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lana [24]
2 years ago
6

Anne fires a toy rocket into the air from the top of a barn. The height of the rocket above the ground in feet after t seconds i

s given by
the function h(t) = -5t^2 + 20t -15. After completing the trajectory, Anne finds that the maximum height the toy rocket reached in the
air is represented by the expression -5(t-__)^2+5 Write the missing piece of the expression
Mathematics
1 answer:
astra-53 [7]2 years ago
5 0

The missing piece of the expression is 2

<h3>Maximum height of the rocket</h3>

From the question, the height of the rocket above the ground in feet after t seconds is given by the function h(t) = -5t^2 + 20t -15

At maximum height, the velocity of the function is zero. Hence;

dh/dt - -5(2)t + 20
dh/dt = -10t + 20

Write the expression in vertex form as shown:

h(t) = -5t^2 + 20t -15

h(t) = -5(t^2 - 4t +3)

h(t) = -5(t^2 - 4t + 2^2 + 3 - 2^2)

h(t) = -5((t+2)^2 +5
h(t) = -5((t+2)^2 + 11

Hence the missing piece of the expression is 2

Learn more on vertex form here: brainly.com/question/525947

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Daniel bought four bags of potatoes. The weight of the first bag was 2.6 pounds. The second bag weighed 0.4 pound less than twic
ipn [44]

Answer:

Average weight of the bags of potatoes is 3.8 pounds.

Step-by-step explanation:

Given:

Weight of the first bag, W_{1}=2.6 pounds.

Weight of the second bag is 0.4 pounds less than twice the weight of first bag. This means,

W_{2}=2W_{1}-0.4=2(2.6)-0.4=5.2-0.4=4.8\textrm{ pounds}

Weight of the third bag is 0.6 pounds more than that of the first bag. This means,

W_{3}=W_{1}+0.6=2.6+0.6=3.2\textrm{ pounds}

Weight of the fourth bag is 0.3 pounds less than that of the second bag. This means,

W_{4}=W_{2}-0.3=4.8-0.3=4.5\textrm{ pounds}

Therefore, the average weight of the bags of potatoes is given as the sum of all the weights and then divide the sum by 4. Therefore,

W_{average}=\frac{W_{1}+W_{2}+W_{3}+W_{4}}{4}=\frac{2.6+4.8+3.2+4.5}{2}=\frac{15.1}{4}=3.775\approx 3.8

Therefore, average weight of the bags of potatoes is 3.8 pounds.

8 0
3 years ago
PLEASE HELP 30 PTS!!! Select ALL the correct answers. Which expressions are equivalent to the following?
Oksanka [162]

Answer:

  D:  -5(-6x^2 + x + 2)

  E:  5(2x + 1)(3x − 2)

Step-by-step explanation:

The <em>first two answer choices have incorrect constants</em> (25 and 3 vs -10). A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:

  30x^2 -5x -10 = 5(6x^2 -x -2)

An additional x cannot be factored from the expression, so <em>choice C can be eliminated</em>.

Multiplying each of these factors by -1 will make the product correspond to answer choice D.

Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:

  E:  2x(-2) +1(3x) = -x, as required

  F:  2x(2) -1(3x) = x, wrong sign

The equivalent expressions are those of choices D and E.

7 0
3 years ago
PLEASE Help will give brainliest :0 (MATH)
steposvetlana [31]

Answer: 12/5 = 2 2/5

Step-by-step explanation:

3 0
2 years ago
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