f(x) = 2x2 + 12x + 1
Determine the vertex

Answer:

a. 304 feet

b. 425 feet

c. 3.75 seconds

d. It will take the rocket approximately 8.9 seconds to hit the ground

Step-by-step explanation:

1. The given data of the question including the question relationships are listed as follows;

The height of the cliff from which the rocket was launched = 200-ft.

The initial velocity of the rocket, u = 120 feet per second

The equation that models the height of the rocket with respect to time 't' is h(t) = -16·t² + 120·t + 200

a. The height of the rocket after 1 second is given by plugging in t = 1 in the equation that models the height as follows;

h(1) = -16 × (1)² + 120 × (1) + 200 = 304

The height of the rocket after 1 second, h(1) = 304 feet

b. The maximum height can be found by finding the value of the maximum point of the curve of the equation for the height as follows;

At the maximum point, h'(t) = d(-16·t² + 120·t + 200)/dt = 0

∴ d(-16·t² + 120·t + 200)/dt = -32·t + 120 = 0

t = 120/32 = 3.75

At the maximum point, t = 3.75 seconds

The maximum height can also be found by finding the vertex of the parabola formed by the height equation as follows;

At the vertex (the maximum point), t = -b/(2·a) = -120/(2 × (-16)) = 3.75

At the vertex (the maximum point), t = 3.75

The height at the maximum point = h(3.75) = -16 × (3.75)² + 120 × (3.75) + 200 = 425

The height at the maximum point, h(3.75) = 425 feet

c. The time it will take the rocket to reach the maximum point is given by the value of 't' at the maximum point, the vertex, which is t = -b/(2·a) = -120/(2 × (-16)) = 3.75

Therefore;

The time it takes the rocket to reach the maximum point, [tex]t_{max}[/tex] = 3.75 seconds

d. The time it takes the rocket to hit the ground (height h(t)) is given by finding the values of 't' that satisfy the height equation where h(t) = 0 as follows;

At the ground level, h(t) = 0 = -16·t² + 120·t + 200

Therefore, we get;

-16·t² + 120·t + 200 =

t = (-120 ± √(120² - 4×(-16) × 200))/(2 × (-16))

t ≈ 8.9 or t ≈ -1.4

Therefore, the time it takes the rocket to hit the ground is given by the natural number, t ≈ 8.9 seconds.

Answer:

3.46

Step-by-step explanation:

plz can i get brainliest:)

Answer:

it's 65 because if u count the inside of the boxes u get 65

Answer:

34

Step-by-step explanation:

to get the perimeter you add the side-A with Base-B and Side-C.

The base at the bottom is 10 and the two symmetrical sides is 12.

P= a + b + c

34= 12 + 10 + 12

Answer:

the pic wont load

Step-by-step explanation:  try and upload again

Answer:

$660

Step-by-step explanation:

Step 1

The number of extra necklaces that valeria needs is calculated as:

477 necklaces - 147 necklaces

= 330 necklaces

Step 2

We are told that

1 extra necklace cost $2

Hence

1 necklace = $2

330 necklaces = x

Cross Multiply

x = 330 × $2

x = $660

Therefore, Valeria need to spend and additional $660

Answer:12/87

Step-by-step explanation: You first have to add up all of the birds present. Then you have to see how many of the type you are looking for is there. The number of the type of bird goes on top of the number of total birds.

Answer: ∠E=55°

Step-by-step explanation:

Concept

- In all similar triangles, their corresponding angle will be the same value

- Triangle angle sum theorem: the three interior angles of a triangle add up to 180°

Given

- Two pairs of corresponding angles

- Two similar triangles

Solve

(6x-15)+4x=(5x-1)+4x ⇔ Add the angles up

6x-15=5x-1 ⇔ Subtract 4x on both sides

x-15=-1 ⇔ Substract 5x on both sides

x=14 ⇔ Add 15 on both sides

 180-4x-(5x-1) ⇔ Find ∠E by subtracting the other two angles from 180

=180-4(14)-([5(14)-1]

=180-56-69

=55°

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Radius = 10 cm

Circumference = 20*pi cm

Step-by-step explanation:

Area of a circle = pi * r^2

100 = r^2

10 = r

Circumference = 2*pi*r

2*pi*10

20*pi

Answer:

6

Step-by-step explanation:

The x intercept is the value of x when y equals zero. The table tells us that when x goes up by one, y goes down by two.

Knowing this, all we have to do is increase x by 1 and decrease y by two until y is zero, and we can look and see what x is.

I also made a visual in the file below if this is confusing

Given:

Three coins are tossed.

To find:

The probability that you will get “heads” no more than once out of 3 flips.

Solution:

If three coins are tossed then the sample space is:

[tex]S=\{HHH,HTH,HHT,HTT,THH,TTH,THT,TTT\}[/tex]

Total possible outcomes = 8

Number of 0 successes means 0 heads in 3 flips, i.e., TTT.

Number of 1 successes means exactly 1 heads in 3 flips, i.e., HTT, THT, TTH.

Now,

[tex]P(0\text{ success})=\dfrac{1}{8}[/tex]

[tex]P(1\text{ success})=\dfrac{3}{8}[/tex]

And, their sum is:

[tex]P(0\text{ success})+P(1\text{ success})=\dfrac{1}{8}+\dfrac{3}{8}[/tex]

[tex]P(0\text{ success})+P(1\text{ success})=\dfrac{4}{8}[/tex]

[tex]P(0\text{ success})+P(1\text{ success})=\dfrac{1}{2}[/tex]

Therefore, the probability that you will get “heads” no more than once out of 3 flips is [tex]\dfrac{1}{2}[/tex].

Answer:

p = 5

Step-by-step explanation:

think of it like this:

2 + p = 7

They just want you to find what number can replace the letter so the equation makes sense.  

Answer:

m∠1=111°

Step-by-step explanation:

Since angle 1 is an exterior angle on a straight line, it is the sum of the two outer angles of the triangle.

64+47=111.

Answer:

Yes

Step-by-step explanation:

What is the question we need to answer? We got the information

Answer:

b po ang tamang sagot

Step-by-step explanation:

i hope its help

Answer:

X > 2

Step-by-step explanation:

Value of x is greater than 2 and the circle is not filled. So.  x > 2

Answer:

158.45

Step-by-step explanation:

Answer:

gYou and your family go out for dinner.  The bill is $146.  There is 8.25% tax.  Find the total price you will pay for dinner including tax.

Step-by-step explanation:vYou and your family go out for dinner.  The bill is $146.  There is 8.25% tax.  Find the total price you will pay for dinner including tax.

Answer:  60

Step-by-step explanation:

Answer:60

Step-by-step explanation:

((−8)(15) (-1/2) =60

Answer:

Option A. {-4, 2, 4}

Step-by-step explanation:

There is no other options because none of them are bigger than -5 except Option A.

Answer:

60 cubic inches

Step-by-step explanation:

first find the area of the right triangle then multiply by 10 in.

=> (3 × 4 ÷ 2) × 10

=> 60 in.³

Answer:

Its the third and fourth answer

Answer:

Probability that the proportion of airborne viruses in a sample of 529 viruses would be greater than 8% is 0.9545.

Step-by-step explanation:

For the given population the distribution of air-borne viruses is given as 6%. Now for this the value of Z score is given as

[tex]Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}}[/tex]

Here

So the Z score is given as

[tex]Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}}\\Z=\dfrac{0.08-0.06}{\sqrt{\dfrac{0.08(1-0.08)}{529}}}\\Z=\dfrac{0.02}{\sqrt{\dfrac{0.08(0.92)}{529}}}\\Z=\dfrac{0.02}{\sqrt{\dfrac{0.0736}{529}}}\\Z=\dfrac{0.02}{0.01179}\\Z=1.6955[/tex]

For this the score, the value of probability is calculated from the table as below:

[tex]P(\hat{p}>0.08)=p(Z>1.6955)\\=1-p(Z<-1.6955)[/tex]

Here value of p(Z<-1.6955) is given as 0.0455

[tex]P(\hat{p}>0.08)=p(Z>1.6955)\\P(\hat{p}>0.08)=1-p(Z<-1.6955)\\P(\hat{p}>0.08)=1-0.0455\\P(\hat{p}>0.08)=0.9545[/tex]

Answer:

you can do this have a great day

Step-by-step explanation:

Answer:

x = - 3

Step-by-step explanation:

- 8x - 10(3) = - 6

- 8x - 30 = - 6

- 8x - 30 + 30 = - 6 + 30

- 8x = 24

- 8x ÷ - 8 = 24 ÷ - 8

x = - 3

Answer:

the answer is A -3

Step-by-step explanation:

-8x-10y=-6 when y=3

-8x-10(3)=-6

-8x-30=-6

-8x=-6+30

-8x=24

-8x÷8=24÷8

x=-3

Answer:

aa is the repuestos yes ok

Answer:

A

Step-by-step explanation:

Answer:

Real numbers have two categories: rational and irrational. If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end.

Step-by-step explanation:

So as to say that irrational numbers can't be a squared root because of there decimals.

Answer:

y = 4x + 1

Step-by-step explanation:

y = mx + b

The line goes thru (0, 1) and (1, 5)

The slope = m = (5 - 1)/ 1 - 0) = 4/1 = 4

The y-intercept is (0, 1), so b = 1

y = 4x + 1 is the equation of the line

Answer:

6 hours

Step-by-step explanation:

Given: A plane is traveling at a constant rate described by d = 525t

where d is the distance and t is the time

We know that ratio  of distance upon time  = d/t = 525 miles per hour

Therefore, time taken to travel 3150 miles  = 3150/525 = 6 hours

Answer:

p-(-Q)

Step-by-step explanation:

Because the thing goes down and i got it correct for that answer your welcome

Answer:

Open circle at 3 going to the right.

Step-by-step explanation:

Let’s look at this.

first, let’s simplify the inequality. 2x +3-3>9-3

2x>6

x>3

since this is just a greater than or less than, it will be an open circle.

now that we have established that, we can see that x is BIGGER than 3. In that case, it will be an open circle at 3 going to the right.

Answer:

$107.60

Step-by-step explanation:

100 [1 + (0.076 * 1)] = 107.6

= $107.60