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2 years ago

A car can go 420 miles on a tank of gas (15 gallons in a tank). How many kilometers can this car go on 6.5 gallons

Mathematics

1 answer:

azamat2 years ago

3 0

Answer:

182 miles

Step-by-step explanation:

15 gallons ------------------------- 420 miles

1 gallons --------------------------- 420/15 miles

1 gallons --------------------------- 28 miles

6.5 gallons -------------------------- 6.5 × 28 miles

6.5 gallons -------------------------- 182 miles

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Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2

Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

5 0

2 years ago

7x to the 2nd power when x=6

topjm [15]

Your answer would be 252 Hope this helps

4 0

2 years ago

This year, a gram planted 400,000 corn stalks.last year, the farm planted 275,650 corn stalks how many more corn stalks did the

In-s [12.5K]

400000-275650=124350

3 0

2 years ago

A group of band instructors answered a survey about hours of rehearsal per week and number of competitions won. The graph shows

IRISSAK [1]

Answer: B. 31

Step-by-step explanation:

This linear regression was constructed by relating the hours practiced per week and the number of competitions won.

Going by this graph, the number of competitions they can expect to win at 5 practices a week is 31.

This is derived by looking for the point where 5 competitions on the x-axis intersects with the line. This point is at 31 competitions on the y axis which would make it the answer.

5 0

2 years ago

Read 2 more answers

Help me with this one please

lesya [120]

For me, it’s easiest when i distribute the negative sign if i need to and then reorder to put the like terms together. and then solve.
(also sorry if it’s a little confusing with all the parentheses, i use them because it helps me organize everything)

21. (4x-9y) + (6x+10) + (8y-4)
= 4x + 6x - 9y + 8y + 10 - 4
= 10x - y + 6
—> D

22. (6x+9y-15) + (2x-9y+8)
= 6x + 2x + 9y - 9y - 15 + 8 (the 9y - 9y = 0, so you can leave it out of the final equation)
= 8x - 7
—> D

23. (9x^2-8x+3) - (5x^2-6x+4)
= 9x^2 - 8x + 3 - 5x^2 -(-6x) - 4
= 9x^2 - 5x^2 - 8x + 6x + 3 - 4 (remember that two - signs next to each other make a + sign)
= 4x^2 - 2x - 1
—> A

24. (9x^3-7x+8) - (5x^2+7x-10)
= 9x^3 - 7x + 8 - 5x^2 - 7x -(-10)
= 9x^3 - 5x^2 - 7x - 7x + 8 + 10
= 9x^3 - 5x^2 - 14x + 18
—> D

25. (6x+14y) - ((7x+5y) + (x-8y))
= (6x+14y) - (7x + x + 5y - 8y)
= (6x+14y) - (8x-3y)
= 6x + 14y - 8x -(-3y)
= 6x - 8x + 14y + 3y
= -2x + 17y
—> B

5 0

2 years ago