What are the quotient and remainder of (3x^4+ 2x^2 - 6x + 1) = (x + 1)

Answers

Answer 1

Answer:

Answer: Im 75% sure the answer is A. Its either A or B.

Step-by-step explanation:

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F)-5y=BYy=F) check
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Please help I don’t know what to do and I have a whole test on it

If bd = 7x - 10, BC= 4x - 29, and cd
= 5x - 9, find each value

Answers

Answer:

BD = 88

BC = 27

CD = 61

Explanation:

Given that,

BD = 7x - 10

BC= 4x - 29

CD = 5x - 9

Here we assume BD is a line segment and C is a point lies between B & D.

BD = BC + CD

7x - 10 = 4x - 29 + 5x - 9

Now combine like terms

7x - 10 = 4x + 5x - 29 - 9

7x - 10 = 9x - 38

Move 7x from left hand side to right hand side

-10 = 9x - 7x - 38

-10 = 2x - 38

Add 38 both the side

-10 + 38 = 2x - 38 + 38

28 = 2x

Divide by 2 both the side

x = 14

Now put the value of x and find the length of BD, CD, BC

BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88

BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27

CD = 5x - 9 = 5*14 - 9 = 61

That's the final answer.

I hope it will help you.

The value of the expression will be:

BD = 88

BC = 27

CD = 61

How to solve the expression

Given that,

BD = 7x - 10

BC= 4x - 29

CD = 5x - 9

Here we assume BD is a line segment and C is a point lies between B & D.

BD = BC + CD

7x - 10 = 4x - 29 + 5x - 9

Now combine like terms

7x - 10 = 4x + 5x - 29 - 9

7x - 10 = 9x - 38

Move 7x from left hand side to right hand side

-10 = 9x - 7x - 38

-10 = 2x - 38

Add 38 both the side

-10 + 38 = 2x - 38 + 38

28 = 2x

Divide by 2 both the side

x = 14

Now put the value of x and find the length of BD, CD, BC

BD = 7x - 10 = 7*14 - 10 = 98 - 10 = 88

BC= 4x - 29 = 4*14 - 29 = 56 - 29 = 27

CD = 5x - 9 = 5*14 - 9 = 61

Learn more about expressions

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PLEASE HELP!A farmer wanted to paint a shed out in his field. Here is the breakdown of the dimensions: the building is sitting on a square slab of cement that is 10' x 10'. It is 8 feet from the bottom of the shed to the bottom of the roof on the edge, and 10 feet from the bottom of the shed to the top of the very tip top of the roof. So A = 10, B = 8 and C = 10. Using the formula for the area of a rectangle, A = l x w and the area of a triangle, 1/2(bh), b is base and h is height, then find the total area that needs to be painted. Total area =

Answers

Answer:

340 square feet

Step-by-step explanation:

If we "unwrap" the painted surface from the shed, it will have the shape shown in the attachment. It is essentially a 40' by 8' rectangle with two 10' wide by 2' high triangles added.

The rectangle area is ...

A = LW = (40 ft)(8 ft) = 320 ft²

The total area of the two triangles is ...

A = 2(1/2)bh = (10 ft)(2 ft) = 20 ft²

Then the painted area is ...

total area = 320 ft² +20 ft²

total area = 340 ft²

Solve this differential Equation by using power series
y''-x^2y=o

Answers

We're looking for a solution

$y=\displaystyle\sum_(n=0)^\infty a_nx^n$

which has second derivative

$y''=\displaystyle\sum_(n=2)^\infty n(n-1)a_nx^(n-2)=\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n$

Substituting these into the ODE gives

$\displaystyle\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=0)^\infty a_nx^(n+2)=0$

$\displaystyle\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=2)^\infty a_(n-2)x^n=0$

$\displaystyle2a_2+6a_3x+\sum_(n=2)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=2)^\infty a_(n-2)x^n=0$

$\displaystyle2a_2+6a_3x+\sum_(n=2)^\infty\bigg((n+2)(n+1)a_(n+2)-a_(n-2)\bigg)x^n=0$

Right away we see $a_2=a_3=0$ , and the coefficients are given according to the recurrence

$\begin{cases}a_0=y(0)\na_1=y'(0)\na_2=0\na_3=0\nn(n-1)a_n=a_(n-4)&\text{for }n\ge4\end{cases}$

There's a dependency between terms in the sequence that are 4 indices apart, so we consider 4 different cases.

If $n=4k$ , where $k\ge0$ is an integer, then

$k=0\implies n=0\implies a_0=a_0$

$k=1\implies n=4\implies a_4=(a_0)/(4\cdot3)=\frac2{4!}a_0$

$k=2\implies n=8\implies a_8=(a_4)/(8\cdot7)=(6\cdot5\cdot2)/(8!)a_0$

$k=3\implies n=12\implies a_(12)=(a_8)/(12\cdot11)=(10\cdot9\cdot6\cdot5\cdot2)/(12!)a_0$

and so on, with the general pattern

$a_(4k)=(a_0)/((4k)!)\displaystyle\prod_(i=1)^k(4i-2)(4i-3)$

If $n=4k+1$ , then

$k=0\implies n=1\implies a_1=a_1$

$k=1\implies n=5\implies a_5=(a_1)/(5\cdot4)=(3\cdot2)/(5!)a_1$

$k=2\implies n=9\implies a_9=(a_5)/(9\cdot8)=(7\cdot6\cdot3\cdot2)/(9!)a_1$

$k=3\implies n=13\implies a_(13)=(a_9)/(13\cdot12)=(11\cdot10\cdot7\cdot6\cdot3\cdot2)/(13!)a_1$

and so on, with

$a_(4k+1)=(a_1)/((4k+1)!)\displaystyle\prod_(i=1)^k(4i-1)(4i-2)$

If $n=4k+2$ or $n=4k+3$ , then

$a_2=0\implies a_6=a_(10)=\cdots=a_(4k+2)=0$

$a_3=0\implies a_7=a_(11)=\cdots=a_(4k+3)=0$

Then the solution to this ODE is

$\boxed{y(x)=\displaystyle\sum_(k=0)^\infty a_(4k)x^(4k)+\sum_(k=0)^\infty a_(4k+1)x^(4k+1)}$

A commercial jet has been instructed to climb from its present altitude of 6000 feet to a cruising altitude of 30,000 feet. If the plane ascends at a rate of 4000 ft/min, how long will it take to reach its cruising altitude? The plane will take nothing minutes.

Answers

An easier way of doing this would be to subtract the initial attitude from the final attitude and divide by the rate of increase
= 30000 - 6000÷4000
= 24000÷4000
=6mins

John ordered five large size pizzas for a party. Five kids each ate 1/10 slice, and twelve adults each at 3/10 slices.a) Find the total number of slices consumed.
41/10
b) Find the leftover pizza if any.

Answers

Answer:

a) 4 1/10 slices eaten

b) cannot be solved because we don't know how many slices in each pizza

Step-by-step explanation:

5*1/10=5/10

12*3/10=36/10

36/10+5/10=41/10

41/10=4 1/10 slices

4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answers

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

$\begin{gathered} A=l* b \n l=\text{length} \n b=\text{breadth or width} \end{gathered}$

Now, let us calculate the area of FACE 1, 3 and 5.

$\begin{gathered} \text{FACE 1:} \n A_1=18*4=72in^2 \n \text{FACE 3:} \n A_3=4*7=28in^2 \n \text{FACE 5:} \n A_5=18*7=126in^2 \end{gathered}$

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

$\begin{gathered} A_S=2*(72+28+126) \n \therefore A_S=452in^2\text{ } \end{gathered}$

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

$\begin{gathered} V=l* w* h \n l=\text{length} \n w=\text{width or breadth} \n h=\text{height or depth} \end{gathered}$

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

$\begin{gathered} V=7*18*4in^3 \n \therefore V=504in^3 \end{gathered}$

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches

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