Mathematics College

Using synthetic division, find (x4 − 2) ÷ (x + 1).

Answers

Answer 1

Answer:

Step-by-step explanation:

We have given:

x^4-2/x+1

Put x+1 = 0

x= 0-1

x= -1

-1 | 1 0 0 0 -2

| -1 1 -1 1

_______________

1 -1 1 -1 -1

Thus it makes the expression:

x^3-x^2+x-1 - 1/x+1

You can further confirm this expression by solving the expression:

(x4 − 2) ÷ (x + 1).

x^4 - 1 -1/x+1

x^4-1/x+1 - 1/x+1

(x^2-1) (x^2+1)/x+1 - 1/x+1

(x-1)(x+1) (x^2+1)/x+1 - 1/x+1

x+1 n the numerator will be cancelled out by x+1 in the denominator.

(x-1) (x^2+1) - 1/x+1

Multiply (x^2+1) by x-1

x(x^2+1) -1(x^2+1) - 1/x+1

x^3+x-x^2-1 - 1/x+1

x^3-x^2+x-1 - 1/x+1 ....

Related Questions

which collection of three side lengths will not form a triangle

6, 10 18
10, 12 ,15
10, 15, 6
10, 18 ,12 please tell me how you figured it out.

Answers

To construct a triangle, the sum of any 2 sides of the triangle should be greater than the third side of the triangle.
lets calculate the sums of all the given choices to find out which three lengths given do not form a triangle.

A.
6,10,18
6 + 10 = 16
16 is smaller than the third side-18
Therefore these 3 lengths do not form a triangle

B.10,12,15
10 + 12 = 22 15+12 = 27 15 + 10 = 25
22>15 (3rd side) 27>10 (3rd side) 25>12 (3rd side)
In this triangle, sum of all the possible pairs of sides are greater than the third side therefore these lengths can form a triangle

C.10,15,6
10 + 15 = 25 15 + 6 = 21 10+6 = 16
25 > 6 21>10 16>15
in this too, sum of all the possible pairs of sides are greater than the third side. These lengths can be used to form a triangle

D.10,18 ,12
10 + 18 = 28 18 + 12 = 30 10 +12 = 22
28> 12 30>10 22> 18
Therefore these lengths can also be used to form a triangle

correct answer is 6,10 and 18 these cannot form a triangle

Final answer:

To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem to each collection of side lengths given, we can determine which ones will form a triangle.

Explanation:

A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For the collection 6, 10, 18, the sum of the two smaller sides (6 + 10) is less than the largest side (18), so this collection will not form a triangle.For the collection 10, 12, 15, the sum of the two smaller sides (10 + 12) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 15, 6, the sum of the two smaller sides (6 + 10) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 18, 12, the sum of the two smaller sides (10 + 12) is greater than the largest side (18), so this collection will form a triangle.

A right triangle has one leg that is 17 centimeters shorter then the other. If the hypotenuse is 25 what is the length of the two legs

Answers

Let x represent the shorter leg. Then the Pythagorean theorem tells us
x^2 +(x +17)^2 = 25^2
2x^2 +34x +289 = 625
x^2 +17x -168 = 0
(x -7)(x +24) = 0 . . . . . the zero product rule tells you x=7 is the solution

The shorter leg is 7 cm; the longer one is 24 cm.

F = {(-1, 2), (3, 2), (4, 2), (0, 2)} Is F a function and why/why not?

Answers

No, because there is one output 2 for all inputs.

For the number -5/8 name the opposite, reciprocal and absolute value

opposite:
Reciprocal:
Absolute value:

Answers

opposite- 5/8
reciprocal- -8/5
absolute value- 5/8

How to find turning point of (c-2)^3+8

Answers

A "turning point" is generally considered to be a point where the first derivative changes sign. This function does not meet that requirement anywhere.

The function has a point of inflection at (2, 8), where the curve is horizontal, but does not reverse direction.

hello there!

to find the turning point, you must have a function, so let's set this expression equal to y.

y=(c-2)^3+8
y'=3(c-2)^2

Now set y' equal to 0...

3(c-2)^2=0
3(c-2)(c-2)=0
c=2

Now that we know c=2, plug this in to the original equation to get the y-value for the turning point.
The turning point is (2,y) we will find y now...
y=(2-2)^3+8
y=0+8
y=8

The turning point is at (2,8)

The explanation for this is that the x values of the zeros of the derivative function are the same as the x values as the turning points on the original function.

I really hope this helps!
Best wishes :)

Volume is always measured in square units. True False

Answers

Hello,

The answer is option B "false".

Reason:

The answer is false because the volume can be measure in anyway for example: feet, yards.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

Hello there!

This statement would be know to be (false).

Volume is something that is used to help add what is already measured. Volume can be measured in all different aspects, not only using squared units. This would be false because volume has to ability to be measure in any way that it would want to, but it would only have to complete its purpose, to add what the object is.

Your answer: False.

geometric mean for 12 and 3

Answers

Geometric mean for 12 and 3 = √12*3 = √36 = 6

answer
Geometric mean for 12 and 3 = 6

hey there! :D

To find the geometric mean, you multiply the numbers and then find the square root.

12*3= 36

The square root of 36 is 6.

The geometric mean is 6.

I hope this helps!
~kaikers

The tangent line has the form y=mx+b . use tl above to find b +juliabox

Answers

Is there a picture?

during the rice of industrialization in the 1840s the majority of immigrants come from

Answers

Most of the immigrants are from Ireland and German.

Hope this helps!

the answer is ireland and germany

Richard goes to the electronics store. He buys 2 memory cards that cost $8.99 each and 3 packages of batteries that are on sale for $7.47 each. He also buys a case for his cell phone for $2.99 and a wireless headset for $29.99. What is the total cost of Richard’s items, before sales tax?

Answers

2*8.99 +3*7.47 +2.99 +29.99 = 73.37

Richard's items cost $73.37 before sales tax is added.

A sandwich shop has 30 stores and 60% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California amd bow many are in Nevada?

Answers

60% of 30 = 0.6 x 30 = 18

There are 18 stores in California.

30 - 18 = 12

Theee are 12 stores in Nevada.

Answer:

Step-by-step explanation:

how to we get radius

Answers

Just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation

Find the points on the surface 4 x^2 + 4 y^2 + 1 z^2 = 1 at which the tangent plane is parallel to the plane -4 x - 4 y + 4 z = -8.

Answers

i dont know i will tell you when i find out

Giving brainiest+points need explanation on this one my answer is 25 is it right?

Answers

yes, the answer of 25 is correct.

Elevator 1 moved up 10 feet from the ground level. Its position is labeled as +10. Elevator 2 moved down 5 feet from the ground level. Its position is labeled as _____. (Use the hyphen for negative such as -1)

Answers

-5. The + or - just tells whether the elevator is above or below ground level.

simplify 4 (-w + 8) by distributing.

Answers

4 ( -w + 8)
you multiply 4 and -w, 4 and 8.
so

-4w + 32

How do you do question number 5? If you do it can you please explain how to do it? Thank you!!

Answers

F(-3) = 4(-3) - 3 = -12 - 3 = -15.
H(2) = -5(2) + 7 = -10 + 7 = -3.

F(-3) + H(2) = -15 + -3 = -18.

The solution is -18.

Answer:

F(-3) = 4(-3) - 3 = -12 - 3 = -15.

H(2) = -5(2) + 7 = -10 + 7 = -3.

F(-3) + H(2) = -15 + -3 = -18.

The solution is -18.F(-3) = 4(-3) - 3 = -12 - 3 = -15.

H(2) = -5(2) + 7 = -10 + 7 = -3.

F(-3) + H(2) = -15 + -3 = -18.

Step-by-step explanation:

Expand the log as a sun or difference

Answers

27. (1/2*log(9) -(4*log(x) +1/3*log(3))/log(a)
= ((1/2)*2*log(3) -4*log(x) -1/3*log(3))/log(a)
= ((2/3)*log(3) -4*log(x))/log(a)
= [tex]\frac{2}{3}\log_a{(3)}-4\log_a{(x)}[/tex]

[tex]\bf \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\\\ \textit{Logarithm of rationals} \\\\ log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y) \\\\\\ \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x)\\\\ -------------------------------[/tex]

[tex]\bf log_a\left( \cfrac{9^{\frac{1}{2}}}{x^43^{\frac{1}{3}}} \right)\implies log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^43^{\frac{1}{3}} \right) \\\\\\ log_a\left( 9^{\frac{1}{2}} \right)-\left[ log_a\left( x^4 \right)+log_a\left( 3^{\frac{1}{3}} \right) \right] \\\\\\ log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^4 \right)-log_a\left( 3^{\frac{1}{3}} \right)\\\\\\ \cfrac{1}{2}log_a(9)-4log_a(x)-\cfrac{1}{3}log_a(3)[/tex]

or more expanded so as

[tex]\bf \cfrac{1}{2}log_a(3^2)-4log_a(x)-\cfrac{1}{3}log_a(3) \\\\\\ \cfrac{1}{2}\cdot 2log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3) \\\\\\ log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3)[/tex]

what id is 29/4 improper

Answers

So, by considering this kind of question, we would want to find out how much does 29 go into 4.

By doing this, we would be able to find the improper fraction.

In the decimal form, this would be 7.25

And in the mixed number, it would look like:

[tex]\boxed{7 \frac{1}{4} }[/tex]

The bottom denominator always stays the same!

this fraction is already in it's improper state
[tex]7 \frac{1}{4} [/tex] is the fraction as a mixed number
7.25 is the fraction as a decimal
725% is the fraction as a percent

hope this helps

How much money does the average professional football fan spend on food at a single football game? that question was posed to 10 randomly selected football fans. the sample results provided a sample mean and standard deviation of $14.00 and $2.50, respectively. use this information to construct a 90% confidence interval for the mean?

Answers

Hi!

When the mean ([tex]\bar{x}[/tex]), the number of samples (n) and standard deviation (σ) are known, you can apply the following equation to determine confidence intervals. The value of z at 90% confidence can be found in tables (It is 1,645).

[tex](\bar{x}-z* \frac{\sigma}{ \sqrt{n} },\bar{x}+z* \frac{\sigma}{ \sqrt{n} }) \\ \\ (14-1,645* \frac{2,50}{ \sqrt{10} },14+1,645* \frac{2,50}{ \sqrt{10} } \\ \\ (12,70\$;15,30\$) [/tex]

Have a nice day!

0.5x+78.2=287 whats the value of x

Answers

0.5x+78.2=287
-78.2 -78.2 SUBTRACT 78.2

0.5x=208.8
/.5 /.5 DIVIDE BY .5

x=417.6 ANSWER

PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Exponential Growth/Decay Function
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years. (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answers

Did you get the answer for part b?

Hannah keeps her marbles in bags with for marbles in each bag she writes 3/4 to show the number of red marbles in each bag find another fraction to name the number of red marbles in 2 bags

Answers

She keeps 4 marbles in every bag and mark it with 3/4 to represent red marbles in the bag. It means there are 3 Red marbles out of total 4 marbles in the bag.

It says to write another fraction to represent number of red marbles in two bags.

Since one-bag contains 3 Red marbles out of total 4 marbles in the bag.

Then two-bags would contain 2x3 Red marbles out of total 2x4 marbles in the bag i.e. 6 Red marbles out of total 8 marbles in the bag.

So, [tex] \frac{6}{8} [/tex] is the another fraction to show number of red marbles.

Write equations for the horizontal and vertical lines passing through the point (5, -6)
Horizontal line:
Vertical line:

Answers

check the picture below.

List 3 values that would make this inequality true 4n <_ 12

Answers

Divide both sides by 4 to get

[tex]4n \le 12[/tex]

[tex]\frac{4n}{4} \le \frac{12}{4}[/tex]

[tex]n \le 3[/tex]

So we can pick n to be 3 or it can be less than 3

Three values we can pick are: n = 0, n = 1, n = 2

Or we could pick: n = 1, n = 2, n = 3

Jake needs to put gas in the delivery van. Regular gasoline is $3.20 per gallon. He only had a $ 20 bill on him. How many gallons can he buy

Answers

Hello,

The answer is "6 gallons".

Reason:

Just divide 20 by 3.20.....

20/3.20=6.25

Round to the nearest whole number will be 6.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

he can buy 6 galons and he got 58 extra

Solve this derivative using the quotient rule

Answers

[tex]\bf y=\cfrac{(-x+5)^5}{3x-4}\implies y=\cfrac{(5-x)^5}{3x-4} \\\\\\ \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{5(5-x)^4(-1)(3x-4)~~-~~(5-x)^5(3)}{(3x-4)^2}} \\\\\\ \cfrac{dy}{dx}=\cfrac{-5(5-x)^4(3x-4)-3(5-x)^5}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\stackrel{common~factor}{-(5-x)^4}[5(3x-4)+3(5-x)]}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[15x-20+15-3x]}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[12x-5]}{(3x-4)^2}\implies \cfrac{dy}{dx}=\cfrac{(5-x)^4~~[5+12x]}{(3x-4)^2}[/tex]

What is the slope of the line that goes through (2, 5) and (-6, -2) ?

Answers

Answer:
slope = 7/8

Explanation:
Slope of the line can be calculated using the following equation:
slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]

The two points given are:
(2,5) representing (x1 , y1)
(-6,-2) representing (x2 , y2)

Substitute with the points in the above equation to get the slope as follows:
slope = [tex] \frac{-2 - 5}{-6 - 2} [/tex] = 7/8

Hope this helps :)

what does x=? I know it is vertical

Answers

the angles are supplementary

7x + x + 20 = 180
8x = 160
x = 20

Hello there!

We know a vertical line = 180 degrees

x + 20 + 7x = 180

we can simplify this

20 + 8x = 180

To solve this, we can work backwards.

180 - 20 = 160

8x = 160

160/8 = 20

x = 20 degrees

Hope I helped!

Let me know if you need anything else!

~ Zoe

A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets an a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets?

Answers

The best expression would be 9.50c + 9.50a.

Question

Answer:

10.50c + a

PLZ GIVE BRAINLYEST!!!

Other Questions

When a fiction writer uses foreshadowing he or she is? A.) giving readers clues about what is to come B.) giving more background information about characters C.) going back in time D.)telling us things the character doesn't know Which verb form correctly completes this conversation? Miranda: Antonio, te gustara cortarte el pelo? Antonio: S, me _______ cortrmelo! gustaramos gustaras gustara gustaran The following question is based on your reading of 1984 by George Orwell. How does the Two Minute Hate work? help plz i want help On average, for every $1.00 earned by working men, working women earn about _____. 1440 tons of grain were brought to a silo over two days. On the second day, 80% of the amount of the grain delivered during the first day was brought in. How many tons of grain were delivered to the silo on the first day? In the sentence "Mary caught a frog," the common noun serves as A. both subject and object. B. the object of the sentence. C. the subject of the sentence. D. the verb of the sentence. Cuntos kilogramos pesa el arroz? (1 point) Express as a fraction or mixed number.30 19 When does the resolution happen in a story?A.the middleB.the turning pointC.the beginningD.the end Do changes that cannot be easily reversed, such as burning, observe the law of conservation of mass? Explain. What is the rationale for administration of ranitidine to a patient who is experiencing acute adrenal insufficiency? What property is l times w = w times l let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0) Americans who opposed the Constitution were called: Compared to that of a plane on the ground, Earths gravitational pull on a plane 7 miles above Earth is approximately A)zero. B)the same. C)half as much. D)twice as much. Whats the original price for this? Read the sentence. Unfazed by the morning frenzy before school, dad gave us our lunches before we left. Which best describes the sentence? The sentence is built around the simple subject school and simple predicate left. It also contains an indirect object us, but not a direct object. The sentence is built around the simple subject morning and simple predicate left. It also contains a direct object us, but not an indirect object. The sentence is built around the simple subject frenzy and simple predicate gave us. But, it does not contain either a direct or indirect object. The sentence is built around the simple subject dad and simple predicate gave. It also contains both a direct object lunches and indirect object us. A basketball player makes 160 out of 200 free throws. we would estimate the probability that the player makes his next free throw to be Where does the falling action or the place In the story where a character faces consequences of his or her decisions occur in Edgar Allan Poes the black cat