Find ( f+g ) (x) for each of the following functions

Find ( F+g ) (x) For Each Of The Following Functions

Answers

Answer 1

Answer:

(f + g)(x) = 2x³ + 3x² + x + 2

Explanation:

If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)

Then, we can simplify the expression adding the like terms, so

(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5

(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)

(f + g)(x) = 2x³ + 3x² + x + 2

Therefore, the answer is:

(f + g)(x) = 2x³ + 3x² + x + 2


Related Questions

can you help me solve this in expanded form. 156 X 687 = ?

Answers

Given data:

The given expression is 156x687.

The given expression can be written as,

[tex]\begin{gathered} (100+50+6)(600+80+7)=60000+8000+700+30000+4000+350+3600+480+42 \\ =107172 \end{gathered}[/tex]

Thus, the value of the given expression is 107172.

Your cousin is building a Sandbox for his daughter how much sand will he need to fill the Box? Explain. How much paint will he need to paint all six surface of the sandbox? Explain. 1ft 4ft 6ft not answer choices

Answers

Since the image is a rectangular prism

The volume of the box can be obtained by using the formula:

Volume = l x b x h

The box has a dimension of 1ft x 4ft x 6ft

The volume of the box = 1 x 4 x 6 = 24 cubic feet

Therefore, the volume of sand needed to fill the box will be = 24 cubic feet of sand

The surface area of the box can be obtained using the formula:

2(lb + lh + bh)

= 2(1x4 + 1x6 + 4x6)

=2(4 + 6 + 24)

=2 (34)

= 68 square feet

Therefore a total surface area of 68 square feet needs to be painted

this lettuce i have is 25 calories per serving. serving size is 85 grams. i had 27 grams. how many calories would that be??

Answers

Answer:

7.94117647059 Calories

Step-by-step explanation:

25 Calories = 85 Grams

25/85 = 0.294117647059

0.294117647059 = 1 Gram

0.294117647059 times 27 = 7.94117647059

Section 5.2-10. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).-2x+3y = 15-x-3y = 12

Answers

[tex]-2x+3y=15\ldots\ldots1)[/tex][tex]-x-3y=12\ldots\ldots\ldots\ldots\text{2)}[/tex]

1)-2x2)

[tex]-2x+3y-(-2x-6y)=15-2\times12\Rightarrow-2x+3y+2x+6y=15-24\Rightarrow9y=-9\Rightarrow y=-1[/tex]

y=-1 implies

[tex]-2x+3\times(-1)=15\Rightarrow-2x-3=15\Rightarrow-2x=18\Rightarrow x=-9[/tex]

Hence the solution is

[tex](-9,-1)[/tex]

A bookstore sells a college algebra book for $90. If the bookstore makes a profit of 25% on each sale,what does the bookstore pay the publisher for each book?

Answers

Okay, here we have this:

Considering the provided information, we obtain that:

The total price = Commission of the bookstore + Payment to the publisher

Replacing:

$90=$90(0.25)+Payment to the publisher

Payment to the publisher=$90-$90(0.25)

Payment to the publisher=$90-$22.5

Payment to the publisher=$67.5

Finally we obtain that the bookstore pay $67.5 to the publisher for each book.

the ratio of the length to the width of a rectangular hall is 5:3. if the width is 1500cm, find the lenght.​

Answers

Answer:Length of the rectangle= 2500 cm

Step-by-step explanation:

The ratio of the length to the width that is- length:width = 5:3

Take x as a common value,

5x= length

3x= width

Width of the rectangle= 1500 cm

3x= 1500 cm

x= 1500/3

x= 500 cm

Length of the rectangle= 5x

x=500 cm

Length= 5*500

=2500 cm

Length of the rectangle= 2500 cm

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The general form of an ellipse is 15x2+4y2+30x−16y−29=0.

What is the standard form of the ellipse?

Answers

The equation of ellipse in standard form is (x + 1)² / 4 + (y - 2)² / 15 = 1.

How to determine the standard form of the ellipse

In this problem we find the equation of an ellipse in general form, whose standard form can be found by algebra properties. The general form of the equation of an ellipse centered at (h, k) is introduced below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

a, b - Lengths of the semiaxes.(h, k) - Coordinates of the center.

The complete procedure is now presented:

15 · x² + 4 · y² + 30 · x - 16 · y - 29 = 0

(15 · x² + 30 · x) + (4 · y² - 16 · y) = 29

15 · (x² + 2 · x) + 4 · (y² - 4 · y) = 29

15 · (x² + 2 · x + 1) + 4 · (y² - 4 · y + 4) = 29 + 15 · 1 + 4 · 4

15 · (x + 1)² + 4 · (y - 2)² = 29 + 15 + 16

15 · (x + 1)² + 4 · (y - 2)² = 60

(x + 1)² / 4 + (y - 2)² / 15 = 1

The equation of ellipse is (x + 1)² / 4 + (y - 2)² / 15 = 1.

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need help asap look at attachmen

Answers

The rectangle has a width of 7 yards and a length of 42 yards.

How to find the length and width?

For a rectangle of length L and width W, the perimeter is:

P  = 2*(L + W)

Here we know that:

L = 6*W

P = 98yd =  2*(L + W)

Then we have the system of equations:

L = 6*W

98yd =  2*(L + W)

If we substitute the first equation into the second one, we get:

98yd = 2*(6*W + W)

98yd = 14*W

98yd/14 = W = 7yd

So the width is 7 yards, and the length is 6 times that, so:

L = 6*7yd = 42yd

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CASSANDRA WENT FOR A JO9.SHE RAN AT A PACE OF 7.3 MILESPER HOUR. IF SHE RAN FOR 0.75HOURS, HOW FAR DID CASSANDRARUN?

Answers

We can use one simple formula, that is d=vt

d=distance

v=pace

t=time

So,

d=(7.3miles per hour)(0.75 hours)=5.475 miles

what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14

Answers

The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.

How to Find the Solution Set of an Inequality?

The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.

Using the key to the given model in the diagram, we can write the inequality as follows:

On the left, we would have, 4x + 12.

On the right, we would have, -8.

The inequality would be expressed as:

4x + 12 ≤ -8

Solve for x

4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]

4x ≤ -20

4x/4 ≤ -20/4

x ≤ -5

The solution set is: A. x ≤ -5.

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4. A teacher can only make 3000 copies in a month. If a teacher-has-made 2700 copies so far this month, what percentage of her copies has she used?

Answers

In order to determine the percentage, let x as the percentage. Then, you can write:

[tex]\frac{x}{100}\cdot3000=2700[/tex]

factor x/100 is the percentage in decimal form. The product of this factor and 3000 equals 2700.

Solve for x and simplify:

[tex]x=\frac{2700}{3000}\cdot100=90[/tex]

Hence, teacher has used 90% of the copies.

Can I Plss get some help I got stuck I don’t know how to find x

Answers

Using Sine of angles to evaluate for x

The formula is,

[tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex]

Given:

[tex]\begin{gathered} Opposite=x \\ Hypotenuse=19 \\ \theta=21^0 \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} sin21^0=\frac{x}{19} \\ \therefore x=19\times sin21^0 \end{gathered}[/tex]

Simplify

[tex]x=6.80899\approx6.81\text{ \lparen2 decimal places\rparen}[/tex]

Hence,

[tex]x=6.81[/tex]

Find the distance between:(4,-9) and(-8,0)Round your answer to the nearest hundredth.

Answers

The distance between 2 points (x1, y1) and (x2, y2) is calculated as:

[tex]\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:

[tex]\begin{gathered} \text{distance}=\sqrt{(-8-4)^2+(0-(-9))^2} \\ \text{distance}=\sqrt{(-12)^2+(9)^2} \\ \text{distance}=\sqrt{144+81} \\ \text{distance}=\sqrt{225} \\ \text{distance}=15 \end{gathered}[/tex]

Answer: the distance is 15

How would these look graphed ? Look at image attached .

Answers

These are two lines intersected ,in one point

One is positive inclined, the other negative.

Then now GRAPH

THEN BOTH LINES INTERSECT AT

a regular octagon has an area of 49 m 2 . find the scale factor of this octagon to a similar octagon with an area of 100 m 2

Answers

Given,

The area of the regular octagon is 49 square metre.

The area of the another regular octagon is 100 square metre.

[tex]\begin{gathered} \text{Scaling factor=}\frac{\sqrt{\text{area of regular polygon}}}{\sqrt[]{\text{area of another regular plogon}}\text{ }} \\ \text{Scaling factor=}\frac{\sqrt[]{\text{4}9}}{\sqrt[]{\text{1}00}\text{ }} \\ \text{Scaling factor=}\frac{7}{10\text{ }} \end{gathered}[/tex]

Here, the scaling factor of the regualar octagon is 7:10

Hence, the scaling factor is 7:10.

For an arc length s, area of sector A, and central angle θ of a circle of radius r, find the indicated quantity for the given value. r= 6.45 in, θ= 5 pi\6, s=?

Answers

Calculate the arc length by using the following formula:

[tex]s=r\theta[/tex]

Replace the values of r and θ and simplify:

[tex]\begin{gathered} s=(6.45in)(5\frac{\pi}{6})=(6.45)(\frac{5}{6})(3.14) \\ s=16.8775in \end{gathered}[/tex]

Hence, the arc length is 16.8775 in

Which equation is equivalent to: 3r=78+14 ?A. −3r=−78+14B. 3r−14=78C. 3r=78−14D. −3r=78−14

Answers

Given[tex]3r=78+14[/tex][tex]3r-14=78[/tex]The final answerOption B

Use the times and corresponding closing prices of the stock to create coordinate pairs. Let X represent the number of weeks since the first at a point, and Y represent the closing price of each time. So, X equals zero represents the data point from five years ago. There are 52 weeks in a year, and you can write the time for each closing price recorded in terms of weeks that have passed since five years ago, when X equals zero. Fill in the table to represent your data as coordinate pairs

Answers

Combining both tables we get:

when graphed on a coordinate plane,Bumby Avenue can be represented by the equation y=-4x-7. primrose can be represented by the equation 8x+2y=17. Are these streets parallel ?

Answers

Answer:

The lines are not parallel because their slopes are opposite reciprocals.

Explanation:

The lines:

[tex]\begin{gathered} y=-4x-7 \\ \text{and} \\ 8x+2y=17 \end{gathered}[/tex]

are not parallel because their slopes are not the same

Note:

Two straight lines are said to be parallel when their slopes are the same, and have different y-intercepts.

Fiona is making a banner in the shape of a triangle for a school project. She graphs the banner on a coordinate plane with vertices at P(0, 4) , Q(2, 8) , and R(−3, 6) . She wants to reflect the banner over the line x=1. Identify the image of the banner reflected in the line x=1.

Answers

The coordinates of the banner after the reflection across x = 1 is P'(2, 4), Q'(0, 8), and R'(5, 6)

How to determine the coordinates of the banner after the reflection?

From the question, the coordinates are given as

P(0, 4), Q(2, 8), and R(−3, 6)

The line of reflection is given as

x = 1

The rule of reflection across the line x = 1 is represented as

(x, y) = (-x + 2, y)

When the above rule is applied, we have

P'(2, 4), Q'(0, 8), and R'(5, 6)

This means that the coordinate of the image are P'(2, 4), Q'(0, 8), and R'(5, 6)

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For the following set of data, find the number of data within 2 population standard deviations of the mean.28, 65, 114, 74, 68, 75, 70, 69, 64

Answers

To determine the data that is within 2 population standard deviations of the mean, let's calculate the mean first.

To determine the mean, let's add all the data and divide the result by the total number of data.

[tex]28+65+114+74+68+75+70+69+64=627[/tex][tex]627\div9=69.66667[/tex]

The mean is 69.66667.

Let's now calculate the standard deviation. Here are the steps:

1. Subtract the mean from each data, then square the result.

[tex]\begin{gathered} 28-69.66667=(-41.66667)^2=1,736.1114 \\ 65-69.66667=(-4.66667)^2=21.7778 \end{gathered}[/tex][tex]\begin{gathered} 114-69.66667=(44.33333)^2=1,965.4441 \\ 74-69.66667=(4.33333)^2=18.7777 \end{gathered}[/tex][tex]\begin{gathered} 68-69.66667=(-1.66667)^2=2.7778 \\ 75-69.66667=(5.33333)^2=28.4444 \end{gathered}[/tex][tex]\begin{gathered} 70-69.66667=(0.33333)^2=0.1111 \\ 69-69.66667=(-0.66667)^2=0.4444 \\ 64-69.66667=(-5.66667)^2=32.1111 \end{gathered}[/tex]

2. Add the results in step 1.

[tex]1,736.1114+21.7778+1,965.4441+18.7777+2.7778=3,744.8888[/tex][tex]28.4444+0.1111+0.4444+32.1111=61.111[/tex][tex]3,744.8888+61.111=3,805.9998[/tex]

The sum is 3, 805.9998.

3. Divide the sum by the total number of data.

[tex]3,805.9998\div9=422.8889[/tex]

4. Square root the result in step 3.

[tex]\sqrt{422.8889}\approx20.56[/tex]

The standard deviation is approximately 20.56.

So, the data that are within 2 population standard deviations of the mean are between:

[tex]\begin{gathered} 69.67-(2)(20.56)=28.55\approx29 \\ 69.67+(2)(20.56)=110.79\approx111 \end{gathered}[/tex]

The data that are within 2 population standard deviations of the mean are between 29 and 111. Based on the given data, the data that are between 29 and 111 are the following: 64, 65, 68, 69, 70, 74, and 75. There are 7 data that are within 2 population standard deviations of the mean.

F(x)=1/x g (x)=x-4 can you evaluate (golf)(0)? Explain why or why not.

Answers

If f(x) = 1/x  and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .

In the question

it is given that the functions

f(x) = 1/x

and g(x) = x-4

to find g=(gof)(x) ,

(gof)(x) = g(f(x))

= g(1/x)               ... because f(x) = 1/x

= 1/x - 4               ....because  g(x) = x-4

On simplifying further , we get

= (1-4x)/4x

On substituting x=0 , we get

gof(0) = (1-0)/4(0)

= 1/0

which is not defined , hence cannot be evaluated.

Therefore , if f(x) = 1/x  and g(x) = x-4 , then (gof)(0) cannot be evaluated as the function becomes not defined .

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The standard normal curve is grafted below. Shade the region under the standard normal curve to the left of x=1.00Use the table to find the area under the standard normal curve to the left of x=1.00

Answers

Explanation

Part A

The shaded area under the standard normal curve to the left of z=1.00 can be seen below.

Part B

Using the z table, the area under the standard normal curve to the left of z.=1.00 is

Answer: 0.8413

Your brother is buying textbooks for college. He has to buy 3 math textbooks and 2 science textbooks. The total cost of his textbooks is $487. Write a linear equation to represent the cost of his textbooks.

Answers

Let's define the following variables,

x: cost of a math textbook

y: cost of a science textbook

He has to buy 3 math textbooks and 2 science textbooks, that is,

Total cost = 3x + 2y

The total cost of his textbooks is $487, then the linear equation is,

487 = 3x + 2y

Solve the following/3x=7-3/x

Answers

Value of x is 8.46 for equation 3x=7-3/x

What is Equation?

Two or more expressions with an Equal sign is called as Equation

The given equation is 3x=7-3/x

3x+3/x=7

3x²+3=7x

3x²-7x+3=0

Use quadratic equation formula

a=3, b=-7, c=3

x=-b±√b²-4ac/2a

x=7±√49-4(3)(3)/2(3)

x=7±√49-36/6

x=7±√13/6

x=7±√2.16

x=7+1.46

x=8.46

Hence value of x is 8.46 for equation 3x=7-3/x

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Solve the missing elements for each problem. Use 3.14 for π. Area = πr^2; C=π D

Answers

Given,

Diameter = 32 cm

Radius

We know the radius is half of the diameter. Thus,

[tex]\begin{gathered} r=\frac{32}{2} \\ r=16 \end{gathered}[/tex]

Radius 16 cm

Circumference

The formula is:

[tex]C=\pi D[/tex]

Where

D is the diameter

So,

[tex]\begin{gathered} C=\pi D \\ C=(3.14)(32) \\ C=100.48 \end{gathered}[/tex]

Circumference = 100.48 cm

Area

The formula is:

[tex]A=\pi r^2[/tex]

Where

r is the radius

So,

[tex]\begin{gathered} A=\pi r^2 \\ A=(3.14)(16)^2 \\ A=(3.14)(256) \\ A=803.84 \end{gathered}[/tex]

Area = 803.84 sq. cm.

Triangle KLM has KL = 28, KM = 28, and LM = 21. What is the area of the triangle?The area of AKLM is about(Simplify your answer. Round to one decimal place as needed.)

Answers

Area = (b * h)/2, b = 21 bu we don't know h, s we have to calculate it

To calculate the height "h" we can use pythagoras with a triangle rectangle with base = 21/2 = 10.5 and hypothenuse = 28, so the height "h" is:

28² = h² + 10.5² ==> h² = 28² - 10.5² = 784 - 110.25 = 673.75

h² = 673.75

h = 25.96

Now that we have the height, the Area of the triangle = (b * h)/2 = (21 * 25.96)/2 = 272.5

Answer:

272.5

in order to clean her aquarium Stephanie much remove half of the water the garden measures 30 inches long 16 inches wide and 12 inches deep the aquarium is currently completely full with volume of water in cubic inches must Stephanie remove?

Answers

Hello!

30in long (length)

16in wide (width)

12in deep (height)

First, we have to calculate the volume when the aquarium is full of water, using the formula:

[tex]undefined[/tex]

Hello, I had a question on how to find the leading coefficient and the degree.

Answers

Given:

given polynomial is

[tex]23v^5-2v+4v^8-18v^4[/tex]

Find:

we have to find the leading coefficient and degree of the polynomial.

Explanation:

The lewading coefficient is the coefficient of highest power term of the polynomial.

Highest power of v is 8 and its coefficient is 4.

Therfore, leading coefficient is 4.

and the degree of the polynomial is equal to the highest power of v in the polynomial, which is 8.

Therefore, the leading coefficient of polynomial is 4 and degree is 8.

The endpoints of diameter in a circle form an angle with point C. What is the measure of angle BCD?

Answers

Answer:

90 degrees

Explanation:

Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;

[tex]\therefore\angle BCD=90^{\circ}[/tex]

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Use inductive reasoning to find a pattern then make a reasonable conjecture for the next three items in the pattern p g q h r I the type of conflict that occurs when individuals agree but, because of inaccurate communication, they think they disagree is called group of answer choices an object undergoing simple harmonic motion has an amplitude of if the maximum velocity of the object is what is the object's angular frequency? an object undergoing simple harmonic motion has an amplitude of if the maximum velocity of the object is what is the object's angular frequency? 6.5 rad/s which of the following statements is (are) true? i. diversifying raises the risk of your portfolio. ii. by picking a lot of stocks, you minimize your overall exposure to things going wrong in any particular company. iii. modern financial markets have made diversification difficult. in which of the following forms of political organization is it most likely that the most important leaders will acquire their positions based upon personal background or ability, rather than heredity? a. tribal societies b. feudal states c. imagined communities d. chiefdoms e. agrarian, preindustrial states mary claire is a citizen of florida. she is walking down a busy street in tallahassee, florida when a large crate flew off a passing truck and hit her, resulting in numerous injuries to mary claire. she incurred a great deal of pain and suffering, plus significant medical expenses, and she could not work for six months. she wants to sue the trucking firm for $300,000 in damages. the trucking company is incorporated in georgia and its headquarters are in atlanta, georgia. the trucking company does ongoing business in florida. what court(s) have jurisdiction in this matter? a. federal courts because the dollar amount exceeds $75,000 and the plaintiff and defendant have diversity of citizenship. b. federal courts because the dollar amount exceeds 75,000 and there is a federal question. c. georgia state courts because plaintiff is from georgia. d. florida state courts because the non-resident defendant has minimum contacts with the state of florida. e. a and d are both correct. The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes? f(x)=x^6+10x^4 - 11x^2 Which of the following can increase your energy levels?OA. Getting enough sleep.OB. Spending plenty of time with your friends and family.OC. Getting your schoolwork done early in the day.D. Reading for an hour each day. Explain why it is important to understand a business vision, mission, values and objectives when developing a business plan. Give an example to illustrate your answer. If 22.4 mL of 0.25 M sodium hydroxide are requiredneutralize 15.0 mL of a hydroiodic acid solution, howmany grams of hydrogen iodide were dissolved in thesolution? Which of the following is true of medieval chivalry A couple who are close family friends of yours are concerned that their children may have a high risk of inheriting cancer from one of them. write a paragraph that describes the steps you would take to 1) Identify if either or both of the parents may contribute to the risk of cancer. 2) explain to the parents how genes may lead to the development of cancers that are not inherited and 3) how they could identify if an embryo ham the genetic components that will lead to cancer? a jeweler is unable to fix a diamond mounting issue on a necklace because he can imagine only the conventional use of his tools. this is an example of: If you are writing a complete sentence, you don't necessarily have to have _____.[can only choose one]1: any of these2: adverbs3: pronouns4: adjectives Under normal conditions, the roots of plants grow downward. This illustrates what type of tropism? In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.What is the profit from 2021? Write & solve an Algebraic Equation. A circle passes through the points (3, 2) and (7, 2) and has radius 22. Find the two possible equations for this circle. The probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, what is the probability that two or more of them will fail the test shuaifu wants to reorganize his beverage bottling company. currently, there are hr, r&d, and purchasing units at each facility. shuaifu feels that by bringing all of those key functions together in one location and deploying them to the facilities only when needed, he will save money and also create consistency. is shuaifu correct?