The function f(t) = t2 + 6t − 20 represents a parabola.Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

Answers

Answer 1

Answer: Part A: f(t) = t² + 6t - 20
  u = t² + 6t - 20
+ 20 + 20
u + 20 = t² + 6t
u + 20 + 9 = t² + 6t + 9
u + 29 = t² + 3t + 3t + 9
u + 29 = t(t) + t(3) + 3(t) + 3(3)
u + 29 = t(t + 3) + 3(t + 3)
u + 29 = (t + 3)(t + 3)
u + 29 = (t + 3)²
- 29 - 29
u = (t + 3)² - 29

Part B: The vertex is (-3, -29). The graph shows that it is a minimum because it shows that there is a positive sign before the x²-term, making the parabola open up and has a minimum vertex of (-3, -29).
------------------------------------------------------------------------------------------------------------------
Part A: g(t) = 48.8t + 28 h(t) = -16t² + 90t + 50
| t |   g(t) | | t | h(t) |
|-4|-167.2| | -4 | -566 |
|-3|-118.4| | -3 | -364 |
|-2| -69.6 | | -2 | -194 |
|-1| -20.8 | | -1 | -56 |
|0 |   -28 | | 0  |   50 |
|1 | 76.8 | |  1 | 124 |
|2 | 125.6| | 2 | 166 |
|3 | 174.4| | 3 | 176 |
|4 | 223.2| | 4 | 154 |
The two seconds that the solution of g(t) and h(t) is located is between -1 and 4 seconds because it shows that they have two solutions, making it between -1 and 4 seconds.

Part B: The solution from Part A means that you have to find two solutions in order to know where the solutions of the two functions are located at.

Answer 2

Answer:

The correct answers are:

Question 1 - Part A: f(t)=(t+3)²-29; Part B: (-3, -29), minimum; Question 2 - Part A: H(1) = 124, g(1) = 76.8; H(2) = 166, g(2) = 125.6; H(3) = 176, g(3) = 174.4; H(4) = 154, g(4) = 223.2; Part B: Between 3 and 4 seconds, because that is where the values of g(t) catch up with H(t).

Explanation:

Our quadratic function is in the form f(x)=ax²+bx+c. Our value of a is 1, b is 6, and c is -20.

To write a quadratic in vertex form, first take half of the b value and square it: (6/2)² = 3² = 9. This is what we will add and subtract to the function:

f(t) = t²+6t+9-20-9

The squared portion will be (t+b/2)²:

f(t) = (t+3)²-20-9

f(t) = (t+3)²-29

Vertex form is f(x) = a(x-h)²+k, where (h, k) is the vertex; in our function, (h, k) is (-3, -29).

Since the value of a was a positive, this parabola opens upward; this makes the vertex a minimum.

For Question 2 Part A, substitute the values 1, 2, 3 and 4 in H(t) and g(t).

For Part B, we can see that the values of g(t) are much less than that of H(t) until 3 seconds. From there, we can see that g(t) passes H(t). This means that the solution point, where they intersect, is between 3 and 4 seconds.

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Camillo estimates the weight of his dog. The veterinarian says that the dog weighs 84 pounds. The percent error in Camillo's estimates is less than 10%.Decide whether each of the following weight estimates could have been Camillo's estimate.
a. 80 pounds yes or no
b. 78 pounds yes or no
c. 94 pounds yes or no
d. 77 pounds yes or no
e. 92 pounds yes or no
f. 75 pounds yes or no

Answers

Answer:

A.Yes B.Yes C.No D.Yes E.No F.No

Step-by-step explanation:

10% of 84 is 8.4 and 84-8.4=76.6 and anything between 76.6-84 could have been the estimate.

Final answer:

Camillo's weight estimate could have been 80 pounds, 78 pounds, 77 pounds, or 92 pounds.

Explanation:

The percent error measures the discrepancy between an estimated value and an actual value. It is calculated using the formula: Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100%. Since the given problem states that Camillo's estimate has a percent error less than 10%, we can calculate the percent error for each weight estimate and determine if it is less than 10%.

a. 80 pounds: Percent Error = (|80 - 84| / 84) * 100% = 4.76%, which is less than 10%. So, yes, this could have been Camillo's estimate.
b. 78 pounds: Percent Error = (|78 - 84| / 84) * 100% = 7.14%, which is less than 10%. So, yes, this could have been Camillo's estimate.
c. 94 pounds: Percent Error = (|94 - 84| / 84) * 100% = 11.9%, which is not less than 10%. So, no, this could not have been Camillo's estimate.
d. 77 pounds: Percent Error = (|77 - 84| / 84) * 100% = 8.33%, which is less than 10%. So, yes, this could have been Camillo's estimate.
e. 92 pounds: Percent Error = (|92 - 84| / 84) * 100% = 9.52%, which is less than 10%. So, yes, this could have been Camillo's estimate.
f. 75 pounds: Percent Error = (|75 - 84| / 84) * 100% = 10.71%, which is not less than 10%. So, no, this could not have been Camillo's estimate.

Learn more about Percent Error here:

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The population of Florida in 2010 was 18,801,310 and the land area was 53,625 square miles. The population increased 5.8% by 2014. To the nearest whole number what is the population density in people per square mile for Florida in 2014? To the nearest whole number how much did the population density in people per square mile increase from 2010 to 2014?

Answers

In 2010 the population density was 341 people per square mile and the population density in 2014 was 361 people per square mile making a change of 20 ppl per sq mile

If water ﬂows into a rectangular tank at the rate of 6 cubic feet per minute, how long willit take to ﬁll the tank, which measures 18''x 32'' x 27''

Answers

v=lwh for a rectangle
18*32*27=v
v=15,552in^3
15,552/12=1296ft^3 converts feet to inches
6*6*6=216ft^3 this is how much is filled up in a minute
1296/216=6 minutes.

the volume of a rectuangular prism is length×width×height

in this case, the volume will be 18×32×27 = 15,552 cubic inches.

water flows in by cubic feet, so we'll need to either transformthe volume of the tank to feet, or the volume of water flow to inches. in this case, it will make our life easier if we turn the tank valume into feet. 15,552 inches is exactly 1296 feet.

water flows in 6 cubic feet per minute, so we calculate that 1,296 ÷ 6 = 216

water will be flowing in for 3 hours and 36 minutes thusly.

Find the product. -mnp(3m - 5n + 7p)

Answers

- mnp ( 3 m - 5 n + 7 p )

= -mnp * 3 + 5mn² - 7 mnp²

=> - 3 m²np + 5 mn² - 7 mnp²

hope this helps!

Answer:

- 3 m²np + 5 mn² - 7 mnp²

Step-by-step explanation:

A class of 24 students is planning a field trip to a science museum. A nonrefundable deposit of $50 is required for the day-long program, plus a charge of $4.50 per student.Determine a linear function that models the cost, c, and the number of students, s.

Which statements about the linear function and its graph are correct? Check all that apply.

Answers

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Step-by-step explanation:

Did it on Edgenuity

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Step-by-step explanation:

Ron grew 224 flowers with 56 seed packets. How many seed packets does Ron need to have a total of 324 flowers in his garden? Assume the relationship is directly proportional.

Answers

Answer:

the relationship is directly proportional.

224 flowers 324 flowers

56 seed packets (324*56)/224=81 seed packets

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