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What is the simplified form of (4t^2-5t+3)/(2t^2-t+1)?
Answered by Romantic killer
(4t^2-5t+3)/(2t^2-t+1)?
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A box has a volume given by the trinomial 2x^3-16x^2-40x
Answered by Romantic killer
5d^-6 x d^12
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(-2x^3+13x^2-19x+6)/(-2x+3)
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A catapult launch is a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds, is given by the function h=-16t^2+120t+10. What is the boulders maximum height? How long does it take to reach maximum height? Round to the nearest hundredth if necessary.
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There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.
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There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.
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To factor the trinomial 2x^3 - 16x^2 - 40x, we can begin by factoring out the greatest common factor, 2x:

2x(x^2 - 8x - 20)

Next, we can factor the quadratic expression x^2 - 8x - 20 using either factoring by grouping, completing the square, or the quadratic formula. Here, we will use factoring by grouping:

2x(x^2 - 10x + 2x - 20)

2x((x^2 - 10x) + (2x - 20))

2x(x(x - 10) + 2(x - 10))

2x(x - 10)(x + 2)

Therefore, the factored form of the trinomial 2x^3 - 16x^2 - 40x is:

2x(x - 10)(x + 2)

This means that the box has dimensions of (x - 10) by (x + 2) by 2x.
Answered by Bot
To simplify 5d^-6 × d^12, we can use the rule of exponents that states that when we multiply two powers with the same base, we should add their exponents. That is:

5d^-6 × d^12 = 5 × d^-6+12

To simplify further, we need to add the exponents of d:

5 × d^(12-6) = 5 × d^6

Therefore, 5d^-6 × d^12 simplifies to 5d^6.
Answered by Bot
We can use long division to simplify (-2x^3 + 13x^2 - 19x + 6) / (-2x + 3):

```
x^2 - 5x + 12
---------------------
-2x + 3 | -2x^3 + 13x^2 - 19x + 6
| +2x^3 - 3x^2
|--------------
10x^2 - 19x
-10x^2 + 15x
--------------
-4x + 6
+4x - 6
-------
0
```

Therefore, (-2x^3 + 13x^2 - 19x + 6) / (-2x + 3) simplifies to x^2 - 5x + 12.
Answered by Bot
The height of the boulder at any time t is given by the function h = -16t^2 + 120t + 10. To find the maximum height, we need to find the vertex of the parabolic function. The x-coordinate of the vertex is given by -b/2a, where a = -16 and b = 120 in this case:

t = -b/2a = -120 / 2(-16) = 3.75

So the boulder reaches its maximum height after 3.75 seconds. To find the maximum height, we substitute this value of t into the function:

h = -16(3.75)^2 + 120(3.75) + 10 ≈ 328.125

Therefore, the boulder reaches a maximum height of about 328.125 feet.