What is the simplified form of (4t^2-5t+3)/(2t^2-t+1)?

Answer 1

There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.

Answer 2

(4t^2-5t+3)/(2t^2-t+1)?

Answer 3

There is no common factor between the numerator and denominator that can be canceled out, so this expression cannot be simplified.

Answer 4

A box has a volume given by the trinomial 2x^3-16x^2-40x

Answer 5

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.

Answer 6

5d^-6 x d^12

Answer 7

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.

Answer 8

(-2x^3+13x^2-19x+6)/(-2x+3)

Answer 9

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.

Answer 10

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.

Answer 11

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.