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4 years ago

Multiply and Simplify (x-4)(x^2 - 5x - 6)

Mathematics

1 answer:

AlekseyPX4 years ago

8 0

Answer:

x^3 - 9x^2 +14x +24

Step-by-step explanation:

(x-4)(x^2 - 5x - 6)

First multiply x by everything in the second term

x (x^2 - 5x - 6) = x^3 -5x^2 -6x

Then multiply -4 by everything in the second term

-4 (x^2 - 5x - 6) = -4x^2 +20x +24

Then we add the results together.

I like to line them up vertically.

x^3 -5x^2 -6x

-4x^2 +20x +24

------------------------------

x^3 - 9x^2 +14x +24

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A new auditorium is begging built for a college the balcony has 200 seats the floor has 25 rows with x seats in each row the num

aliya0001 [1]

Question:

A new auditorium is being built for a college. The balcony has 200 seats. The floor has 25 rows with x seats in each row. The number of people in the auditorium must be under 750 to meet safety regulations. What is the solution of this inequality, and what is its meaning?

Answer:

$200 + 25x < 750$

Number of seats in a row must be less than 22

Step-by-step explanation:

Given

Total = Less than 750

Current Seats = 200

Rows = 25

Seat per row = x

Required

Represent as an inequality

The scenario will be represented as:

$Current\ Seats + Rows * x = Total$

Substitute 200 for Current Seats

$200 + Rows * x = Total$

Substitute 25 for Rows

$200 + 25* x = Total$

$200 + 25x = Total$

Substitute <750 for Total.

The equation then becomes

$200 + 25x < 750$

Solving further:

$25x < 750 - 200$

$25x < 550$

$x < \frac{550}{25}$

$x < 22$

This means that:

Number of seats in a row must be less than 22

3 0

3 years ago

What's the value of x ?

Helen [10]

the formula for the Pythagorean theorem is a squared plus b squared is equals to c squared we don't have our a so it will be 8 * 8 =64which is 64 is equals to 10 * 10 which is 100 - 64 is equals to 36 then you square root do square roots the 36 which is 6

5 0

4 years ago

What’s the remainder for this synthetic division problem?

Vesna [10]

3 | 1 5 -8 6

. | 3 24 48

- - - - - - - - - - - - - - - -

. | 1 8 16 54

That is to say,

$\dfrac{x^3+5x^2-8x+6}{x-3}=x^2+8x+16+\dfrac{54}{x-3}$

The remainder is 54.

Another way of doing it is to apply the polynomial remainder theorem, which says the remainder upon dividing a polynomial $p(x)$ by $x-c$ is exactly $p(c)$ . So recognizing that the listed coefficients refer to