Mathematics College

Here are two expressions whose product is a new expression, A: 1. What could we put in the boxes to make A be a polynomial?

Answers

Answer 1

We are given the following product:

[tex](-2x{}^3+B)(x^n+15)=A[/tex]

For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:

[tex]ax^n[/tex]

We will use a constant. We will substitute the first box for "1":

[tex](-2x^3+1)(x^n+15)=A[/tex]

For the second box, we need to use an exponent that is a positive whole number.

We will use 2:

[tex](-2x^3+1)(x^2+15)=A[/tex]

With these values, the result of the product is a polynomial.

Related Questions

Z divided 12 equal 9

Answers

Answer:

108

Step-by-step explanation:

12×9=108

just for the extra characters

Answer:

108

Step-by-step explanation:

z/12 = 9

z = 9 × 12

z = 108

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A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, then at what annual rate is the population growing? Round the answer to the nearest tenth of a percent.

Answers

The population is growing at an annual rate of 16.2%

Here, we want to calculate the exponential growth rate

Mathematically, we can write the exponential equation of growth as follows;

[tex]\begin{gathered} P=I(1+r)^t \\ \\ \end{gathered}[/tex]

Where P is the population after a certain number of years ( 270 after 3 years

I is the initial popultaion which is 200

r is the percentage we want to calculate

t is the number of yeats to reach P which is 3 in this case

[tex]\begin{gathered} 270=200(1+r)^3 \\ (1+r)^{3\text{ }}\text{ = }\frac{270}{200} \\ \\ (1+r)^3\text{ = 1.35} \\ \\ 1\text{ + r = }\sqrt[3]{1.35} \\ \\ 1\text{ + r = 1.162} \\ \\ r\text{ = 1.162 - 1} \\ \\ r\text{ = 0.162} \end{gathered}[/tex]

To the nearest tenth of a percentage, this is 16.2%

The state transportation commission counted cars traveling east and west across a toll bridge. 75% of the 588 cars counted were traveling east. How many eastbound cars did the commission count?

Answers

Answer: the answer is 441

Step-by-step explanation: 75% of 588 is 441

Ainsley had 3 yards of string. She used 1/4 yard for a project. She wants to divide the rest into pieces 5/6 yard long. How many pieces can she make?

Answers

She can make 3.3 pieces from the remaining length

How to determine the number of pieces to make?

From the question, the given parameters are:

Length of string = 3 yardsAmount used for project = 1/4 yardLength of each piece = 5/6 yard

We start by calculating the length of the remaining pieces as a whole

This is calculated as

Length of remaining piece + length used for project = Length of string

Substitute the known values in the above equation

So, we have

Length of remaining piece + 1/4 yard = 3 yards

Subtract 1/4 from both sides

Length of remaining piece = 2.75 yards

The number of pieces is then calculated as

Pieces = Length of remaining pieces/Length of each piece

This gives

Pieces = 2.75 yards/(5/6 yards)

Evaluate the quotient

Pieces = 3.3

Hence, the number of pieces she can make is 3.3

Answers

Angle IJL is 54 because congruent angles have equal measure.

What are congruent angles?

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.

According to question, angle m IKL = 54

And AB// CD and EF// GH

Angle IKL is alternate interior angle to angle HLK

m angle HLK= m angle IKL (congruent angles have equal measure)

m angle HLK= 54

Similarly, m angle IJL = m angle HLK

Hence, angle IJL= 54

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1. Fiber-Brite could clean 48 rugs in 12 hours. At that rate, how many rugs could Fiber-Brite
clean in 20 hours?

Answers

80 rugs cleaned in 20 hours

Translate Pre image coordinates right 14 units and up 13 units.

Answers

We will have the following:

We translate the points:

A(-12, 3)

B(-6, -3)

C(-12, -9)

The transformation rule is (x, y) -> (x + 14, y + 13); so:

A'(2, 16)

B'(8, 10)

C'(2, 4)

how do I find the given z score

Answers

The formula for calculating a z-score is

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Where:

*x is the raw score

*μ is the population mean

*σ is the population standard deviation

twice the difference of a number 4 is 5.

Answers

Answer:25

Step-by-step explanation:

what is the shape of a cross section that is perpendicular to the basis

Answers

If we get the cross section perpendicular to the base of this image, we would get the same shape as the image.

Through the diagram, we can see that if we cut the image to get the cross section perpendicular to its base, we would get the same shape as the image, which is a pentagon.

Roseanne makes 1 1/2 of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does Roseanne's brother drink? Which expression can be used to determine the amount of lemonade Roseanne's brother drank? A. 1 1/2 - (1/4 x 2/5) B. (1 1/2 + 1/4) x 2/5 C. (1 1/2 - 1/4) x 2/5 D. (1 1/2 - 1/4) ÷ 2/5

Answers

we know that

the total lemonade is 1 1/2 liter

She pours 1/4 of a liter of lemonade into a thermos

Her brother drinks 2/5 of the remaining lemonade

the remaining lemonade is equal to

1 1/2-1/4=3/2-1/4=5/4 liters

Multiply by 2/5

(5/4)(2/5)=10/20=1/2 liter

therefore

answer is option

C. (1 1/2 - 1/4) x 2/5

The formula for the area of a triangle is A = -bh, in which b represents the length of the base and h2represents the height. If a triangle has an area of 115 mm2 and the height is 10 mm, what is the measureof the base?The measure of the base ismm.

Answers

The formula for the area of a triangle is A is;

S is the midpoint of segment OU. OS= 7x-9 and SU=4x+3. Determine the length of segment OU.

Answers

Answer:

The equation for the value of OU is;

[tex]OU=11x-6[/tex]

Explanation:

Given that S is the midpoint of segment OU.

Then;

[tex]OU=OS+SU[/tex]

Given in the question;

[tex]\begin{gathered} OS=7x-9 \\ SU=4x+3 \end{gathered}[/tex]

Substituting the values of OS and SU to get OU;

[tex]\begin{gathered} OU=OS+SU \\ OU=7x-9+4x+3 \\ OU=7x+4x-9+3 \\ OU=11x-6 \end{gathered}[/tex]

Therefore, the equation for the value of OU is;

[tex]OU=11x-6[/tex]

given the preimage coordinates complete the translation provide and give the image Coordinates

Answers

The coordinates are made up of an x-coordinate and a y-coordinate, written in the form (x, y), the translation given is (x + 1, y - 1), which means adding +1 to all x-coordinates and subtracting -1 to all y-coordinate.

Then, the pair B(0, -4) will be transformed into B'(0 + 1, -4 - 1) → B'( 1, -5)

C( -1, 1) → C' (-1 + 1, 1 - 1) → C'( 0, 0)

D( 1, 3) → D' ( 1 + 1, 3 - 1) → D'( 2, 2)

E( 4, -1) → E' ( 4 + 1, -1 - 1) → E'( 5, -2)

The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?

Answers

Answer:

If the half-life of a nuclide is 44.5 days, then 178 days is four half-lives.

explanation:

After four half-lives, 0.0625 (0.54) of the original nuclides remains. If 50g is the original mass, then the mass after 4 half-lives is 3.125g.

AT = A0 2(-T/H)

A178 = (50) 2(-44.5/178)

A178 = 3.125

4 thousands +12 hundreds =

Answers

Answer:

that's too easy

4 thousands=4000

12 hundreds=120

4000+120=4120

4 thousands and 12 hundreds

4000
4000+
4000+120
4000+120=
Answer is 4,120

(4,000+120=4,120)

2 5 4 Q Find the area of the shaded region above.

Answers

As you can see in the given figure, there are two different shapes.

One is a rectangle and the other is a triangle.

Recall that the area of a rectangle is given by

[tex]A_R=L\cdot W[/tex]

Where L is the length and W is the width.

As you can see from the figure,

W = 4

L = 5

So the area of the rectangle is

[tex]A_R=L\cdot W=5\cdot4=20[/tex]

Recall that the area of a triangle is given by

[tex]A_T=\frac{1}{2}\cdot b\cdot h[/tex]

Where b is the base of the triangle and h is the height of the triangle.

As you can see from the figure,

b = 4

h = 2

So the area of the triangle is

[tex]A_T=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot4\cdot2=\frac{1}{2}\cdot8=\frac{8}{2}=4[/tex]

Now the total area of the shaded region is the sum of the area of the rectangle and the area of the triangle.

[tex]A=A_R+A_T=20+4=24[/tex]

Therefore, the area of the shaded region is 24

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Determine the odds against rolling a 4 on one roll
of a die.
Solution
P(4)=1
6
5
P (fails to roll a 4)=-
6

Answers

Answer:

1/6

Step-by-step explanation:

SIX possible rolls 1,2,3,4,5,6

4 is 1 out of 6 or 1/6

Find the percentage decrease and round to the nearest tenth

Answers

Answer:

16.6%

Step-by-step explanation:

First, find the difference between the prices:

$3.95 - $3.45 = $0.50

Then, divide the difference by yesterday's price.

$0.50 ÷ $3.95

≈ 0.166

≈ 16.6%

Answer:

12.7%

Step-by-step explanation:

$3.95 - $3.45 = $.50

$.50 / $3.95 = .127 = 12.7%

can you give me some examples of how to simplify

Answers

Let's check out the expression

[tex]2x+4+6y+7+2+3x[/tex]

To simplify, you have to add up similar terms. That is, add up everything that has an x, add up everything that has a y, and add up every independent term (no variable), as following:

[tex]\begin{gathered} 2x+4+6y+7+2+3x\rightarrow2x+3x+6y+4+7+2 \\ \rightarrow5x+6y+13 \end{gathered}[/tex]

And there we have the simplified expression.

Which of the following lists of data has the largest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:22, 25, 25, 22, 25, 23, 24, 23, 26, 2413, 11, 11, 11, 10, 14, 14, 10, 11, 1116, 14, 15, 15, 16, 16, 15, 16, 18, 1425, 23, 25, 22, 21, 25, 22, 21, 25, 237, 14, 19, 18, 4, 16, 5, 11, 11, 12

Answers

Answer:

7, 14, 19, 18, 4, 16, 5, 11, 11, 12

Explanation:

The standard deviation is a statistic that measures the spread of a dataset relative to its mean.

From the given options, find the range in each of them:

[tex]Range=Highest\;Value-Lowest\;Value[/tex]

• Option 1: Range = 26-22=4

• Option 2: Range=14-10=4

• Option 3: Range=18-14=4

• Option 4: Range = 25-21=4

• Option 5: Range = 19-4=15

We see that the dataset in Option 5 has a far greater range and thus the dataset will have the biggest spread relative to its mean.

Option 5 has the largest standard deviation.

The table shows a proportional relationship.

x 12 8 24
y 3 2 6

Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).

Answers

A graph of which best describes what the proportional relationship would look like is: D. A line passes through the point (0, 0) and continues through the point (12, 3).

What is a graph?

In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Additionally, a graph that represents a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).

Since the graph represents a proportional relationship we have:

Constant of proportionality, k = 12/3 = 8/2 = 24/6 = 4

Ratio = 24:6 = 12:3.

Therefore, (0, 0) and (12, 3) are points on this graph that represents a proportional relationship.

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Answer:d

Step-by-step explanation:trust

Solve and check the equation X-23=16

Answers

Answer:x=39

Step-by-step explanation:

x-23=16

x=16+23

x=39

Which of the following would result in an integer?
O a.) 120
O b.) √144
O c.) √52
O d.) √24

Answers

The answer is either Option (a) or option(b) or both the options i.e, 120 or √144

What is Integer ?

An integer is a whole number from the set of -ve , non-negative , +ve and 0 numbers.

Let's see how both the option is correct

we know, integers are 0,1, 2, 3, .... or -1, -2 , -3 ......

Means the number which is not in fraction or decimal value or root.

so, by seeing option(a) we can say it's an integer

but in option(b) it's the root so how it is integer

The answer is simple it's perfect square of 12 so √144 = 12 so that means it have the value which is not in fraction. By that we can say that option(b) is also an integer

Now, in option(c) and (d) they are not the perfect square and their root results in decimal values. so we cannot tell them as an integer value.

Hence, the answer is either Option (a) or option(b) or both the options.

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if the sum of the first three terms of a GP is half it's sum to infinity. find it's positive common ratio.

Answers

Answer:

See below

Step-by-step explanation:

Sum of n = inf = a / ( 1-r) one half of this = 1/2 ( a/(1-r) )

Sum of first 3 terms = a ( 1- r^n) / ( 1-r) = a (1-r^3) / (1-r)

The underlined value are equal ( given in the Q)

1/2 a / (1-r) = a ( 1-r^3) / (1-r) Multiply both side by ( (1-r) )

1/2 a = a ( 1-r^3) divide both sides by a

1/2 = 1- r^3 subtract 1 from both sides

-1/2 = - r^3

1/2 = r ^3

r = cuberoot ( 1/2) = 1/2 ^(1/3) = .793700526

question shown in picture below!!(i only need the 2nd one)

Answers

Given the following sequence:

[tex]\mleft\lbrace17,14,11,8,\ldots\mright\rbrace[/tex]

notice that the common difference between each term is -3, therefore, we can use the explicit formula for a sequence:

[tex]\begin{gathered} a_n=a_1+(n-1)\cdot d \\ d=-3 \\ a_1=17 \\ \Rightarrow a_n=17+(n-1)(-3) \\ \Rightarrow a_n=17-3n+3=20-3n \\ a_n=20-3n \end{gathered}[/tex]

we have that the explicit formula is a_n=20-3n, while the recursive formula is:

[tex]\begin{gathered} a_n=a_{n-1}+d \\ d=-3 \\ \Rightarrow a_n=a_{n-1}-3 \end{gathered}[/tex]

1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?

Answers

[tex]x+y+z=107[/tex]

where x is the first, y the second and z the third

the second gear has 13 more teeth than the first gear

[tex]x+13=y[/tex]

The third gear has 15 more teeth than the second gear

[tex]y+15=z[/tex]

we need solve z form the third equation and solve x from the second equation an replace on the first

[tex]\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}[/tex]

replacing

[tex]\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}[/tex]

so, the second gear have 35 teeth

I need help with the question above. I took a picture of it.

Answers

The answer is: It will be a line.

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the around it to two decimal places if necessary.8i4 + 5i

Answers

SOLUTION

The given complex expression is:

[tex]\frac{-8i}{4+5i}[/tex]

Rationalize the denominator

This gives

[tex]\begin{gathered} \frac{-8i}{4+5i}\times\frac{4-5i}{4-5i} \\ =\frac{-32i-40}{16+25} \\ =-\frac{40}{41}-\frac{32i}{41} \end{gathered}[/tex]

Evaluate: base 6 exponent 0

Answers

Answer:

Explanation:

Given:

[tex]6^0[/tex]

To evaluate the expression above, apply the law of indices below.

[tex]a^0=1,a\neq0[/tex]

That is, whenever a number (except 0) is raised to the power of 0, the result is always 1.

Therefore:

[tex]6^0=1[/tex]

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