1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
RUDIKE [14]
3 years ago
9

The function f(t) = t2 + 6t − 20 represents a parabola.

Mathematics
2 answers:
Shalnov [3]3 years ago
7 0

The <em>correct answers</em> 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.

Novay_Z [31]3 years ago
4 0
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.
You might be interested in
Joanne has a cylindrical, above ground pool. the depth (height) of the pool is 1/2 of its radius, and the volume is 1570 cubic f
diamong [38]

Answer:

314 ft²

Step-by-step explanation:

Data provided in the question:

Depth (height) of the pool = \frac{1}{2} of its radius

let the radius be 'r' ft

thus,

Depth (height) of the pool, h = \frac{r}{2} ft

Volume of the pool = 1570 ft³

also,

Volume of cylinder = πr²h

thus,

1570 ft³ = πr²h

or

1570 ft³ = \pi r^2(\frac{r}{2})

or

3140 = 3.14 × r³                     [ π = 3.14 ]

or

r³ = 1000 ft³

or

r = 10 ft

Thus,

Area of the bottom surface = πr²

= 3.14 × 10²

= 314 ft²

5 0
3 years ago
Can someone please help me with 10-16 it’s due tomorrow!!! Please
VMariaS [17]
10) V=πr² *h= π*10²*12≈3770
11) V=A(base)*h= (3√3/2)*(9²)*10=2104
A(base)=(P*a)/2=(6*9*3√3)/2=9*9*3√3/2

12)V=πr² *h=π*18² *6≈6107
13)V=4*3*12=144
14) h(triangle)=√(5²-3²)=√16=4
A(base)=(3*4)/2=6
V=A(base)* height (prism)=6*2=12
15)  V=A(base)*h= (3√3/2)*(6²)*11= 1029
16)V=A(base)*h=2(1+√2)5²*22≈2656
7 0
3 years ago
Compute the permutations and combinations.<br><br> 6 P 4<br><br> 15<br> 30<br> 360
3241004551 [841]
The answer is c.
6 P 4 = 360
7 0
3 years ago
Read 2 more answers
Help please Question is in the picture
anzhelika [568]

Answer:

360 degrees in total.

Step-by-step explanation:

We are given that the m∠1 is 145 degrees, and because ∠1 and ∠2 form a straight line we can tell that 180-145 = 35.

So now here's what we know:

m∠1 = 145

m∠2 = 35

After that, we need to look at ∠5 and ∠6.

One thing we can notice right away is that ∠5 and ∠6 should measure the same as ∠1 and ∠2 (respectively) because they are corresponding angles.

Now we will add them all together to find the sum of all four angles.

m∠1 = 145 + m∠2 = 35 = 180

m∠5= 145 + m∠6 = 35 = 180

180 + 180 = 360

8 0
3 years ago
Sara had 182 dollars to spend on 7 books. After buying them she had 14 dollars. How much did each book cost
Afina-wow [57]
I believe the answer is 24 if not im sorry
5 0
3 years ago
Other questions:
  • Which point is not in the solution set of 3x+2y&lt;12? A (1,4) B (2,3) C (3,1) D(4,-1)
    10·2 answers
  • A plumber has a 2.5 meter long copper pipe. He needs to cut lengths of 60cm,35cm and 90cm
    12·1 answer
  • 78km into miles<br> 32km into miles<br> 54km into miles
    15·2 answers
  • Lee’s teacher gave her a picture of an angle and asked her to perform a common construction on the figure. Lee used a compass to
    11·2 answers
  • The sample space of rolling a six sided die twice is shown in the table.
    11·1 answer
  • Three less than the quotient of a number and 3 is 15. What is the number?
    5·1 answer
  • PLEASE HELP ME I NEED THE ANSWER
    11·1 answer
  • Find the slope using points ( 7,-3) and (11,-4)
    9·2 answers
  • How to find square root ?​
    12·2 answers
  • What is f(3) for: f(x)=x2-x+5 f(3)=
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!