help me

The fire department is setting off fireworks. They notice that the casings of the fireworks hit the ground 78 seconds after the firework was launched. The firework exploded at a maximum height of 760.5 meters.

Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)

Answers

Answer 1

The firework is an illustration of the equation of a parabola.

The x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

The casings hit the ground after 78 seconds.

This means that, a point on the graph is:

[tex]\mathbf{(x,y) = (78,0)}[/tex]

The firework exploded at a maximum of 760.5.

This means that, the vertex is:

[tex]\mathbf{(h,k) = (39,760.5)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

So, we have:

[tex]\mathbf{0 = a(78 - 39)^2 + 760.5}[/tex]

[tex]\mathbf{0 = a(39)^2 + 760.5}[/tex]

Subtract 760.5 from both sides

[tex]\mathbf{a(39)^2 =- 760.5}[/tex]

[tex]\mathbf{1521a =- 760.5}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{760.5}{1521}}[/tex]

[tex]\mathbf{a =- 0.5}[/tex]

Substitute [tex]\mathbf{a =- 0.5}[/tex] and [tex]\mathbf{(h,k) = (39,760.5)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex]

See attachment for the graph of [tex]\mathbf{y = -0.5(x - 39)^2 + 760.5}[/tex].

From the graph:

The x and y intercepts are the points where the graph crosses the x and y axes. The vertex is the maximum point on the graph

From the equation:

Set x to 0, to calculate the value of y for the y-interceptSet y to 0, to calculate the value of x for the x-intercept.The vertex is represented as: (h,k)

Hence, the x-intercepts are 0 and 78, the y-intercept is 0, and the vertex is (39,760.5)

Read more about parabolas at:

https://brainly.com/question/5430838

Help Me The Fire Department Is Setting Off Fireworks. They Notice That The Casings Of The Fireworks Hit

Related Questions

20 POINTS PLEASE HELP ASAP!

Answers

Answer: increasing . . . positive . . . 2

Step-by-step explanation:

As best as I can tell . . .:

increasing . . . positive . . . 2.

The equation describing this line is y = 2x + 2

It has a positive (increasing) slope of 2 (with a y-intercept of +2).

Which graph represents the following relationship between X and y. Y=3x

Answers

Answer:

B

Step-by-step explanation:

Because each Y value is found by multiplying X value by 3

Riley has r red peppers and 51 green peppers. Write an expression that shows how many peppers Riley has.

Answers

Answer:

r+51 peppers

Step-by-step explanation:

QUICK HURRY I NEED THE ANSWER TOO 10(-11) HURRY!!!!!

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Answer:

-110

Step-by-step explanation:

Answer:

-110

Step-by-step explanation:

5 raised by 2- 5 (68-60)=
(with explanation plz)

Answers

Step-by-step explanation:

2-5(68-60)=2-5×8=2-40=38

Q is a degree 5 polynomial that passes through the origin, has zeros i and 7 - i, and q(-1)= -520. find the equation for q​

Answers

Using the factor theorem, the equation for q is:

[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, ..., x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]

In which a is the leading coefficient.

In this problem:

Passes through the origin, so x = 0 is a zero, that is [tex]x_1 = 0[/tex].x = i is a zero, and thus, it's conjugate also is, that is, x = -i, hence [tex]x_2 = i, x_3 = -i[/tex]x = 7 - i is a zero, and thus, it's conjugate also is, that is, x = 7 + i, hence [tex]x_4 = 7 - i, x_3 = 7 + i[/tex]

Then, the equation is:

[tex]q(x) = a(x - 0)(x - i)(x + i)(x - 7 + i)(x - 7 - i)[/tex]

[tex]q(x) = ax(x^2 - i^2)((x-7)^2 - i^2)[/tex]

Considering that [tex]i^2 = -1[/tex]

[tex]q(x) = ax(x^2 + 1)(x^2 - 14x + 50)[/tex]

[tex]q(x) = ax(x^4 - 14x^3 + 51x^2 - 14x + 50)[/tex]

[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]

q(-1) = -520 means that when [tex]x = -1, q = -520[/tex], and this is used to find a.

[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]

[tex]-520 = a(-1 - 14 - 51 - 14 - 50)[/tex]

[tex]130a = 520[/tex]

[tex]a = \frac{520}{130}[/tex]

[tex]a = 4[/tex]

Hence, the equation is:

[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]

A similar problem is given at https://brainly.com/question/24380382

PLEASE PLEASE HELP ASAP

Answers

Ok I’ll help u what do you need help with

Translate the sentence into an equation.
Eight more than the quotient of a number and 2 is 6.
Use the variable b for the unknown number.

Answers

Step-by-step explanation:

8 + b/2 = 6

8 more than the quotient of is 6

a number and 2

A group of friends wants to go to the amusement park. They have no more than $280
to spend on parking and admission. Parking is $19.50, and tickets cost $33.75 per
person, including tax. Which inequality can be used to determine p, the maximum
number of people who can go to the amusement park?

Answers

Answer:

Step-by-step explanation:

5.25 + 17.75x ≤ 165

17.75x ≤ 159.75

x = 9 people (Assuming they all fit in one vehicle)

Wish You the Best in your Studies.

The number of people who can enter in the amusement park is 7.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Several buddies want to visit the theme park. They may only spend a total of $280 for parking and entrance. Tickets cost $33.75 per person, including tax, and parking is $19.50.

Let p be the number of people who can enter in the amusement park. Then the inequality is given as,

33.75p + 19.50 ≤ 280

Simplify the inequality, then the value of p is given as,

33.75p + 19.50 ≤ 280

33.75p ≤ 260.50

p ≤ 7.72

Thus, the number of people who can enter in the amusement park is 7.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ5

Which of the following is a polynomial?
A.
(x - 2)
(x4 +3)

B. X2 - 1

C. A + x 4 + 16

D. 1/x +2

Answers

Answer:

A, B, C

Step-by-step explanation:

Assuming the choices are:

A. [tex](x-2)(x^{4}+3)[/tex]

B. [tex]x^{2} -1[/tex]

C. A+[tex]x^{4} +16[/tex]

D. [tex]\frac{1}{x} +2[/tex]

Put simply, a polynomial in this case will be a function that has at least one variable raised to a power greater than 1.

Choice A already has a variable raised to a power greater than 1 ([tex]x^{4}[/tex]), so no additional manipulation is needed.

Choice B also has a term that is already raised to a power greater than 1 ([tex]x^{2}[/tex]). It is the same for choice C ([tex]x^{4}[/tex]).

Choice D does not have an obvious variable raised to a power greater than 1. When the equation is manipulated it becomes [tex]x^{-1} +2[/tex]. Since -1 is less than 1, choice D is not a polynomial.

Answer:

Option D

Step-by-step explanation:

[tex]\\ \sf\longmapsto \dfrac{1}{x}+2[/tex]

Simplify

[tex]\\ \sf\longmapsto x^{-1}+2[/tex]

Degree is less than 1 .It's not a polynomial

Expand the brackets in these expressions
1.(a²)²
2.(3c)³
3.(2z²)³
4.a(2b)²
5.5(q2)2
6.(xy)²
7. i(jk)²

Answers

Answer:

1. a^4.

2. 9c³.

3. 8z^6.

4. 4b²a.

5. 20q(if the 2 isn't an exponent)

if it is,

20q².

6.x²y².

7. j²k²i.

All the best.

Answer:

Step-by-step explanation:

[tex]1.(a^{2})^{2}= a^{2*2}=a^{4}\\\\\\2. (3c)^{3}=3^{3}*c^{3} = 27c^{3}\\\\\\3.(2z^{2})^{3}=2^{3}*(z^{2})^{3}=8z^{2*3}=8z^{6}\\\\\\4.a(2b)^{2}=a*2^{2}b^{2}=4ab^{2}\\\\\\5.5(q^{2})^{2} = 5q^{2*2}=5q^{4}\\\\\\6.(xy)^{2}=x^{2}y^{2}\\\\\\7i(jk)^{2}=ij^{2}k^{2}[/tex]

If Sean reads 1 1/2 pages in 3 1/3 minutes, how many pages does he read in 1 minute?

Answers

Sean reads about 1 pages in one minute I believe because 1/2 in 1/3 is like a half of a page

PLEASE HELP THANK YOU AND HAVE A GOOD DAY!

Answers

Answer:c

Step-by-step explanation:c because u gotta look closwely

c

brainlest if you answer right.

Answers

i think it is 60 but I’m not totally sure

hii i need help! write the inequality represented by the graph below.

Answers

95252226!!
0363373
44448

136 is 0.8​% of what​ number? Use pencil and paper. Would you expect the answer to be a lot less than 136​, slightly less than 136​, slightly greater than 136​, or a lot greater than 136​? Explain.

Answers

Bbbnnbbnnnnnnnjjjjhgcccyhcvhjvvjjbjvivvi

The table shows the shipping fee options for two online marketplaces.



Online Market Shipping Fees
Deals Flat fee of $12
Sell Ur Stuff 11% of selling price


If you sell a smart phone online for $115, how much will you pay if you use the online market with the lesser fee?

Answers

Since 11% of $115 is $12.65, it is convenient to pay the flat fee of $12.

If you sell a smart phone online for $115, to determine how much you will pay if you use the online market with the lesser fee, the following calculation must be performed:

115 x 0.11 = X 12.65 = X

Thus, since 11% of $115 is $12.65, it is convenient to pay the flat fee of $12.

Learn more in https://brainly.com/question/25206811

What is the area of the rectangle?

Answers

Answer:

60

Step-by-step explanation:

multiply length times width l x w

length is 10

width is 6

10 x 6 is 60

The area of the rectangle is 54.
The length of the rectangle is 9, while the width of the rectangle is 6. To find the area, you must multiply length • width.
9•6=54

Consider the following incomplete deposit ticket:A deposit ticket. The amounts deposited were 782 dollars and 11 cents and 564 dollars and 64 cents. The subtotal was 1346 dollars and 75 cents. The total after cash received is 888 dollars and 18 cents.How much cash did Liz receive?

Answers

The amount of cash Liz received is; 458 dollars and 57 cents.

The amounts deposited were as follows;

782 dollars and 11 cents 564 dollars and 64 cents

The subtotal is therefore; 1346 dollars and 75 cents.

Since, the total after cash received is; 888 dollars and 18 cents.

The amount of cash received by Liz is;

1346 dollars and 75 cents - 888 dollars and 18 cents.

=458 dollars and 57 cents.

Read more on deposit ticket:

https://brainly.com/question/3044615

Answer:

A) 1145.39 on Edge

Step-by-step explanation:

Just took test :)

tan9°. tan27°. tan45°. tan72°. tan81°= 1​

could u plz solve it with clear process

Answers

Correct question:-

Prove that tan9.tan17.tan45.tan73.tan81=1

LHS

[tex]\\ \sf\longmapsto tan9.tan17.tan45.tan73.tan81[/tex]

[tex]\\ \sf\longmapsto tan9.tan81.tan17.tan73.tan45[/tex]

[tex]\\ \sf\longmapsto tan(90-81).tan81.tan(90-73).tan73.1[/tex]

[tex]\\ \sf\longmapsto cot81.tan81.cot73.tan73[/tex]

[tex]\\ \sf\longmapsto 1.1[/tex]

[tex]\\ \sf\longmapsto 1[/tex]

If the chick grows at a rate of 4.8 grams/day and weighs 53.8 grams on day 4, how much did the chick weigh (in grams) the day it hatched?

Answers

Answer:

Step-by-step explanation:

y = 4.8x + C

53.8 = 4.8(4) + C

53.8 = 19.2 + C

C = 34.6

porfavor ayuda ayuda

Answers

Answer:

b is 3/5 then 9/5 and lastly 15/25

c is 2/3 then 6/12 then 12/18

¿What are Fractions?

Fractions is that fraction whose fractional number is the expression of a quantity divided by another quantity; that is, it represents an unrealized quotient of numbers.

[tex] \bold{a) \dfrac{2}{4} = \dfrac{4}{8} = \dfrac{6}{12} = \dfrac{8}{16} = \dfrac{10}{20} }[/tex]

[tex]\bold{b) = \dfrac{3}{5} = \dfrac{6}{10} = \dfrac{9}{15} = \dfrac{12}{20} = \dfrac{15}{25} }[/tex]

[tex] \bold{c) \dfrac{2}{3} = \dfrac{4}{6} = \dfrac{6}{12} = \dfrac{10}{15} = \dfrac{12}{18} }[/tex]

Please help me! It’s for geometry

Answers

The answer to this is 2 67.5

I will mark brainiest plz help

Answers

Answer:

96

Step-by-step explanation:

The length of the large rectangle is: 5 units

The width of the large rectangle is: 7 units

- > Area of the large rectangle = length × width  = 7*5 = 35 square units

The length of the middle rectangle is: 7 units

The width of the middle rectangle is: 4 units

- > Area of the middle rectangle = length × width  = 7*4 = 28 square units

The length of the small rectangle is: 7 units

The width of the small rectangle is: 3 units        

- > Area of the small rectangle = length × width  = 7*3 = 21 square units

Area of top and the bottom triangles =2* 1/2(bh) = 4*3 = 12 square units

Then we find the total surface surface area by adding up all of these  

- > 35 + 28 + 21 + 12 = 96 square units

The queen marys 2’d height above water is about the same as a 14 story building, what is the queen mary twos height above water, pls help this is due today

Answers

Answer: Length 1,132 ft

Step-by-step explanation: Im not sure if this is the one your talking about but here.

What is the missing measure

Answers

Answer:

119

Step-by-step explanation:

Answer:

look at the photo...............

expand the brackets (x+5)(3x-2).

Answers

Answer: 3x^2 +13x - 10

Step-by-step explanation:

(x+5)(3x-2) = x(3x-2) + 5(3x-2)

x(3x-2) + 5(3x-2) = 3x^2 - 2x + 15x - 10

3x^2 - 2x + 15x - 10 = 3x^2 + 13x - 10

Answer:

3x²+13x-10

Step-by-step explanation:

(x+5)(3x-2)x(3x-2)+5(3x-2)3x²-2x+15x-103x²+13x-10

What is the slope of this line?

Answers

Answer:

Slope = 2

Step-by-step explanation:

(x₁ , y₁) = ( 1 , 1)   & (x₂,y₂) = (-1,-3)

[tex]Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-3-1}{-1-1}\\\\=\dfrac{-4}{-2}\\\\=2[/tex]

A plane travels a distance of 6,000 km in a time of 6.2 hours.
What is its average speed rounded to the nearest whole number?

Answers

Answer:

distance =6,000km

time =6.8 hrs

speed =distance /time =6,000/6.8=60000/68=882 km/h

plz make brainiest

I need help please and thank you

Answers

Answer:

I believe it's B ............

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