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

A term may be written in index form to?
a) Make calculation easier
b) Represent large numbers
c) Show repeated multiplication
d) All the above​

Answers

Answer:

A.make calculation easier

Can someone help me with this

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-6 + x = -7

+6        +6        add 6 to both sides, 6's cancel out on the left.

________

x = -1, is the answer.

Hope this helps! Let me know if you have any other questions related to this problem. :)

Answer:

x= -1

Step-by-step explanation:

-6+x = -7

x = -7+6

x= -1

Quick I need Helpppp!!

Triangle EFT is congruent to triangle JKL. What is KL, in units

Answers

Answer:

KL = 6 units.

Step-by-step explanation:

Congruent means the same or similar.

Hope this helps!

what is 3/4 times 8/9?! plzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

2/3

Step-by-step explanation:

= 3/4 * 8/9

= 24/36

simplify by 4

= 6/9

simplify by 3

= 2/3

Answer:

24 /36 or 2/3

Step-by-step explanation:

3 x 8 = 24

4 x 9 = 36

24/36

Simplify the fraction to get 2/3

Therefore, 2/3 would be your answer.

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3y^2 i don’t know for sure

i am never able to do these, their so confusing yet SO easy- please help!

Answers

Answer:

a) independent: area to be painted in sq ft

dependent: amount of paint needed in gallons

b) independent: amount of milligrams

dependent: amount of sleep

Step-by-step explanation:

Easy tip to remember that is almost always right:

Your X variable is always independent, and your Y variable is always dependent.

If you aren't given these variables, another thing you can do is ask for example, question a, ask yourself, "is the area you paint dependent on the amount of paint you need?" , or "is the amount of paint you need, dependent on how much your painting?"

Which variable depends on your other variable? Would help you find your dependent variable.

It makes sense that, the number of paint you need depends on how much sq ft you are painting.

Answer:

a) Independent variable: x (area to be painted)

   Dependent variable: y (amount of paint needed)

b) Independent variable: x (amount of medication)

    Dependent variable: y (amount of sleep)

Step-by-step explanation:

Independent variables are variables that do not depend on other variables to determine their values.

Dependent variables are variables that depend on other variables to determine their values.

The sum of two consecutive odd numbers is 1408. What are the numbers?
Put the smaller number first comma then the larger number.

Answers

Answer:

703,705

Step-by-step explanation:

divide 1408 by 2

add one for one number

subtract one for the other

12 lightbulbs are tested to see if they last as long as a manufacturer claims they do three lightbulbs failed a test two light bulbs are selected at random without replacement find the probability that both light bulbs failed the test

Answers

Using the hypergeometric distribution, it is found that there is a 0.0455 = 4.55% probability that both light bulbs failed the test.

The bulbs are chosen without replacement, and this is why the hypergeometric distribution is used to find the probability.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.

In this problem:

12 bulbs, thus [tex]N = 12[/tex]3 failed the test, thus [tex]k = 3[/tex].2 are selected, thus [tex]n = 2[/tex].

The probability that both failed the test is P(X = 2), thus:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,3) = \frac{C_{3,2}C_{9,0}}{C_{12,2}} = 0.0455[/tex]

0.0455 = 4.55% probability that both light bulbs failed the test.

A similar problem is given at https://brainly.com/question/24826394

1/(2+i)²

Solve this question....​

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

Given complex number is

[tex]\rm \longmapsto\:\dfrac{1}{ {(2 + i)}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{1}{4 + {i}^{2} + 2 \times 2 \times i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{4 - 1 + 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{3+ 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{3+ 4i} \times \dfrac{3 - 4i}{3 - 4i} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{ {3}^{2} - {(4i)}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 -16 {i}^{2} } [/tex]

We know,

[tex] \rm \longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: } \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 -16( - 1)} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{9 + 16} [/tex]

[tex]\rm \:  =  \: \dfrac{3 - 4i}{25} [/tex]

[tex]\rm \:  =  \: \dfrac{3}{25} - \dfrac{4}{25}i[/tex]

Please help I have 15 minutes left for my assessment. Thank you!

Answers

Answer:

57kg

Step-by-step explanation:

We need to find the length of each piece of metal:

We already know that 2 of them are 6m and 8m and this would be the same for the pieces of metal opposite.

So we have four lengths - 6m, 6m, 8m, and 8m

To find the last length, we need to use pythagoras theory

a² + b² = c² where c is the slanted side, or the diagonal

6² + 8² = c²

36 + 64 = 100

c² = 100

c = √100 = 10

So the five lengths are 6m, 6m, 8m, 8m, and 10m and the total is 38m

If:

1m = 1.5kg

38m = ?kg

We have to multiply both sides by 38

1m × 38 = 38m

1.5kg × 38 = 57kg

So, the total weight of metal in the frame is 57kg

8.5 inches to centimeters

Answers

answer: 21.59

I hope this helps! Let me know if you have any questions! Good luck on the rest of your assessment!

Mark this as Brainliest (if i helped of course) if you get a chance:)

Answer:

21.59cm

Step-by-step explanation:

Multiply 8.5 by 2.54 to convert in. to cm.

The scale of a blueprint is 1 in.=20 ft.
The length of a wall in the blueprint is 2.5 in. What is the length of the actual wall?
What is the blueprint length of an entrance that is 5 ft wide?

Answers

Answer:

1) 50 feet

2) 0.25 or 1/4 inches

Step-by-step explanation:

If one inch is equal to 20 feet, then multiply 20 by 2.5 to find the length of the actual wall

5 feet is a fourth of 20 feet, and since 1 inch is equal to 20 feet, it would also be a fourth of an inch

Synthetic Division x^3+9x^2-11x-13

Answers

Answer:

You can't synthetic divide since there's no dividend. As you can't factor it so I figure you must've forgot to include something or there's no solution.

-16>x divided by 2
Solve for x.

Answers

Answer:

x < -32

Step-by-step explanation:

Find the quotient of 902÷27
(It has a remainder)

Answers

Answer:

The quotient of 902 divided by 27 equals 33 and the remainder is 11.

Simplify the radical please I need sleep it's 1 am I wake up at 4

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Answer:

[tex]4cba*\sqrt{5bc}[/tex]

Step-by-step explanation:

[tex]\sqrt{4^{2} *5a^{2}b^{2}bc^{2} c }[/tex]

[tex]4cba*\sqrt{5bc}[/tex]

solve −2 1/4⋅(−2 1/3)

a −5 1/4
b −4 1/1
c 4 1/12
d 5 1/4

Answers

Answer:

5 1/4

The answer is d (d 5 1/4)

Answer: D

Step-by-step explanation:

[tex]-2\frac{1}{4}[/tex] × [tex]-2\frac{1}{3}[/tex]

= [tex]\frac{-9}{4}[/tex] × [tex]\frac{-7}{3}[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]7[/tex]

= [tex]\frac{21}{4}[/tex] or [tex]5\frac{1}{4}[/tex]

please give me a brainliest answer

There are 2304 students sitting in the auditorium in such a way that each row contains as many students as the number of rows. How many rows are there in the auditorium? ​

Answers

Answer:

48

Step-by-step explanation:

[tex]\sqrt{2304}[/tex] = 48 * 48

To have the same number of rows and students, it shall be each row contains 48 students and 48 rows overall

2304 is a perfect square . So if you know that 48 x 48 is 2304 . Then you would figure out that there are 48 rows with 48 students in each row .
The answer is : 48 rows in the auditorium

Evaluate the expression (ill give brainiest)

Answers

Answer:

2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Substitute the given values into the expression

2 ( [tex]\frac{1}{16}[/tex] + ([tex]\frac{1}{4}[/tex] )² ) + 5([tex]\frac{1}{2}[/tex] )

= 2 ( [tex]\frac{1}{16}[/tex] + [tex]\frac{1}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]

= 2 ([tex]\frac{2}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]

= 2 ([tex]\frac{1}{8}[/tex] ) + [tex]\frac{5}{2}[/tex]

= [tex]\frac{1}{4}[/tex] + [tex]\frac{10}{4}[/tex]

= [tex]\frac{11}{4}[/tex]

= 2 [tex]\frac{3}{4}[/tex]

Where is the velocity negative?
E
B
A
G

Answers

Hello! The answer is

D-F

The V is negative when the velocity graph goes down. Hope this helps!

#HaveAnAmazingDay

[tex]GraceRosalia[/tex]

Marie bought 6 pounds of apples for $0.87 per pound and
paid for them with a $10 bill. How much did she get back
in change?

Answers

Answer:

5.22

Step-by-step explanation:

rjskstks5oslyatkao5sylslgsltsirsotzktzo

Answer:

$4.78

Step-by-step explanation:

6 x 0.87 = 5.22

10.00 - 5.22 = 4.78

Maire got $4.78 back

in change

1.4×10−5 and 2.8×10−4

Answers

Answer:

Step-by-step explanation:

Step one- is solving the left side of the equation using PEMDAS, 1.4x10 = 14

Step two- 14-5 = 9

Step 3 - 2.8 times 10 = 28

Step 4 - 28- 4 = 24

The answer is 9 and 24

HELP ME PLEASE I AM DESPERATE THIS IS ALMOST DUE!!!!!
What is the slope for this graph?

Answers

Answer: The answer is 2

Step-by-step explanation:

Please mark me as Brainiest

Answer: The answer is 2

Step-by-step explanation:

50 POINTS!
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Answer: the last one i think if i'm wrong then im so sorry

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2 and 5. Because of congruence rule. It tries to confuse u but don’t let it. Also always remember if those lines are there u know there congruent no matter what.

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Answer:

The equation is 39=3r-6

Step-by-step explanation:

Let x = # of years from the start of the Great Depression to the first Presidential election of Nixon

Let r = Raul's age

The question gives us what x equals so...

x=39

Now we just turn the sentence into an equation.

"The number of years from the start of the Great Depression to the first Presidential election of Nixon [(x)] is six years less than three times Raul's age [(3r-6)]"

Remove the icky words...

x=3r-6

replace x with what it equals (39)

39=3r-6

Now you can go on to olve it

Overal Raul is only 15 :)

HELPPPP MMEEE

PLEASE

Answers

Answer:

x2 and 7x

Step-by-step explanation:

thats correct

x2 + 7x =18

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Answers

Answer:

why do you want to know

Step-by-step explanation:

hahahahahahahaha

The line through (-2, 3) with slope 2/3 in point slope form​

Answers

Answer:

y - 3 = 2/3(x + 2)

Step-by-step explanation:

slope = 2/3

point-slope form --> y - y1 = m(x - x1)

y - 3 = 2/3(x - -2)

y - 3 = 2/3(x + 2)

point slope form of the line is y - 3 = 2/3(x + 2)

Answer:

y - 3 = 2/3(x + 2)

Matt's pool table is 3 feet wide and 9 feet long. Matt wants to replace the felt on the pool table. The felt costs $4.00 per square foot. How much would it cost in total to replace the felt on the pool table?

Answers

Answer:

$108

Step-by-step explanation:

3X9= 27square foot. Then you multiply 27 by 4, which equals $108

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