Mathematics College

f(x)=x^6+10x^4 - 11x^2

Answers

Answer 1

You can notice that the given function is symmetric respect to the y-axis.

It means that the value of the function for both x and -x is the same:

[tex]f(-x)=f(x)[/tex]

This is the characteristic of a even function.

Hence, the answer is B

Related Questions

Hello, I need some assistance with the following question. Q1.

Answers

Given the expression f/g

Which is a rational expression.

The domain is all real numbers of (x) except the zeros of the denominators

The zeros of the denominators can be calculated using the equation g(x)=0

So, the answer will be as follows:

The domain of f/g consists of numbers (x) for which g(x) ≠ 0 that are in the domains of both f and g

Find the average rate of change of f(x)=3x^2-8x from x=1 to x=6

Answers

Answer:

The answer is 13

If f(x) = 2x+3, what is f(-2)

Answers

Answer: f(-2) = -1

Step-by-step explanation:

2x + 3

2(-2) +3

-4 + 3

-1

Answer:

Step-by-step explanation:

you plug in the -2 to the equation for x

f(-2)= 2(-2)+3

f(-2)=-1

there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.

Answers

ANSWER

There are 8 kittens

EXPLANATION

If the sum of the number of adult cats, middle aged cats and kittens is 19:

[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]

factor the trinomial6x² + 17x + 12

Answers

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function

[tex]6x^2\text{ + 17x + 12}[/tex]

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes

[tex]\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}[/tex]

The factor of the above function is (2x + 3) (3x + 4)

Use the substitution u = (2x - 2) to evaluate the integral x³e(^2x^4-2) dx

Answers

The substitution u = (2x - 2) to the integral x³e(^2x^4-2) dx is (2x – 2)/4 +c

What is meant by integral?In mathematics, an integral assigns numerical values to functions in order to describe concepts like displacement, area, volume, and other outcomes of the combination of infinitesimally small data. Integral discovery is a process that is referred to as integration. One of the fundamental, crucial operations of calculus, along with differentiation, is integration[a]. It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape. The integrals listed here are those that fall under the category of definite integrals, which can be thought of as the signed area of the region in the plane that is enclosed by the graph of a particular function between two points on the real line.

Therefore,

Use the substitution

U = (2x -2)

to evaluate integral x³e(^2x^4-2) dx

let u = 2x -2

du = x dx or dx =du/2

u = 2x-2

du = d(2x – 2)

du = 2dx

dx = du/2

∫ (2x -2)dx = ∫u du/2

=1/2 ∫u du

= ½ u square /2 +c

= u square /4 +c

= (2x – 2)/4 +c

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The Cunninghams are moving across the country. Mr.Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 55 mph and sheaverages 75 mph, how many hours will it take Mrs. Cunningham to catch up to Mr. Cunninham to catch up to mr.cunningham

Answers

Solution:

Remember, distance traveled is the rate times the time. (d = rt) Mrs. Cunningham will overtake Mr. Cunningham when they have traveled the same distance.

Mrs. Cunningham's equation will be:

[tex]d=\text{ }75t[/tex]

Since he was traveling 3 hours longer, Mr. Cunningham's equation will be:

[tex]d=55(t+3)[/tex]

If they travel the same distance, the equations can be set equal to each other:

[tex]\text{ }75t=55(t+3)[/tex]

applying the distributive property, this is equivalent to:

[tex]\text{ }75t=55t\text{ +165}[/tex]

this is equivalent to:

[tex]75t-55t\text{ = 165}[/tex]

this is equivalent to:

[tex]20t\text{ = 165}[/tex]

solving for t, we obtain:

[tex]t\text{ =}\frac{165}{20}=8.25[/tex]

So that, we can conclude that the correct answer is:

It will take Mrs. Cunningham 8.25 hours to overtake her husband.

Can someone please help me with this drag and drop? I would appreciate It a lot! Please explain :) I’ll give brainliest

Answers

Answer:

move B to true then everything is right ✅

Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?

Answers

Okay, here we have this:

Considering the provided information we obtain the following:

Replacing in the Compound Interest formula we obtain the following:

[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]

After 1 year (t=1):

[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]

We obtain that after one year the balance is aproximately $17,161.06.

After 2 years (t=2):

[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]

We obtain that after two years the balance is aproximately $18,331.90

After 5 years (t=5):

[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]

We obtain that after five years the balance is aproximately $22,345.90.

After 10 years (t=10):

[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]

We obtain that after ten years the balance is aproximately $31,082.44.

In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:

[tex]32130=16065e^{0.066t}[/tex]

Let's solve for t:

[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]

Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.

Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(

Answers

Answer:

The correct option is D

8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares

Explanation:

To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.

The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).

The area of a square is the square of its side length.

Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.

[tex]2\sqrt[]{3},4,2\sqrt[]{5}[/tex]

This is NOT a Pythagorean triple.

[tex]\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}[/tex]

This is NOT a Pythagorean triple.

[tex]2,\sqrt[]{5},2\sqrt[]{3}[/tex]

This is NOT a Pythagorean triple

[tex]2\sqrt[]{2},4,2\sqrt[]{6}[/tex]

This is a Pythagorean triple.

CHECK[tex]\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}[/tex]

Yea I can see if it works if it’s okay

Answers

SOLUTION

We want to find the derivative of

[tex]y=sin(1.2t-3.7)[/tex]

(a) So, using chain rule, the inside function is u,

we have the inside:

[tex]u=1.2t-3.7[/tex]

outside becomes

[tex]y=sin(u)[/tex]

(b) The derivative of

inside, we have

[tex]\frac{du}{dt}=1.2[/tex]

derivative of the outside, we have

[tex]\frac{dy}{du}=cos(u)[/tex]

chain rule we have

[tex]\begin{gathered} \frac{dy}{dt}=\frac{dy}{du}\times\frac{du}{dt} \\ =cos(u)\times1.2 \\ =cos(1.2t-3.7)\times1.2 \end{gathered}[/tex]

Hence the answer is

[tex]\frac{dy}{dt}=1.2cos(1.2t-3.7)[/tex]

A manager measured the number of goods, y, that his company produced in a hours. The
company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45
goods.
Which equation, in point-slope form, correctly represents the goods produced by the company
after x hours?
Oy-45 = 5(x-9)
Oy+9= 5(x +45)
Oy 45= 5(x + 9)
Oy-9=5(x - 45)

Answers

Answer:

[tex]y-45=5(x-9)[/tex]

Step-by-step explanation:

Definition of the variables:

y = total number of goods produced.x = time in hours.

Given information:

The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.

As the rate of change is constant and linear, the rate of change is the slope of the line. Therefore, the slope is 5.

At hour 9 (x-value) the company had produced 45 (y-value) goods. Therefore, this can be represented by the point (9, 45).

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-45=5(x-9)[/tex]

Therefore, the equation that correctly represents the goods produced by the company after x hours is:

[tex]\boxed{y-45=5(x-9)}[/tex]

the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?

Answers

Answer:

-144 feet

Step-by-step explanation:

-211 plus the added 67 feet it is above equals an altitude of -144ft

find the value of x

Answers

For supplementary angles, we can do the following equality

[tex]3x+4=x+70[/tex]

What we have to do, is to clear "x" to find its value.

[tex]\begin{gathered} 3x-x=70-4 \\ 2x=66 \\ x=\frac{66}{2} \\ x=33 \end{gathered}[/tex]

In conclusion, the value of x is 33

Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in 4 years? ƒ(t) = ae^rt

Answers

To determine the amount that will be on the account after 4 years you have to apply the given exponential function that models the amount of money on the account with respect to the time.

[tex]f(t)=ae^{rt}[/tex]

Where

a represents the initial amount

r represents the interest rate expressed as a decimal value

t is the time period in years

The initial amount on the account is a= $600

The time period is t= 4 years

The interest rate is r=5%, divide it by 100 to express it as a decimal value:

[tex]r=\frac{5}{100}=0.05[/tex]

Using this information, you can calculate the final amount:

[tex]\begin{gathered} f(t)=ae^{rt} \\ f(4)=600e^{0.05\cdot4} \\ f(4)=600e^{0.2} \\ f(4)=732.84 \end{gathered}[/tex]

After 4 years there will be $732.84 on the account. The correct option is B.

7. 4×= 3yy=-4x + 39. y+2=0x+ 2 = 011.x-5y=45x + y = 4Determine if the graphs will show parallel or perpendicular lines, or neither.

Answers

Given:

[tex]\begin{gathered} 4x=3y \\ y=-4x+3 \end{gathered}[/tex]

Sol:.

If the both line are perpendicular then multipilcation of slope is -1 then:

[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=4x \\ y=\frac{4}{3}x \\ m_1=\frac{4}{3} \end{gathered}[/tex][tex]\begin{gathered} y=-4x+3 \\ m_2=-4 \end{gathered}[/tex][tex]\begin{gathered} =m_1m_2 \\ =\frac{4}{3}\times-4 \\ m_1m_2\ne-1 \\ \text{That mean its not perpendicular } \end{gathered}[/tex]

For parallel line slope are same then its not a parallel line

So line neither perpendicular or parallel.

I need help with this question Write and expression that models the situation:Sarah has spent x dollars out of the 30 dollars she started with.

Answers

Okay, here we have this:

Considering that it says "spent", it represents an outflow of money, therefore we take it as negative, so we obtain:

Actual Situation: Initial money - money spent

Actual Situation: 30 - x

A number cube is rolled once, {1,2,3,4,5,6)Determine the likelihood of each situation,Column AColumn B1.rolling an even numbera. unlikely2.rolling a 7b. impossible3.rolling a number greater than 0Ccertain4.rolling a number that is greater than 2d. likely5.rolling a 2 or 3e equally likely

Answers

The likelihood of the following situations:

1. rolling an even number is likely.

2. rolling a 7 is impossible.

3. rolling a number greater than 0 is certain.

4. rolling a number that is greater than 2 is likely.

5. rolling a 2 or 3 is equally likely

Factor the following polynomials. Remember, factoring strategies for quadratic polynomials may be needed here.

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For this problem, we are given a polynomial, and we need to factor it.

The polynomial is given below:

[tex]64-324x^4[/tex]

We can use the difference between two squares to factor this polynomial. The base form of this notable product is shown below:

[tex]\begin{gathered} (a-b)(a+b)=a^2-b^2\\ \\ \end{gathered}[/tex]

We can do the same with the original polynomial:

[tex]64-324x^4=8^2-(18x^2)^2=(8-18x^2)(8+18x^2)[/tex]

The answer is (8-18x²)(8+18x²).

he multiplication table below can be used to find equivalent ratios.

A multiplication table.

Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30

Answers

Answer:

15:20

Step-by-step explanation:

18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]

I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]

[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]

number one name three collinear points number to name four coplanar Point number three name two sets of lines intersect number for name two points not contained in the plane

Answers

The points lying on a single line are called colinear points. So here,

KJD are colinear points as they are lying on a same line.

Points lying on the same plane are called coplanar points. So here, IJFE are coplanar points.

The two sets of line intesects are KD and CF, IG and FH.

The two points that are not in the plane are A and B.

50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?

Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?

Answers

The expression that represents the area of the rectangle is 6x²+29x+35.

Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.

What is the area of a rectangle?

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Part A:

Now, area = (2x+5)(3x+7)

= 2x(3x+7)+5(3x+7)

= 6x²+14x+15x+35

= 6x²+29x+35

So, the area of a rectangle is 6x²+29x+35

Part B:

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

Here, the degree of the expression 6x²+29x+35 is 2.

Part C:

Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.

Here, we obtained product of two binomials is trinomial

Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.

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The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =

For part c) and e), Is the assumption of normal necessary? NoYes

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem: