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3 years ago

10

In how many different ways can 8 books be arranged on a shelf?

1 answer:

iren [92.7K]3 years ago

5 0

You can stack the eight books on top of each other is one way. And then you can changed the order of how you stack the book 64 different ways. You can also do this vertically standing up. With the spin of the book facing in or out. You can arrange the. By height, color, alphabetically, thickness, year published... basically any individual characteristic they can have can be a way you stack a book.

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Line FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through

stiks02 [169]

Answer:

$x + 2y= 2$

Step-by-step explanation:

Given

Points:

$F = (4,9)$

$G = (1,3)$

Required

Determine the equation of line that is perpendicular to the given points and that pass through $(2,0)$

First, we need to determine the slope, m of FG

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$F = (4,9)$ --- $(x_1,y_1)$

$G = (1,3)$ --- $(x_2,y_2)$

$m = \frac{3 - 9}{1 - 4}$

$m = \frac{- 6}{- 3}$

$m =2$

The question says the line is perpendicular to FG.

Next, we determine the slope (m2) of the perpendicular line using:

$m_2 = -\frac{1}{m}$

$m_2 = -\frac{1}{2}$

The equation of the line is then calculated as:

$y - y_1 = m_2(x - x_1)$

Where

$m_2 = -\frac{1}{2}$

$(x_1,y_1) = (2,0)$

$y - 0 = -\frac{1}{2}(x - 2)$

$y = -\frac{1}{2}(x - 2)$

$y = -\frac{1}{2}x + 1$

Multiply through by 2

$2y = -x + 2$

Add x to both sides

$x + 2y= -x +x+ 2$

$x + 2y= 2$

Hence, the line of the equation is $x + 2y= 2$

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Mandarinka [93]

Answer:

n=4

Step-by-step explanation:

because 4x10=40

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Suppose a triangle has two sides of length 3 and 4 and that the angle

rodikova [14]

Answer:

B

Step-by-step explanation:

We can use the law of cosinse:

$c^{2}$ = $a^{2} + b^{2}$ − 2ab cos(C)

Suppose the two sides are a and b, and the angle betweent them is C.

$c^{2}$ = $3^{2} + 4^{2}$ − 2*3*4 cos(60)

We can simplify this to get $c^{2}$ =25-12=13

c= $\sqrt{13}$

Answer choice B

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Answer:

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Step-by-step explanation:

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