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4 years ago

Divide -x^3-2x^2-2x+4 by x -3

Mathematics

1 answer:

Lostsunrise [7]4 years ago

5 0

Answer:

− x 2 − 5 x − 17 − 47 x − 3

Step-by-step explanation:

Divide using polynomial division.

Polynomial :

An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.

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A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine w

Alenkinab [10]

Answer:

The diagonals of the polygon ABCD bisect each other

Step-by-step explanation:

The given vertices of the polygon are;

A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1)

Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB

By the midpoint formula, we have;

$(x_m , \ y_m) = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )$

Where;

$(x_m , \ y_m)$ = The midpoint coordinates

Therefore, the midpoint of diagonal AC = $\left (\dfrac{1 + (-1)}{2} , \ \dfrac{4 + (-4)}{2} \right ) = (0, 0)$

The midpoint of diagonal DB = $\left (\dfrac{(-4) +4}{2} , \ \dfrac{1 + (-1)}{2} \right ) = (0, 0)$

Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other

Each diagonal passes through the midpoint of the other diagonal.

3 0

3 years ago

13) Bubba's Pizza-o-rama is setting up a buffet for a banquet.

liubo4ka [24]

I think it’s 3 ways

8 0

3 years ago

Solve this system of equations 5x + 4y = 6 10x -2y = 7

Akimi4 [234]

Answer:

x = 4/5

y = 1/2

Step-by-step explanation:

8 0

3 years ago

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

3 years ago

(plz solve asap) find the value of x i dont know how to solve it so anyone can help

k0ka [10]

Answer:

I tried but sorry couldn't figure it out.

7 0

3 years ago