (3/4)(x - 4)

Simplifying the equation we get

y = (3/4)x + (33/4)

This is the equation of the line in standard form.

The value of x is equal to 0.660441.

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here: The exponential function 2(3e)ˣ=8

Simplifying further we get, (3e)ˣ=4

Taking log both sides we get x (ln3+1)=ln4

                                              x×2.0986=1.386

                                                       x=0.660441

Hence, The value of x is equal to 0.660441.

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The expression that represents the statements are

1. R = 114+P

2. M = 10+2B

3. H = 1/2M -29

Linear expressions are those statements that each term is either a constant or a variable raised to the first power.

In linear expressions, the highest power of the variable is 1.

In the first statement 'Rhona got 114 more votes Tham Petro'. Let's represent the votes for Rhona by R and for Pedro by P

therefore R = 114+ P

In the second statement 'Matt took 10 minutes longer than twice as long as Bryce took to do his assignment'

Let's represent the time it took Matt to do his assignment' by M and time it took Bryce by B.

then,

M = 10+2B

In the third statement 'A hamburger costs 29 cents less than half as much as a full meal'.

Let's represent the cost of hamburger by H and the cost of full meal' by M, then,

H = 1/2M -29

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1 is a factor of every whole number. Every whole number can be evenly divided by 1, so 1 is a factor of every whole number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

Every whole number is the product of 1 and itself so, each number is a factor of itself.

Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.

Every number other than 1 has at least two factors, namely the number itself and 1.

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Answer:

To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.

Food: 20% of $25,000 = $25,000 x 0.20 = $5000

Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250

Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750

So the family has $5000 for food, $6250 for shelter and $3750 for clothing.

The price of an adult ticket is $20

The price of a child's ticket is $19

Let x represent the price of a child ticket

Let y represent the price of an adult ticket

Three adults and four children must pay 136

3y + 4x= 136.........equation 1

Two adults and three children must pay $97

2y + 3x= 97.........equation 2

From equation13 1

3y+4x= 136

3y= 136-4x

y= 136-4x/3

Substitute 136-4x/3 for y in equation 2

2(136-4x) + 3x= 97

272-8x/3 + 3x/1= 97

272-8x+9x/3= 97

cross multiply

272-8x+9x=291

collect the like terms

-8x+9x= 291-272

x= 19

Substitute 19 for x in equation 1

3y+4x= 136

3y + 4(19)= 136

3y+ 76= 136

3y= 136-76

3y=60

y= 60/3

y= 20

Hence children tickets cost $19 and adult tickets cost $20

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A good sampling method for this scenario would be a probability-based method called Simple Random Sampling.

In Simple Random Sampling, each individual from the population of individuals who have high cholesterol has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and that each individual in the population has a known non-zero probability of being selected.

This method can be supported by the fact that it is easy to implement, and it does not require any prior knowledge of the population characteristics. It also ensures that the sample is unbiased and has a good chance of being representative of the population.

Additionally, Simple Random Sampling is also a cost-effective sampling method as it is less expensive and time-consuming than other sampling methods such as stratified random sampling or cluster sampling.

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The potential energy of a 50kg boulder at the ledge of a cliff 250m high is 122500 J.

Potential energy is the energy carried by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The PE energy of a boulder 250 m from the ground is given by the formula

PE = h x m x g    where h is the height above the ground, m is the mass, and g is the acceleration of gravity.

Putting the given values in the equation

PE = 250m x 50 kg x 9.8 m/s²  =  122500 J

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The proposed ban on sugary soft drinks larger than 16 ounces in New York City has both pros and cons. Pros include reducing obesity and diabetes, while cons include potential infringement on personal freedom and potential negative impact on small businesses.

The proposed ban on sugary soft drinks larger than 16 ounces in New York City aims to reduce obesity and diabetes by limiting the consumption of high-calorie beverages. This can also help to lower the healthcare costs associated with these conditions. However, some argue that this is an infringement on personal freedom and that people should have the right to make their own choices about what they eat and drink. Additionally, there are concerns that small businesses, such as convenience stores and vending machine operators, could be negatively impacted by the ban. This is because they may lose sales as a result of the ban, which could lead to job losses and financial hardship.

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Answer:

L^2 = area of square = As

As = 14 L H / 2      where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7    or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2        area of square

H = 7     height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2      Seems to checkout

The probability that a randomly selected family owns a dog or a cat is 0.61 and family owns a dog or doesn't own a cat is 0.39

AS we all know the rule of the probability is defined as the amalgamation of set theory and the probability theory yields some rules which form a part of the basic probability theory

Here we have listed down the rules as Multiplication Rule, Addition Rule and Complement Rule

Here we have given Information the following that is written as

=> Probability that a family can own a dog = 0.38.

=> Probability that a family can own a cat = 0.23.

Then the probability that a randomly selected family owns a dog or a cat is calculated as follows,

=> (0.38 + 0.23)

=> 0.61

And the the probability that a randomly selected family owns a dog or doesn't own a cat.

=> 1 - (0.38 + 0.23)

=> 1 - 0.61

=> 0.39

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There are 37,837,800 ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively.

We are trying to find the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that each box has 1, 2, 3, 4, and 5 objects in them, respectively.

We can use the formula for combination to solve this problem. The number of ways to distribute n distinct objects into r distinct boxes where the first box has k1 objects, the second box has k2 objects, ..., and the last box has kr objects is:

n! / (k1! * k2! * ... * kr!)

Where n! is the factorial of n, k1! is the factorial of k1 and so on.

In this case, we have 15 distinct objects and 5 distinct boxes where the first box has 1 object, the second box has 2 objects, the third box has 3 objects, the fourth box has 4 objects, and the fifth box has 5 objects.

So, the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively is:

15! / (1! * 2! * 3! * 4! * 5!) = 15! / (1×2×6×24×120)

= 37,837,800

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Answer:

84

Step-by-step explanation:

this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°

48° +48° =96°

180°- 96° = 84°

<ABC = 84°

Answer: x=5

Step-by-step explanation:

[tex]\displaystyle(\frac{125}{27} )*(\frac{125}{27} )^x=(\frac{5}{3})^{18} \\\\(\frac{5^3}{3^3})*(\frac{5^3}{3^3})^x=(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*((\frac{5}{3})^3)^x =(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3*x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3})^{3x+3}= (\frac{5}{3} )^{18}\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\[/tex]

Divide both parts of the equation by 3:

[tex]x=5[/tex]

The length in order for the quadrilateral JKLM to be a parallelogram are:

i. JK = 10

ii. JL = 7

A quadrilateral is a family of shapes or figures which has four straight sides, and four measures of internal angles. Examples are: trapezium, rhombus, kite, square, parallelogram etc.

To determine the length of each sides, we have;

opposite sides of a parallelogram are equal, so that;

3x - 2 = x - 6

collect like terms

3x - x =  2 + 6

2x = 8

x = 4

Thus,

i. JK = 3x - 2

       = 3(4) - 2

       = 12 - 2

JK = 10

ii. JL = 2x - 1

         = 2(4) - 1

         = 8 - 1

JL = 7

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The percent error of Alex's measurement is 5.714%.

Percent error is a measure of how accurate a measurement is compared to the true value. It is calculated by taking the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplying by 100%.

In this case, the measured value is 3.7 cm and the true value is 3.5 cm.

To calculate the percent error, we can use the following formula:

Percent error = |(measured value - true value) / true value| x 100%

Plugging in the given values, we get:

Percent error = |(3.7 - 3.5) / 3.5| x 100%

= |0.2 / 3.5| x 100%

= 0.05714 x 100%

= 5.714%

This means that Alex's measurement is off by 5.714% from the true value, indicating that the measurement has a low accuracy.

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Answer:

50.3 square units

Step-by-step explanation:

area of rectangle: 11 x twice the radius

radius = 2

A(rect): = 11(4) = 44 sq units

A (semi-circle) = (π·r²) / 2

A = 4π / 2 = 2π = 6.28 sq units

44.0 + 6.28 = 50.28

You can get a number between two numbers by adding the two numbers together and then dividing by two.

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On solving the provided question, we can say that integral so the value = (2/108) [429981697] = 7962624,02

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas

∫C) y³ × ds = 7962624,02 surface units

 F (r(t)) =   y³ . = t³ .          r ( t³ , t )  then .    dr/dt = (3×t² , 1 )

|| dr/dt|| = √ ( 3×t²)² + (1)²

|| dr/dt|| = √9×t⁴ + 1

∫C) y³ × ds   = ∫∫R) F(r(t) × dr . =  ∫₀⁴ t³ ×√9×t⁴ + 1    ×dt

9×t⁴ + 1  = v .  then .    36×t³ ×dt = dv

And when  t = 4 .  then . v = 9×(4)⁴ + 1 . = 2305

integral

∫₁²³⁰⁵ [ 1/36)× √v × dv . =   (1/36) ×∫₁²³⁰⁵ (v)¹/² dv  

= (1/36)×(2/3) × v³/² |₁²³⁰⁵ = (2/108)× √v³|₁²³⁰⁵ =

= (2/108) [ √( 9×t⁴ + 1 )³|₀⁴ =  (2/108) [ √( 9⁴×4¹⁶ + 1  - √(9)⁴×0 + 1)

=  (2/108) [√( (9⁴×4¹⁶ + 1 ) . + 1 ]

= (2/108) [429981697]

= 7962624,02

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Answer:

0.0021645

Step-by-step explanation:

The value of 0/infinity is Zero but not undetermined value.

Generally zero in numerator and any other number in the denominator gives the result zero always. i.e 0/ x where x is any other number and the number can be real, imaginary or complex. But the case with infinity is different as zero upon infinity gives the result as zero only it's because infinity is never can be a member of set of number. Because infinity is  just an expression that is greater than any assignable quantity or countable number. In mathematics, the concept of infinity describes something  larger than the natural number. It usually describes something without a limit. This concept is not only used in the mathematics but also in physics. In mathematics and physics, this concept is utilized in a wide range of fields. The term infinity can also be employed for an extended number system.

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Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.

The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.

The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.

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The general solution of the given higher-order differential equation is y(x) = e2x + x2 + c4e3x + c5e-3x.

A general solution is an answer that can be applied to a wide range of problems. It is a broad-based approach that can be used to solve any problem, regardless of its complexity or specific details. General solutions take into account the overall goal of a problem, rather than its individual elements, and look for a way to achieve the desired result. Additionally, they are often easy to implement and can be applied to a variety of scenarios.

The general solution of the given higher-order differential equation, y(4) + y''' + y'' = 0, is given by

y(x) = c1e2x + c2e-2x + c3x2 + c4e3x + c5e-3x + c6x3.

Here, c1, c2, c3, c4, c5 and c6 are constants of integration.

To determine the values of these constants, we must use initial conditions. Suppose we are given y(0)=1 and y'(0)=2, then we can solve for the constants using this information.

Substituting y(0)=1 and y'(0)=2 into the equation, we get

1 = c1 + c2 + c3(0)2 + c4 + c5 + c6(0)3
2 = 2c3 + 3c6(0)2

Solving these equations, we get c1 = 1, c2 = 0, c3 = 1 and c6 = 0.

Therefore, the general solution of the given higher-order differential equation is

y(x) = e2x + x2 + c4e3x + c5e-3x.

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The provided integral may be expressed as follows using the following statement as a guide: 128/3 - 31 [tex]\sqrt{17}[/tex] /3

An integral in mathematics is either a number that depicts the area underneath the graph of a function over a specific period of time or a about before, the reversed of which includes the initial result (indefinite integral). To complete the whole, an essential component is required. The term crucial is a close synonym in this context. Integrals of functional and equations are a concept in mathematics. The word "aal" is derived from Middle English, which is derived from Latin Word integralis "thinking up unity," from Latin "with, entire."

To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]

Put [tex]$16+r^2=t^2$[/tex]

[tex]$2 r d r=2 t d t$[/tex]

[tex]$r d r=d t$[/tex]

[tex]$r=0 \Rightarrow t=4$[/tex]

[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} t d t$[/tex]

[tex]$=\left[\frac{t^3}{3}-16 t\right]_4^{\sqrt{7}}$[/tex]

[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]

[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

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Allocating the congressional seats among the states in a fair manner would mean that the seats per state would be:

The fairest way to allocate the seats in a fair manner would be by proportional representation where the population of a state determines the seats it gets in Congress.

State A seats :

= Population / Total population x Number of seats available

= 258 / 1, 858 x 90

= 13 seats

State B seats :

= 377 / 1, 858 x 90

= 18 seats

State C seats :

= 456 / 1, 858 x 90

= 22 seats

State D seats :

= 767 / 1, 858 x 90

= 37 seats

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The greatest number of police officers needed is 28.

In a scenario where there are n straight lines in a city, and none of the lines are parallel to each other, the maximum number of police officers needed at the intersections can be determined by using the summation formula. The summation formula for the series of numbers from 1 to n-1 is (n-1) * n / 2.

Thus, if there are 8 straight lines in a city, the maximum number of police officers needed at the intersections is (8-1) * 8 / 2 = 28. This is because there will be 8-1 = 7 intersection points in total, and at each intersection point, one police officer is needed.

It's important to note that this is the maximum number of officers needed and it assumes that all lines are intersecting at different points. In case of any parallel lines this number would be less.

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(a) Mean of given sample = 75

(b) Mean (60, 80) = 70

(c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

The given sample is (60, 70, 80, 90)

(a) Mean of sample = (60+70+80+90)/4 = 300/4 = 75

(b) Mean of any 2 of scores

let's take (60,80)

mean(60,80) = (60+80)/2 = 70

(c) All possible samples of size 2 are

(60,70), mean(60,70) = 65

(60,80), mean(60,80) = 70

(60,90), mean(60,90) = 75

(70,80), mean(70,80) = 75

(70,90), mean(70,90) = 80

(80,90), mean(80,90) = 85

Therefore, for the given sample (a) Mean of the sample = 75, (b) Mean (60, 80) = 70, (c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

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The complete question is:

How did the Chapter 6 test go? Today, we will be taking a sample from a population. We will use the average from the sample to estimate the average for the population. Let's start with a very simple example. My 5th period is very small. There were only 4 students who took the chapter 6 test. Their scores were: 60, 70, 80, and 90. Answer the following questions:

(a) Find the mean of the sample

(b) Take a sample of any 2 of the scores. Find the mean of your sample.

(c) Figure out all of the possible samples of size two. Calculate a sample mean for each sample of 2.

The coordinate pair of the given solution of the system would be= (g, h) (1,-8).

Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.

4g + h = -4 ---->. eq 1

12g + 2h = -4 ----> eq 2

Make h the subject of formula;

h = -4 - 4g -----> eq 3

Substitute equation 3 into equation 2;

12g + 2( -4 - 4g) = -4

12g - 8 -8g = -4

4g -8 = -4

4g = -4 +8

4g = 4

g = 4/4= 1

Solve for g = 1 in equation 1;

4(1) + h = -4

4 + h = -4

h = -4-4

h = -8

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