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Arisa [49]
3 years ago
14

The sketch shows the distance three runners travel during a race. Describe what occurs at times A,B,C and D. In what order do th

e runners finish. Explain.

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
6 0

Answer:

Notice that the distance is in the y-axis, and the time in the x-axis.

First, let's see what happens in the four points:

A) You can see that in point A, the steepness of the line increases, this means that the speed of the runner increases in that point.

B) In this point, the runner that increased his/her speed in point A crosses the graph of another runner, this means that they are at the same distance to the end and at the same time.

C) In this point again two runners are at the same distance and the same time, and we also can see that the runer that increased his/her speed at point A, now has reached the end of the race (because his line stops increasing, wich means that he/she already finished the race)

D) The las runner finishes the race at point D.

Then the first runner that finishes the race is the one with the shorter graph (shorter graph means that he ran for less time than the others, wich means that he/she finished first)

The last runner is the one that finished at point D,

The middle one finishes right after the point C.

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Simplify the expression to a polynomial in standard form:
maksim [4K]

Answer:

(144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2)

Step-by-step explanation:

To better understand the question we need to properly format the expression

(4x^2+x-1)(-3x^2-3x-3)(4x^2+x-1)(-3x^2-3x-3)

as we can see we have three brackets, we can proceed by first opening the first two brackets, we have.

(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\

we then continue by collecting like terms

=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)

we then solve for the remaining two brackets

(4x^2+x-1)(-3x^2-3x-3)\\=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\

we then continue by collecting like terms

=-12x^4-12x^3-12x^2-3x^3-3x^2-3x+3x^2+3x+3\\=-12x^4-12x^3-3x^3-12x^2-3x^2+3x^2-3x+3x+3\\=(-12x^4-15x^3-12x^2+3)

from the two brackets we obtained(-12x^4-15x^3-12x^2+3) each, we now have to multiply both terms together and solve we have

(-12x^4-15x^3-12x^2+3)(-12x^4-15x^3-12x^2+3)\\=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\

collecting and summing all like terms we have

=144x^8+180x^7+144x^6-36x^4+180x^7+255x^6+180x^5-45x^3+144x^6+180x^5+144x^4-36x^2-36x^4-45x^3-36x^2+9\\=144x^8+180x^7+180x^7+144x^6+255x^6+180x^5+180x^5-36x^4+144x^4-36x^4-45x^3-45x^3-36x^2-36x^2\\\\\=144x^8+360x^7+369x^6+360x^5+72x^4-90x^3-72x^2

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4 years ago
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Gnesinka [82]
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6 0
3 years ago
Need help asap please
iVinArrow [24]

Answer:

see below

Step-by-step explanation:

The car will have some value.  It will not decrease to nothing

We take 1/3 away from the value each year

This means we keep 2/3 of the value

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Year 1       value  18000 *2/3

Year 2      value  18000 * 2/3 * 2/3

Year 3     value   18000 * 2/3 * 2/3 * 2/3

Year 6      value   18000 * 2/3 * 2/3 * 2/3* 2/3 * 2/3 * 2/3

                  value   18000 * 2/3 ^6

Year t       value = 18000 * 2/3 ^ t

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3 0
3 years ago
What is 3x + 5x + 6x -2x​
Maurinko [17]

Answer:

12x

Step-by-step explanation:

8x+6x-3x

8x+3x

12x

hope it helped.

3 0
3 years ago
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The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?
sweet [91]
Area of a triangle= 1/2 base times height
substitute

40=1/2*10*x
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the height is 8 inches

7 0
4 years ago
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