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3 years ago

15

There are 15 runners in a race. Prizes are given to the first, second, and third place finishers. How many ways can the prizes b

e awarded?

1 answer:

maxonik [38]3 years ago

3 0

Answer:

45

Step-by-step explanation:

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Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation

Kryger [21]

Answer:

$y + x - 6 = 0$

Step-by-step explanation:

Given

$M(0,6) \ and \ N(6,0)$

Required

Find the equation of the line

First, the slope of the line has to be calculated using the following formula;

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

$where\ (x_1,y_1) = (0,6) \ and \ (x_2,y_2) = (6,0)$

So, the equation becomes

$m = \frac{0 - 6}{6 - 0}$

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

$m = -1$

The equation of the line can then be calculated using

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

$Using \ m = \frac{y - y_1}{x - x_1}$

$-1 = \frac{y - 6}{x -0}$

$-1 = \frac{y - 6}{x}$

Multiply both sides by x

$-1 * x = \frac{y - 6}{x} * x$

$-x = y - 6$

Add x to both sides

$x -x = y - 6 + x$

$0 = y - 6 + x$

Reorder

$y + x- 6 = 0$

$Using \ m = \frac{y - y_2}{x - x_2}$

$-1 = \frac{y - 0}{x - 6}$

$-1 = \frac{y}{x - 6}$

Multiply both sides by x - 6

$-1 * (x-6) = \frac{y}{x - 6} * (x-6)$

$-1 * (x-6) = y$

$-x+6 = y$

Add x - 6 to both sided

$x - 6 -x+6 = y +x - 6$

$0 = y + x - 6$

$y + x - 6 = 0$

Hence, the equation of the line is $y + x - 6 = 0$

3 0

3 years ago

Sam bought a new car for $26,500. The car depreciates approximately 13% of its value each year. What is the approximate value of

madreJ [45]

The approximate value of the car in 10 years is about $6583.22

7 0

3 years ago

Read 2 more answers

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53.

horrorfan [7]

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.

So we have

So we can apply the rule to obtain

8 0

1 year ago

F is directly proportional to a. If F=36 when a=9 , find F when a=4

kicyunya [14]

Step-by-step explanation:

f=ka

36=9k

k=4

f=4×4

f=16

8 0

2 years ago

Write 2x2 – 16x + 14 = 0 in the form (x - p)2 = q by completing the square.

Fed [463]

completing the square we get: $(x-4)^2=23$

Step-by-step explanation:

We need to write $2x^2-16x+14=0$ in the form (x-p)^2 =q by completing the square.

For completing the square, the formula used is: $(a+b)^2=a^2+2ab+b^2$

$2x^2-16x+14=0$

Taking 2 common:

$2(x^2-8x+7)=0$

Divide both sides by 2

$x^2-8x+7=0$

Now making complete square:

We know a but we need to find b for completing the square formula.

Since the middle term of formula is 8x which is obtained by 2(a)(b) where 2(x)(4) so, b=4 and b^2=(4)^2

So, if we add and subtract (4)^2 then we can make it complete square

$(x)^2-2(x)(4)+(4)^2-7-(4)^2$

$(x-4)^2-7-16=0\\(x-4)^2-23=0\\(x-4)^2=23$

So, completing the square we get: $(x-4)^2=23$

Keywords: Completing the square

Learn more about completing the square at:

#learnwithBrainly

7 0

3 years ago

Read 2 more answers