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
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 graphFrom 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
Related Questions
help please !! geometry
Answers
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)
Need help asap pls pls pls
Answers
Answer:
why do you want to know
Step-by-step explanation:
hahahahahahahaha
please help me!!!!!
Answers
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 :)
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.
-kiniwih426
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
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
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
The answer is : 48 rows in the auditorium
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:
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
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!
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]
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.
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
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
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]
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.
-16>x divided by 2
Solve for x.
Answers
Answer:
x < -32
Step-by-step explanation:
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
HELPPPP MMEEE
PLEASE
Answers
Answer:
x2 and 7x
Step-by-step explanation:
thats correct
x2 + 7x =18
i need an explanation what....wajfasjf
Answers
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]
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
50 POINTS!
PLEASE HELP THIS MAKES NO SENSE AT ALL!! IM BEING TIMED
Answers
Answer: the last one i think if i'm wrong then im so sorry
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
Can someone help me with this
Answers
-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
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
8.5 inches to centimeters
Answers
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.
Simplify the radical please I need sleep it's 1 am I wake up at 4
Answers
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]
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.