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3 years ago

In how many different ways can 6 runners be assigned to 6 lanes at the start of a race?

1 answer:

5 0

Well you have runner 1 in lane 1. runner 1 in lane 2 and so on. so it becomes 1,1 1,2 1,3 1,4 1,5 1,6 and then 2,1 2,2 2,3 2,4 2,5 2,6 then 3, and so on

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3x + y = -21<br> x+y=-5<br> solving systems of equations by substitution

katen-ka-za [31]

First : x=-5-y and then put x in the phrase above

7 0

2 years ago

Three of the four vertices of a rectangle are located at (4, 2), (7, 2) and (4, 8). a. What are the coordinates of the missing v

34kurt

Answer:

a) The coordinates of the missing vertex = (7, 8)

b) Area = 18 square units

Perimeter = 18 units

Step-by-step explanation:

a) We know three of the four vertices:

A: (4, 2) C ______ D(?)

B: (7, 2) | |

C: (4, 8) A |______| B

To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:

$B_{x} - A_{x} = 7 - 4 = 3$

Hence, the distance of point D from point C in the x-direction is:

$D_{x} = C_{x} + 3 = 4 + 3 = 7$

Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:

$C_{y} - A_{y} = 8 - 2 = 6$

Then, the distance of point D from point B in the y-direction is:

$D_{y} = B_{y} + 6 = 2 + 6 = 8$

Therefore, the coordinates of the missing vertex (point D) are:

$D = (D_{x}, D_{y}) = (7, 8)$

b) The area of the rectangle is:

$a = (B_{x} - A_{x})*(C_{y} - A_{y}) = 3*6 = 18 units^{2}$

The perimeter is given by:

$p = 2*(3 + 6) = 18 units$

I hope it helps you!

8 0

2 years ago

The graph of the parent function f(x) = x3 is translated such that the resulting graph can be represented by the function g(x) =

kirill115 [55]

Answer:

Translated 1 to the right and up one

Step-by-step explanation:

When the number is inside the parenthesis with x, that value represents a horizontal shift. because the original equation is (x-h), the opposite sign of the x value must be taken. so in this case the x value would be +1 because that is the opposite of -1, which means the function is being moved one to the right. when the number is being added to the outiside of the parenthesis, then you take that value for the vertical translations of the graph. because the original equation is (x-h)+k, then in this case there would be a vertical shift up by 1

8 0

3 years ago

Read 2 more answers

6 is what percent of 8?

kvasek [131]

6 is 75% of 8. 6/8 can be simplified to 3/4, which is easier to see as 75%.

8 0

2 years ago

Which table represents y as a function of x?

tankabanditka [31]

Answer:the top right

Step-by-step explanation: