How many ways are there for 15 track runners to win 1st place, 2nd place and 3rd place?

Mathematics

2 answers:

const2013 [10]3 years ago

6 0

Answer:

Step-by-step explanation: 15x3

Olin [163]3 years ago

3 0

2,730 ways. You multiply 15x14x13 to get the answer of 2,730.

Further explanation: when you are looking for ways to find 1st place you have 15 ways total. After one of those spots are taken, you have one less way and therefore have 14 ways. Subtract one more way and you have 13 ways left. You multiply these together and that is how you get the answer <3

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The given line segment has a midpoint at (3, 1).

Katena32 [7]

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ .

Therefore the line passing through (2, 4) and (4, -2) has an equation:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10$

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

$m_1m_2=-1$ .

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

$m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}$

Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

$\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x$

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is $y=\frac{1}{3}x$

7 0

3 years ago

Read 2 more answers

Dvds are for $24 each,felipe write the expression 4 times 24 to find the costin dollars of buying 4 dvds, how can i rewrite feli

Karo-lina-s [1.5K]

The distributive property states that:

a(b+c)=ab+bc.

or more generally: a(b+c+d)=ab+av+ad.

This is a very useful tool to perform multiplication.

For example, if we want to multiply 7 by 234, we can proceed as follows:

7*234=7(200+30+4)=7*200+7*30+7*4=1400+210+28=1610+28=1638

back to our problem,

4 * 24 = 4(20+4)=4*20+4*4=80+16=96 ($)

So, instead of multiplying 4 by 24, we multiplied 4 by 20 and 4, which is easier, and then added these together.

Answer:

4 * 24 = 4(20+4) [=4*20+4*4=80+16=96 ($)]

5 0

3 years ago

Can someone please do this for me?

san4es73 [151]

Answer:

64°

Step-by-step explanation:

So supplement angles are equal to 180, so first our two angles added together will be 180:

x + x = 180

Now one of these angles is 6 greater than half:

x + (x/2 + 6) = 180

Then we will solve for x: