The height of an object launched into the air can be modeled by the graph shown.
Enter your answer as a number, like this: 42
Answers
The maximum height reached by the object is 12.5 feet.
Describe Parabola?The vertex of a parabola is the point where the curve changes direction, and is located at the minimum or maximum point of the quadratic equation. If the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents a minimum value. If the coefficient is negative, the parabola opens downwards and the vertex represents a maximum value.
To find the maximum height reached by the object, we need to find the vertex of the parabola.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x² term, and b is the coefficient of the x term in the quadratic equation that represents the parabola.
In this case, the equation is of the form y = ax² + bx + c, where y is the height and x is the time. Using the given coordinates, we can set up a system of equations to solve for a, b, and c:
0 = a(1)² + b(1) + c
16 = a(5)² + b(5) + c
0 = a(9)² + b(9) + c
Simplifying each equation, we get:
a + b + c = 0
25a + 5b + c = 16
81a + 9b + c = 0
Solving for c in the first equation, we get c = -a - b. Substituting this into the other two equations, we get:
25a + 5b - a - b = 16
81a + 9b - a - b = 0
Simplifying these equations, we get:
24a + 4b = 16
80a + 8b = 0
Solving for b in the second equation, we get b = -10a. Substituting this into the first equation, we get:
24a + 4(-10a) = 16
4a = 2
a = 1/2
Substituting this value of a into the equation b = -10a, we get b = -5. Finally, substituting a, b, and c = -a - b into the equation for the x-coordinate of the vertex, we get:
x = -b/2a = 5
So the maximum height is achieved at time x = 5, which corresponds to a height of:
y = ax² + bx + c = (1/2)(5)² - 5(5) = -12.5
However, we are looking for the maximum height, so we take the absolute value of this result, which gives:
|y| = 12.5
Therefore, the maximum height reached by the object is 12.5 feet.
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Related Questions
Which data set is the farthest from a normal distribution? a. 2, 3, 3, 4, 4, 4, 5, 5, 6 b. 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10 c. 0.9, 1.0, 1.0, 1.1, 1.1, 1.1, 1.2, 1.2, 1.3 d. 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8 e. 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
Answers
The farthest from a normal distribution is,
e) 2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given are 4 data sets.
And, We have to check which is farthest from normal distribution.
We know that a normal distribution is bell shaped with mean = median = mode.
Also 99% lie within 3 std deviations from the mean.
Here, This data set has a bimodal distribution with two distinct peaks, which is not characteristic of a normal distribution.
And, The other data sets have a unimodal distribution with a more symmetrical shape, which is closer to a normal distribution.
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Answer:2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
Step-by-step explanation:
2, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10
Is the following function linear or nonlinear
t = -8k + 2k - 4
a) linear
b) nonlinear
NEED HELP FAST
Answers
An english test has 20 questions. A student answers 76% correctly. How many questions does the student answer correctly?
Answers
ASAP
“A map uses the scale 3 of an inch represents 3/4 miles. If the actual distance between two cities is
25 miles, then what is the length on the map?”
Answers
Answer:
3 = 3/4
but 3/4= 0.75
3 = 0.75
x = 25
cross multiply
0.75x = 75
divide both sides by 0.75
x = 100
therefore 25miles represent 100inch on a map
Which is equivalent to 50 - 10 - 15? A. 50 - (-10) + (-15) … B. 50 + (-10) - (-15) C…. 50 + (-10) + (-15) D…. 50 - (-10) - (-15)
Answers
The equivalent expression of the given expression 50 - 10 - 15 will be 50 + (- 10) + (- 15). Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
→ 50 - 10 - 15
Then the expression can be written as
→ 50 + (- 10) + (- 15)
Thus, the correct option is C.
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Find the range of the data.
52,40,49,48,62,54,44,58,39
How do I find the range?
Answers
Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.49
Answer:
The range is 23
Step-by-step explanation:
1. Organize least to greatest:
39, 40, 44, 48, 49, 52, 54, 58, 62
2. Find the largest and the smallest nmber:
39 and 62
3. Subtract:
62
-39
=23
What is the solution of
5/2x-7=3/4x+14
A. X=-6
B. X=6
C.x=8
D. X=12
Answers
Answer:
D. x=12
Step-by-step explanation: quick maths
Draw a quadrilateral that does not belong. Then explain why.
Answers
Step-by-step explanation:
Rhombus since the other 3 have lines that go accross the graph horizontally for 3 squares.
Work out the value of 8^2+4^3, 5^3-7^2
Answers
Answer:
302
Step-by-step explanation:
A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 9, the vertical shift is 11 units down, and the period of the function is 12π7. The graph of the function does not show a phase shift.
What is the equation of the cosine function described?
Drag a value into each box to correctly complete the equation of the function
Answers
Answer
f(x) = -9 cos((12(pi) / 7)x) -11
The base equation for a cosine graph is
f(x) = a cos(b(x-c))+d
a = amplitude
b = period
c = phase shift
d = vertical shift
if there's a reflection over the x-axis then there is a negative sign in front of the amplitude
I wrote the equation previously but it got deleted so let me know if you have any problems with this explanation
simplify (2x²-6x-8)÷(x-4)
Answers
Answer: Heyaa!
The Answer is 2x+2
Step-by-step explanation:
Simplify the expression.
hopefully this helps you !
- Matthew ~
answer is in the attachment hope it helps you ^_^
hello I NEED HELP PLSSS
Answers
SOMEONE HELP ME PLEASE??
Answers
Explanation: This triangle is an equilateral; Meaning all sides are equal.
42 / 3 = 14.
Complete the conversion.
1 foot = 12 inches
4;, feet =
inches
Answers
Answer:
48 in
Step-by-step explanation:
1ft=12in so 12in x 4ft= 48 in
Is it
Write and solve an equation to find the measure of angle B.
Answers
Answer:
∠B = 40°
Step-by-step explanation:
The given angle relations can be expressed in two equations.
__
setupA + B = 90° . . . . . . . . angles are complementary
A×(1 -20%) = B . . . . . B is 20% smaller
__
solutionUsing the second equation to substitute for B in the first equation, we get ...
A + 0.80A = 90° . . . . . . substitute for B
A = 90°/1.8 = 50° . . . . . collect terms, divide by the coefficient of A
B = A(0.80) = 40° . . . . find B from A
The measure of angle B is 40°.
Before training for the obstacle course, Helena bought a new pair of athletic shoes. She placed the shoes on the floor next to each other and noticed that the right shoe looked just like a reflection of the left shoe. If she had accidentally purchased two left shoes, how would this comparison change?
Answers
The comparison of shoes placed on the floor by Helena next to each other change from reflection to translation.
What do you mean by reflection?The reflection of a plane or shape is flipping the original figure with respect to a reference line.
The rule of reflection are given below,
Reflection about x-axis (x,y)-->(x,-y)Reflection about y-axis (x,y)-->(-x,y)Before training for the obstacle course, Helena bought a new pair of athletic shoes.
She placed the shoes on the floor next to each other and noticed that the right shoe looked just like a reflection of the left shoe. This is because, the separating line works as the symmetry line between both the shoes.Now she had accidentally purchased two left shoes. Now, if she puts a left shoe to another left shoe, then it looks like the translated image of the first shoe.
Hence, the comparison of shoes placed on the floor by Helena next to each other change from reflection to translation.
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Christine, Kareem, and Trey have a total of $133 in their wallets. Kareem has $5 more than Christine. Trey has 4 times
what Kareem has. How much do they have in their wallets?
Answers
Answer:
Christine has $18, Kareem has $23, and Trey has $92.
Step-by-step explanation:
This can be solved by using variables to represent the unkown values.
x = Christine's money
x + 5 = Kareem's money.
4(x + 5) = Trey's money.
x + (x + 5) + 4(x + 5) = 133
2x + 5 + 4x + 20 = 133
6x = 108
x = $18
This means that Christine has $18, Kareem has $23, and Trey has $92.
Hope this helps
need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight.
Answers
Answer:
2412.7 ft^3
Step-by-step explanation:
If a circle has a diameter 16ft, it's radius is half that, or 8ft. The are of the circle/base of the cylinder is given by the formula [tex]\pi r^2[/tex] where r is the radius. This means the area is 64π ft^2.
To find the volume of a cylinder, you multiply the base area and the height, so the volume would be 64π x 12 which is 2412.74315796. When rounded to the nearest tenth, this is 2412.7.
Since we want to find the volume of a cylinder:
⇒ must know the formula: [tex]V = \pi r^2h[/tex]
r: radiush: heightConsider the information given:
Height: 12 ftDiameter: 16 ft ⇒ Radius: 8 ft (radius is half of the diameter)Let's solve:
[tex]V = \pi r^2*h=3.14*(8)^2*12=2411.52_.cm^3[/tex]
Answer: 2411.5 cm³
Hope that helps!
yanni crable deposits $122 in an ordinary annuity at the end of every quarter. The annuity earns 6% interest compounded quarterly. After 4 quarters, the value of $1 with this interest rate is $4.0909. What is the future value of the annuity after 1 year?
Answers
Step-by-step explanation:
future value of annuity after 1 year is:
$122× $4.0909=$499.089
=$499.09
The mean of the following data is 509. {419,450,462,499,520,521,589,612}
What is the mean absolute deviation for the data set?
Enter your answer as a number rounded to the nearest tenth, like this: 42. 5
Answers
- - - - - - - - - - - - - - - - - - - - - - - -
" The mean of the following data is 509. {419, 450, 462, 499, 520, 521, 589, 612} "
- - - - - - - - - - - - - - - - - - - - - - - -
First, divide the mean (or average) by the population size (amount of numbers in the set).
509 / 8 = 51.5
There you go! Your absolute deviation.
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck!
~pinetreee
The mean absolute deviation for the data set is 51.5.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that;
Mean= 59
{419,450,462,499,520,521,589,612}
Now,
Count the number of data values in the set. In this case, n = 8.
Subtract the mean from each data value and take the absolute value. For example:
∣419−509∣=90
∣450−509∣=59
∣462−509∣=47
∣499−509∣=10
∣520−509∣=11
∣521−509∣=12
∣589−509∣=80
∣612−509∣=103
Add up all the absolute differences and divide by n. For example:
MAD=890+59+47+10+11+12+80+103
MAD=412/8
MAD=51.5
Therefore, by mean the answer will be 51.5.
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Fynn is using the Pythagorean theorem to calculate the slant height of an object. Which object is Fynn most likely working with?
a right cone
a sphere
a right cylinder
an elliptical cylinder
Answers
What is the height of the cone below?
= 90 cm°
B = 18 cm-
© 5 cm
0 6 cm
• 15 cm
© 30 cm
Answers
Answer:
Nearly the answer is 15 cm
because answer is in decimals
Find the sum of these polynomials. (x2 - 5x + 3) + (2x2 - 3x - 7) = A.3x2 - 8x - 10 B.3x2 - 2x - 4 C.3x2 - 8x - 4 D.3x2 - 2x - 10
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The sum of the two polynomial expressions (x² - 5x + 3) + (2x² - 3x - 7) is (3x² - 8x - 4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The sum of the two polynomial expressions are:
(x² - 5x + 3) + (2x² - 3x - 7)
= x² - 5x + 3 + 2x² - 3x - 7
= 3x² - 8x - 4
Hence, The sum of the two polynomial expressions (x² - 5x + 3) + (2x² - 3x - 7) is (3x² - 8x - 4).
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Answer:
yk
Step-by-step explanation:
Please Help me find the figure , area formula and the area
Answers
Answer:
figure: parallelogram
area formula: base× height
A=bh
A= 13×6
A=78
Step-by-step explanation:
Opposite sides of a parallelogram are congruent.: AD=BC
DC=AB
Kaitlyn and Hakim each bought a tube
of candy. Both containers cost the same
amount. Which container required more
plastic to make?
d = 7 cm
CANDY
122 cm
d = 11 cm
CANDY
85 cm
Answers
Container A:
diameter- 7 cm
height- 122 cm
radius- 3.5 cm
calculating for the surface areaSA=2×π×r×r+2×π×r×h
SA=2(3.14)(3.5)(3.5)+2(3.14)(3.5)(122)
SA=76.93+2681.56
SA=2758.49 cm^2
Container B:diameter- 11 cm
height- 85 cm
radius- 5.5 cm
calculating for the surface areaSA=2×π×r×r+2×π×r×h
SA=2(3.14)(5.5)(5.5)+2(3.14)(5.5)(85)
SA=189.97+2935.90
SA=3125.87 cm^2
Container B required more plastic to makeWhich group had the highest percentage of students like Sport.
………………………………………
b) Which group had the less percentage of students like English.
………………………………………
c) Calculate the percentage of students like Math for each group.
Group A = ……………………………………..
Group B = …………………………………….
Answers
The group that had the highest percentage of students that like Sports is group B.
The group that had the less percentage of students that like English is group A.
the percentage of students like Math in group A is 30% and 10% in group B
What are the percentages?
A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees
Percentage of students that like sports in:
Group A = [20 / (20 + 15 + 5 + 10)] x 100 = 40%Group B = [22 / (5 + 4 + 9 + 22)] x 100 = 55%Percentage of students that like English in:
Group A = [5 / (20 + 15 + 5 + 10)] x 100 = 10%Group B = [5 / (5 + 4 + 9 + 22)] x 100 = 22.5%Percentage of students that like Maths in:
Group A = [15 / (20 + 15 + 5 + 10)] x 100 = 30%Group B = [4 / (5 + 4 + 9 + 22)] x 100 = 10%To learn more about pie charts, please check: https://brainly.com/question/26250795
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a laptop that was originally priced at $650 was placed on sale for 25% off. when it did not sell it was put on clearance for 30% off the sale price. what was the clearance price of the laptop
Answers
Answer:
$48.75
Step-by-step explanation:
To find 25% of 650 you find 50%. To do this you divide 650 by 2 which is 325. you then divide that by 2 again to get $162.50. That is the sale price.
You now need to find 30% of 162.50. To do that you find 10% 3 times because 10x3 is 30. To find 10% you divide 162.50 by 10 to get 16.25.
16.25x3 is $48.75 which is our answer.
This triangle can be called obtuse or __________.
A: equilateral
B: isosceles
C: scalene
D: right
Answers
ITS THE LAST QUESTION HELP!!!!!!!!!!!!
Answers
Answer:
ans willbe -8
Step-by-step explanation:
-1/2 × 2 =-1
-1×2=-2
-2×2=-4
-4×2=-8
Determine whether the series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. 10 + 7 + 4 + . . .; n = 5
Answers
Answer:
10 + 7 + 4 + . . .; n = 5
The series is arithmetic
Common difference between terms = (-3)
10 - 3 = 7
7 - 3 = 4
Or:
10 + (-3) = 7
7 + (-3) = 4
--------------------------------------------------------------------------
Another example:
Arithmetic:
5, 9, 13, 17
common difference = 4
5 + 4 = 9
9 + 4 = 13
Geometric:
4, 8, 16, 32
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
common ratio = 2
--------------------------------------------------------------------------
10 + 7 + 4 + . . .; n = 5
a₁ = 10
a₂ = 7
a₄ = a₃ + d = 4 + (-3) = 4 - 3 = 1 (d = common difference)
a₅ = a₄ - 3 = 1 - 3 = -2
Or with formula:
[tex]d=a_{n} -a_{n-1}[/tex]
d = a₂ - a₁ = 7 - 10 = -3
aₙ = a₁ + (n - 1)d
fourth term = a₄ = 10 + (4 - 1)(-3) = 10 + 3(-3) = 10 + (-9) = 10 - 9 = 1
fifth term = a₅ = 10 + (5 - 1)(-3) = 10 + 4(-3) = 10 + (-12) = 10 - 12 = -2
Sum of the finite series (if n = 5):
[tex]S_{n} =\frac{n(a_{1} +a_{n} )}{2} \\S_{5} =\frac{5(a_{1} +a_{5} )}{2} \\S_{5} =\frac{5(10 +(-2) )}{2} \\S_{5} =\frac{5(8 )}{2} =\frac{40}{2} =20[/tex]
Manual count: S₅ = 10 + 7 + 4 + 1 + (-2) = 20
