The given function for the height of the firework is a quadratic function
1. Time at which the firework reaches the maximum height is 1 seconds
2. The maximum height of the firework, is 25 yards
3. Time after which the firework will fall to the ground is (1 + √5) seconds
Reason:
The given function that represents the height of the fireworks with time is
presented as follows;
h(t) = -5·t² + 10·t + 20
1. The time at which the firework reaches its maximum height is given by
the maximum point of the given function as follows;
The x-value of the maximum point of a quadratic function is [tex]x = \dfrac{b}{2 \cdot a}[/tex]
Where;
a, and b, are the coefficient of x² and x, in the general form of a quadratic function f(x) = a·x² + b·x + c
By comparison, we have;
[tex]t = -\dfrac{10}{2 \times (-5)} = 1[/tex]
The time at which the firework reaches the maximum height is t = 1 seconds2. The maximum height is given by plugging in the value of t, at the maximum point into the given function as follows;
h(1) = -5×1² + 10×1 + 20 = 25
The maximum height of the firework, f(1) = 25 yards3 The time at which the firework will fall to the ground, is given by the zero of the function as follows;
When the firework falls to the ground, h(t) = 0 = -5·t² + 10·t + 20
Dividing both sides by (-5) gives;
[tex]\dfrac{0}{-5} = \dfrac{ -5 \cdot t^2 + 10 \cdot t + 20}{-5} = t^2 - 2 \cdot t - 4[/tex]
t² - 2·t - 4 = 0
By the quadratic formula [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex], we get;
[tex]t = \dfrac{2\pm \sqrt{(-2)^{2}-4\times 1\times (-4)}}{2\times 1} = \dfrac{2\pm \sqrt{20}}{2\times 1} = \dfrac{2\pm 2 \times \sqrt{5}}{2\times 1} = 1 \pm \sqrt{5}[/tex]
Therefore;
The time after which the firework will fall to the ground, t = 1 + √5 secondsLearn more here:
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3/7x2/3 tyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:
2/7
Step-by-step explanation:
3x2=6
7×3=21
6/21 = 2/7
Write the equation of the line in fully simplified slope intercept form
Answer:
y = -0.5x - 7 or y = -1/2x - 7 (both are same)
Step-by-step explanation:
m = slope
slope = y2 - y1 / x2 - x1
-9 - (-8) / 4 - 2 = -1/2 = -0.5
m = -0.5
b = y-intercept
b = -7
y = mx + b
y = -0.5x + (-7)
y = -0.5x - 7
(negative slope)
hey anyone wanna check my answer(s)??
nothing I can't say english :[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Answer:
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You run 6 miles in one hour and 12 miles in two hours.
a. 2 miles per hour
b. 6 miles
c. 6 miles per hour
d. 2 hours
Which expression should appear on Line 3?
3,000 + 600 + 42
3,000 + 60 + 13
3,000 + 60 + 42
300 + 60 + 42
Answer:
3000+60+42
Step-by-step explanation:
the order of operations says to multiply and divide from left to right before adding or subtracting from left to right. Putting the numbers in parenthesis helps.
(500*6)+(10*6)+(7*6)
(3000)+(60)+(42)
3000+60+42
Hope this helps!
How many points of intersection are on the graph of the following system?
lbrace y = x2 + 3x − 7
y − x = 9
The linear-quadratic system has
(select)
points of intersection.
Answer:
2 points of interception of (3.12 , 12./12) and (-5.12 , 3.87)
Step-by-step explanation:
y − x = 9
y = x + 9
x+9 = x²+3x-7
x²+2x-16=0
x = (-2±√2²-4(1)(-16)) / 2 = (-2 ± √68) / 2 = -1 ± √17
x = 3.12 or x = -5.12
y = 12.12 or y = -3.87
in a class of 37 students, 24 study history, 15 study Geography and 6 other study neither History nor Geography. find how many students study both history and Geography brainly
Answer: 16
Step-by-step explanation: your welcome
Answer:
39
Step-by-step explanation:
15 students study Geography and 24 study history.
15+24=39
SOMEONE WHO'S GOOD AT MATH PLEASE ANSWER THIS ASAP TODAY WILL GIVE BRAINLIEST
Answer:
1-(-9)=10
Step-by-step explanation:
Question
Identify the parallel lines.
Lines and are parallel.
Answer:
4 and 1, 2 and 3, 5 and 8, 6 and 7
Step-by-step explanation:
Lines that are parallel are lines that never meet each other.
If a man can walk 40 km in 2 days. how many km can he travel in 7 days?
Answer:
280
Step-by-step explanation:
If he can walk 40 in 2 days, multiply 7 by 40 to get 280 km total
Mark is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 12 inches × 13 1/3 inches. He needs to cut another rectangle that is 10 1/4 inches x 10 1/3 inches
How many total square inches of construction paper does Mark need for his project?
PLS I NEED TO GO TO SCHOOL PLS
Answer: 265.9167 square inches (rounded)
Step-by-step explanation:
Shoot, okay if this is wrong, shame on me:
All you do is find the areas of each rectangle and add them together.
(12 × 13 1/3) + (10 1/4 x 10 1/3) = 265.9167 (rounded) square inches. Or as a fraction: 3191/12
Which expression illustrates the commutative property applied to the product?
(−8/9)⋅(−13)⋅(18)
A. (−8/9)⋅(18)⋅(−13)
B. (−8/9)⋅(−13)⋅(18)
C. (−8/9)⋅[(−13)⋅(18)]
D. [(−8/9)⋅(−13)]⋅(18)
simplify the folowing equations
(x2 + 2xy + y2)(x+1)
x3 + x2 +2x2y +xy2 + y2 + 2xy
(6x -8)(2x -3)
(-2x – 1) (9x +2)
(2x2 - 4xy + 2y2) (3x-4)
6x3 – 12x2y + 6xy2 – 8x2 + 16xy-8y2
must show steps
Use FOIL method...
1. (x^2 + 2xy + y^2)(x+1)
x^3 + 2x^2y + xy^2 + x^2 + 2xy + y^2
Add Like Terms
There are no like terms.
2. x^3 + x2 +2x2y +xy2 + y2 + 2xy
3. (6x -8)(2x -3)
4. (-2x – 1) (9x +2)
5. (2x^2 - 4xy + 2y^2) (3x-4)
6. 6x^3 – 12x^2y + 6xy^2 – 8x^2 + 16xy-8y^2
please answer this write
Answer:
k
Step-by-step explanation:
sorry if its wrong
24.4 divided by 0.4 im stuck like step bro
Natasha has a job putting letters in envelopes to be mailed. in 1 hour she put 42 letters in envelopes. which equation best represents y, the total number of letters natasha puts in envelops in x hours if she continues
Answer:
36 pages .394kb
Step-by-step explanation:
that's it well done
You can use multiplication along with converting statements to symbols.
The equation for the given condition is given by [tex]y = 42x[/tex]
where y represents the total number of letters Natasha puts in envelops in x hours.
How to form symbolic expressions from the description?You need to know how to convert the statement to symbolic expression.
Suppose if it is said that a thing is increased by 4,then we write it as
that thing + 4
Suppose if it is written that 'x' objects are sold on p price per object. Since 1 object is sold at p price, then x objects will be sold at:
[tex]p + p + ... + p \: \: \: (x \: \: times) = p \times x[/tex]
Such conversion can help us to form symbolic expressions from the given description.
Since for the given case, in 1 hour, Natasha put 42 letters in envelopes, then in x hour she will put:
[tex]42 + 42 + ... + 42 \: \: (x \: times) = 42 \times x[/tex]
Since in x hours, she puts y envelopes but envelopes put in x hours came out as 42 times x, thus, both the values are equal, or
[tex]y = 42 \times x = 42x \text{\:\:(written in short)}[/tex]
The equation for the given condition is given by [tex]y = 42x[/tex]
where y represents the total number of letters Natasha puts in envelops in x hours.
Learn more about linear relationship here:
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Write 5^2/5 square root 5 as a single power of 5
hope you like my answer its -15
please make me brainliest
pls help me with this math problem
Answer:
Graph D (last graph)
Step-by-step explanation:
y + 2 > 5
first subtract 2 from both sides
y > 3
Now that we know the solution to y we can plot it. We know it must start at 3, but also not be included because our solution is not ≥. This means we have an open box at 3 and an arrow in the positive direction.
Suppose the temperature outside is dropping 3 degrees each hour. How much will the temperature change in 8 hours? is it negative
Answer:
The temperature will drop 24 degrees
Step-by-step explanation:
-3 degrees/hour for 8 hours
-3 x 8 = -24
It is negative.
Answer:
In 8 hours time it will be drop 24 degrees
8x3 = 24
. The speeds of cars on the highway have a mean of 65 mph with a standard deviation of 5 mph.
If a police car stopped cars that were going more than80mph, how many cars would they stop ifthere were 8000 cars on the highway
Answer:
do 65 / 5 then multiply 80 * it 100
Can anyone help out with this algebra 1 question? It’s 2 am and I’m just exhausted here man, I’d really appreciate it.
Answer:
y = 3x/4 + 3
Step-by-step explanation:
y = mx + b
b = 3
(-4,0), (0,3)
m = 3/4
If the perimeter of the polygon below is 52 ft, solve for x, and identify the length of each side in the corresponding spaces below (figure not drawn to scale). Don't forget to include units in your answer!
Answer:
x = -3
a) 6 ft
b) 7 ft
c) 9 ft
d) 11 ft
e) 5 ft
f) 14 ft
Step-by-step explanation:
set up the equation
-2x + 4 - x +x +12 + 3x + 20 + 2x + 11 + 7x + 35 = 52
combine like terms
10x + 82 = 52
single out the variable
10x = -30
x = -3
substitute x in all the following equations
a) -2(-3) = 6
b) 4 - -3 = 7
c) -3 + 12 = 9
d) 3(-3) + 20 = 11
e) 2(-3) + 11 = 5
f) 7(-3) + 35 = 14
have a lovely day <3
A family spent $169 at the movies. Admission tickets cost $12 apiece, and a bucket of popcorn costs $7 which equation written in standard form.
How many buckets of popcorn could be bought if a family buys 7 admission tickets?
Answer:
12
Step-by-step explanation:
7 (number of tickets) times 12 (cost of ticket) = 84 169 (total spent) - 84 (total ticket price) = 85 85 divided by 7 (price of popcorn) = 12.14 round down as they wouldn't have enough money to buy more than 12 popcorns.
Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. (Please Show your work)
Answer:
8.8 ydStep-by-step explanation:
Use Pythagorean:
[tex]x=\sqrt{5.5^2+6.9^2} =\sqrt{77.86} =8.8[/tex] yd (rounded)Mason loves collecting sea glass from the beach. He recorded the weight of each jar full of sea glass. If he decided to distribute the sea glass equally among the jars, how much would each jar weigh?
(3 m^6 n^2)^3 * 2mn^4
2. What is the tangent ratio of angle & within a right triangle?
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
According to Trigonometry,
[tex] \tan( \theta) = \dfrac{opposite }{adjacent} [/tex]Answer:
Tangent = Opposite/Adjacent
Step-by-step explanation:
SOH = Sin = opposite/hypotenuse
CAH = Cos = adjacent/hypotenuse
TOA = Tan = opposite/adjacent
Expand this expression by using the distributive property. 4( -2g + 4 -3t)
Answer:
-8g + 16 + 12t
Step-by-step explanation:
multiply 4 with -2g
multiply 4 with 4
multiply 4 with -3t
8 1/2- 1 1/4? Show work
Answer:
[tex]7\frac{1}{4}[/tex]
Step-by-step explanation:
Change to improper fraction.
[tex]8\frac{1}{2}[/tex] ⇒ [tex]\frac{17}{2}[/tex]
[tex]1\frac{1}{4}[/tex] ⇒ [tex]\frac{5}{4}[/tex]
Find the least common denominator (LCD) of the two fractions. ⇒ 4
[tex]\frac{34}{4}[/tex] - [tex]\frac{5}{4}[/tex] = [tex]\frac{29}{4}[/tex]
Convert to a mixed number.
[tex]\frac{29}{4}[/tex] ⇒ [tex]7\frac{1}{4}[/tex]
Hence, [tex]8\frac{1}{2} - 1\frac{1}{4} = 7\frac{1}{4}[/tex]