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3 years ago

A right rectangular pyramid is sliced by a plane that is perpendicular to the base of the pyramid.

2 answers:

5 0

A right rectangular pyramid is sliced by a plane the is perpendicular to the base of a pyramid.

which of the following shapes could result from the slicing?

O rectangle

O square

O pentagon

Papessa [141]3 years ago

3 0

Answer:

Step-by-step explanation:

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Factor x^4 - 2x^3 - 33x^2 + 50x + 200 completely using the given factor x^2 - 25.

PIT_PIT [208]

You can do synthetic division twice immediately (or once if you know how to handle x^2 - 25 all at once. I'll use 2 divisions. x^2 - 25 is (x + 5)(x - 5). Both of them are zeros to the given equation which means that x = +5 and

x = - 5 are both zeros of the given quartic.

5 1 -2 -33 50 200

5 15 -90 -200

=====================================

1 3 -18 -40 0

What you have now is x^3 + 3x^2 - 18x - 40 = 0

Do another synthetic division

-5 1 3 -18 -40

-5 10 40

============================

1 -2 -8 0

The result is

x^2 - 2x - 8 = 0 which factors.

(x + 2)(x - 4) = 0

Answer

The factors are (x + 2)(x - 4)(x + 5)(x - 5) = 0

Long division

x^2 + 0 + 25 ||x^4 - 2x^3 - 33x^2 + 50x + 200 ||x^2 - 2x - 8

x^4 + 0 + 25x^2

==================

-2x^3 -8x^2 + 50x

-2x^3 + 0 + 50x

=================

-8x^2 + 0 +200

-8x^2 + 0 + 200

==================

5 0

4 years ago

Which graph Represents the solution to the given system y=-x+5 y=1/4x+10

ollegr [7]

Shown below

<h2>Explanation:</h2>

In this exercise, we have the following system of linear equations in two variables:

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=-x+5\\y=\frac{1}{4}x+10\end{array}\right.$

From the first equation:

$y=-x+5 \\ \\ \\ Slope \ m=-1 \\ \\ y-intercept \ b=5$

Here as x increases one unit, then y decreases by one unit too. Therefore, if (0, 5) is a point on the line, then (1, 4) is also a point on the line. From here, we know that the line must pass through these two points.

From the second equation:

$y=\frac{1}{4}x+10 \\ \\ \\ Slope \ m=\frac{1}{4} \\ \\ y-intercept \ b=10$

Here as x increases 4 units, then y increases by one unit Therefore, if (0, 10) is a point on the line, then (4,11) is also a point on the line. From here, we know that the line must pass through these two points.

By using graphing tool, we realize that both graphs intersect at a single point, which is:

$(-4, 9)$