Answer:
The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground
Step-by-step explanation:
The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.
First, lets find h0 and v(0)
h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.
Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.
Second, find max height.
To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.
b=20
a=-16
t = -b/2a = -20/2(-16) = .625 seconds
h(.625) = 11.25 feet
The max height is 11.25 feet
Third, find how long.
To find this, we need to find the t-intercepts of the equation.
set h(t) = 0
-16t^2 + 20t + 5 = 0
Use quadratic formula to find t
t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)
t = {1.464}, -.214
The ball will take 1.464 seconds to hit the ground.
PLEASE HELP W PRECALC QUESTION
Answer: [tex]2tan(theta)[/tex]
Step-by-step explanation:
I know this is pre-calculus, but I want to let you know what this is actually used for in real calculus. This is a method of integration called "u-substitution" which tranforms the function of 'x' into a function of 'theta'. If we allow the value of 'x' to equal 2sec(theta), we can plug this into the function to get:
[tex]\sqrt{x^2-4} =\sqrt{(2sec(theta)^2-4} =\sqrt{4sec^2(theta)-4}[/tex]
Factor out a 4 to get:
[tex]\sqrt{4(sec^2(theta)-1)}[/tex]
Take the square root of 4 to get a 2 on the outside of the radical:
[tex]\sqrt{4(sec^2(theta)-1)}=2\sqrt{sec^2(theta)-1}[/tex]
Use the trig identity below to convert the secant to tangent:
[tex]tan^2(theta)+1=sec^2(theta)[/tex]
[tex]tan^2(theta)=sec^2(theta)-1[/tex]
Therefore our expression becomes:
[tex]2\sqrt{sec^2(theta)-1}=2\sqrt{tan^2(theta)}[/tex]
The square root of tangent is simply tangent:
[tex]2\sqrt{tan^2(theta)} =2tan(theta)[/tex]
Write a congruence statement for the pair of triangles shown.
Answer:
Triangle UTS is congruent to Triangle RST.
Step-by-step explanation:
When stating congruence, the corresponding angles and sides must be listed in order. In triangle uts, based on the points, the angle is U, and the side is US. This means that for the other triangle, the first point needs to be the angle, and the last one needs to be the other point for the side. This gives us Triangle UTS is congruent to triangle RST. Hope this helps!
solve major part of my grade <33
0 3 6 9 12 15 18
(each tick mark = +3)
a. Convert 5x^2 + 55x + 140 from standard to vertex form
b. Describe the transformation.
Answer:
The transformation will be 5
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
5x^2 + 55x + 140 ---> required
Coefficients a=5, b=55, c=140 yield
[tex]h=\frac{-h}{2*a} =\frac{-(55)}{2*5} =\frac{-55}{10} =-5.5[/tex]
Thus, the x-coordinate of the vertex is [tex]\boxed{h = -5.5 }[/tex]
Plugging x=-5.5 into the given equation yields:
[tex]k=5*(-5.5)^{2} +55*-5.5+140=-11.25[/tex]
Thus, the y-coordinate of the vertex is [tex]\boxed{k = -11.25 }[/tex]
Altogether, the vertex of the given parabola is
[tex]\boxed{ (h,k)=(-5.5,-11.25) }[/tex]
Plugging (h,k)=(−5.5,−11.25) into the vertex formula
[tex]\boxed{ y=(x-h)^2+k }[/tex]
yields the vertex form of the parabola
[tex]\boxed{ y=(x+5.5)^2-11.25 }[/tex]
To find the vertex of a parabola in standard form, first, convert it to the vertex form y=a(x−h)2+k y = a ( x − h ) 2 + k .Donnie lives 3 miles from the park . He rode his bicycle from his house to the park at a constant speed of 9 miles per hour. How long did it take Donnie to get to the park?
Answer:
20 minutes, or 1/3 hour
Step-by-step explanation:
Donnie travels at 9 miles/hr.
The relationship between speed, distance, and time is Time = Distance/Speed. [from Distance = Speed*Time]
Time to bike 3 miles at 9 miles/hr is = (3 miles)/(9 miles/hr) = (1/3) hr
It took 1/3 hour, or 20 minutes, to bike the three miles, with no stops for soda and hot dog.
Two concentric circles are of radii 10 cm and 8 cm, then the length of the chord of the larger circle which touches the smaller circle is
Answer:
12 cmStep-by-step explanation:
Let O be the centre of the circle of radii 10 cm and 8 cm.
In given figure,
AP = PB and OP⊥AB
Applying Pythagoras theorem in ∆OPA, we get
↠ OA² = OP² + AP²
↠ (10)² = (8)² + AP²
↠ 100 = 64 + AP²
↠ 100 - 64 = AP²
↠ 36 = AP²
↠ √36 = AP
↠ 6 = AP
Now,
↠ AB = 2AP
↠ AB = 2(6)
↠ AB = 12 cm
Hence,
The length of the chord of the larger circle 12 cm
HELPPPP WHATS THE AREA
Answer:
the answer is 42
Step-by-step explanation:
you multiply the sides to get the area
If m greater-than-or-equal-to n, which inequalities must be true? check all that apply. m 2.1 greater-than-or-equal-to n 2.1 m - (-4) greater-than-or-equal-to n -(-4) m - 3 greater-than-or-equal-to n 3 16.5 m greater-than-or-equal-to 16.5 n m greater-than-or-equal-to n one-half 6 m greater-than-or-equal-to 9 n
The true statements are m + 2.1 > n + 2.1, m - (-4) > n - (-4) and 9 + m > 6 + n
How to determine the true statements?The inequality is given as:
m > n
When the same constant k is added to both sides of the inequality, we have:
m + k > n + k
This means that the following inequality is true
m + 2.1 > n + 2.1
When the same constant k is subtracted from both sides of the inequality, we have:
m - k > n - k
This means that the following inequality is true
m - (-4) > n - (-4)
Also, if a greater constant is added to m, then the inequality still remains the same.
This means that the following inequality is true
9 + m > 6 + n
Hence, the true statements are m + 2.1 > n + 2.1, m - (-4) > n - (-4) and 9 + m > 6 + n
Read more about inequalities at:
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Answer:
It´s actually A, B, D
Step-by-step explanation:
Find the square number
5
8
15
30
36
name the two operations used for converting weight measurement
Answer:
grams and kilograms it got delted for some reason
Step-by-step explanation:
An event has a probability of 2/7. How would you best describe the likelihood of this event? (Hint: Change it to a decimal)
A. Impossible
B. Less likely
C. Equally likely
D. More likely
E. Certain
Answer:
Less Likely
Step-by-step explanation:
A 2/7 probability means that it will happen less than half the time.
The eliminates equally likely, more likely, and certain as those are 50% or greater.
The probability is also greater than 0%, so it's not "impossible"
Therefore, the answer must be B, Less Likely.
It happens less than half the time, but can at times happen.
Hope this helps!
The solution is, Less Likely, best describe the likelihood of this event.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
An event has a probability of 2/7.
now, we get,
A 2/7 probability means that it will happen less than half the time.
The eliminates equally likely, more likely, and certain as those are 50% or greater.
The probability is also greater than 0%, so it's not "impossible"
It happens less than half the time, but can at times happen.
Therefore, the answer must be B, Less Likely.
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help me!
[tex]\frac{x}{3}+10=\frac{3x-8}{2}[/tex]
Answer:
[tex] \frac{x}{3} + 10 = \frac{3x - 8}{2} \\ \\ \frac{3x - 8}{2} - \frac{x}{3} = 10 \\ \\ taking \: lcm \\ \\ \frac{9x - 24 - 2x}{6} = 10 \\ \\ 9x - 24 - 2x = 60 \\ \\ 7x = 60 + 24 \\ \\ 7x = 84 \\ \\ x = \cancel\frac{84}{7} \\ \\\fbox{ x = 12}[/tex]
hope helpful ~
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex] \frac{x + 30}{3} = \frac{3x - 8}{2} [/tex]
[tex]2x + 60 = 9x - 24[/tex]
[tex]60 + 24 = 9x - 2x[/tex]
[tex]84 = 7x[/tex]
[tex]x = 12[/tex]
I hope it will be helpful
A report says that the average amount of time a 10-year-old American child spends playing outdoors per day is between 20.18 and 24.96 minutes. What is the margin of error in this report
Answer:
The study, The Nature of Americans National Report, found that more than half of adults reported spending five hours or less in nature each week, and being satisfied with this small amount of time spent outdoors.
Step-by-step explanation:
The margin of error in the report is 2.39.
What is the margin of error?The margin of error is a statistic that describes how much random sampling error there is in survey data.
Given that, the upper interval is 24.96 and the lower interval is 20.18.
The margin of error is half of the difference between the upper and the lower interval.
Therefore, the margin of error is:
Margin of error = (24.96 - 20.18)/2
= 4.78/2
= 2.39
Hence, the margin of error in the report is 2.39.
Learn more about the margin of error:
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Your friend leaves your house. She later calls you on her cell phone, saying that she's been driving at 60 miles an hour directly away from you the whole time and is now 60 miles away. How long has she been gone?
Answer: 1hr
Step-by-step explanation: Distance = speed × time
Time = Distance / Speed = 60/60
CHOOSING BRAINLIEST PLEASE HELP
Answer:
The answer is the 2nd 1
Step-by-step explanation:
It's a basic graph
probabiltity of 8 and 23
Answer:
huh
Step-by-step explanation:
Xavier opened a savings account with a deposit of $12,000. the account earned simple interest. he did not make any additional deposits or withdrawals. at the end of 3 years, the account balance was $12,324. what is the annual interest rate on this account? question 5 options: 0.9% 1.8% 2.7% 3.6%
Answer:
0.9%
Step-by-step explanation:
I took the test
Please help me with this question .
2 ÷ 9/10 =
Answer:
20/9
Step-by-step explanation:
2/1–>20/10 x 10/9
200/90 / 10
20/9
Hope that helps. :)
[tex]2 \div \frac{9}{10} [/tex]
solution:[tex] \frac{2}{1} \div \frac{9}{10} [/tex]
[tex] = \frac{2}{1} \times \frac{10}{9} [/tex]
[tex] = \frac{2 \times 10}{1 \times 9} [/tex]
[tex] = \frac{20}{9} or2 \frac{2}{9} [/tex]
Jina makes eight dollars for each hour of work. Write an equation to represent her total pay ‘p’ after working ‘h’ hours
Answer:
p = 8h
Step-by-step explanation:
Simple math my guy
Answer:
p=8h
Step-by-step explanation:
For each hour, she gets paid $8. So the total pay would be the number of hours multiplied by 8.
y=3x-7
-4x+5y=20
solve algebraically
Answer:
so x=5 and y= 8
Step-by-step explanation:
[tex]y = 3x - 7 \: \\ 20 = - 4x +5y \\ 20 = - 4x + 5(3x - 7) \\ 20 = - 4x + 15x - 35 \\ 20 + 35 = 11x \\ 55 = 11x \\ x = 5 \\ now \: you \: put \: x = 5 \: into \: the first \: equation \: \\ 5 \\ y = 3(5) - 7 \\ y = 8[/tex]
Can someone help me understand on how to simplify this ?
Answer:
So first you have to make all the denominaters (bottom #s) the same so we would get 12/20-8/20+5/20 and you would solve this to equal 9/20 and to divide it by 1/6 would equal 2 7/10.
Hope this helps! (pls read the comment for free gift cards)
You fill the entire fish tank with water. Then you dump out some of the water. The volume of the water in the tank decreases by 96 cubic inches. How deep is the water now? (The height is 12 inches, the base is 48)
Answer:
1. 6/10 – 2/5 =
Ans: 2/10, which can be reduced to 1/5.
2. If a tank is 5/8 filled with solution, how much of the tank is empty?
Ans: 3/8 of the tank is empty. Since the whole tank would equal 8/8, or 1, and 5/8 of it is filled, then that
means 3/8 of it remains empty.
3. 1/2 x 3/5 x2/3 =
Ans: 6/30, which can be reduced to 1/5.
4. 5/9 ÷ 4/11 =
Ans: 55/36. You cannot reduce this fraction any further.
5. Convert 27/4 to a decimal.
Ans: 6.75. This answer is arrived at by dividing 4 into 27.
6. Convert 0.45 to a fraction.
Ans: 45/100, which can be reduced to 9/20.
7. 4.27 x 1.6 =
Ans: 6.832
8. 6.5 ÷ 0.8 =
Ans: 8.125
9. 12 + 4.52 + 245.621 =
Ans: 262.141
Step-by-step explanation:
I hope this helps
In a concert band, the probability that a member is in the brass section is
0.50. The probability that a member plays trombone, given that he or she is in
the brass section, is 0.24.
What is the probability that a randomly selected band member is in the brass
section and plays trombone?
• A. 0.74
•
B. 0.12
• C. 0.26
• D. 0.48
Answer:
the answer is C. 0.26
Step-by-step explanation:
Because 0.50 + 0.24 is 0.74 and I'm guessing it goes to 1.0
So you subtract 1.0 from 0.74 to get 0.26
which type of function describes her total savings after m months and why?
Answer:
A.
Step-by-step explanation:
I would advise finding the difference between 300 and 200 and 450 and 300:
[tex]300-200=100\\450-300=150[/tex]
We can eliminate C and D since she saves 100 the first month and 150 the second month.
The next step would be to find the increase every month:
[tex]\frac{Final value}{initial value}=x\\\\\frac{300}{200}=1.5 \\\\\frac{450}{300} = 1.5[/tex]
If we would write the increase as a function, we would get:
[tex]y= 1.5x[/tex]
we can check this by substituting values:
[tex]y=1.5*200\\y=300\\\\\\y=1.5*300\\y=450[/tex]
An exponential function looks like this:
[tex]y= a^x[/tex]
A linear function looks like this:
[tex]y=mx+b[/tex]
Our m is 1.5, a linear increase by 150% and our b is 0, which can be written like:
[tex]y=1.5x+0\\y=1.5x[/tex]
Therefore our function resembles a linear function more than an exponential function, eliminating answer B.
Give full working and explanation
And I reward you with stars.
Answer this easy question ;-)
Answer:
1309 marbles
Step-by-step explanation:
Kadon has 727 marbles.Simon has: 727 - 145 = 582 marblesAll together:
Kadon marbles + Simon marbles727 marbles + 582 marbles1309 marblesSolve the system of inequalities and indicate all the integers which are in the solution set: The answer isn't an inequality like -5
Answer:
{- 4, - 3, -2, -1, 0, 1, 2, 3}Step-by-step explanation:
Solve each inequality in the system:
3 - 2a < 13 ⇒ 2a > 3 - 13 ⇒ 2a > - 10 ⇒ a > - 55a < 17 ⇒ a < 17/5 ⇒ a < 3.4The solution is:
- 5 < a < 3.4The integer solution set is:
{- 4, - 3, -2, -1, 0, 1, 2, 3}[tex]\\ \rm\rightarrowtail 3-2a<13[/tex]
[tex]\\ \rm\rightarrowtail -2a<10[/tex]
[tex]\\ \rm\rightarrowtail -a<5[/tex]
[tex]\\ \rm\rightarrowtail a>-5[/tex]
And
[tex]\\ \rm\rightarrowtail 5a<17[/tex]
[tex]\\ \rm\rightarrowtail a<17/5[/tex]
[tex]\\ \rm\rightarrowtail a<3\dfrac{2}{5}[/tex]
So
solution set
[tex]\\ \rm\rightarrowtail a\in\left(-5,3\dfrac{2}{5}\right)[/tex]
So
a={-4,-3,-2,-1,0,1,2,3}Hi, I’m doing some review and I just wanted to know if I am on the right track with PEMDAS.
Answer:
yes ur on track
Step-by-step explanation:
divide the sum of 39 and product of 18 and 6 by the difference of 50 and 14
Answer:
the imino acid found in protein strcjure
Roger has a rope that is 3 feet long.He needs to cut it into 12 equal length pieces.How many feet loń should each piece of the rope be?
Answer:
0.25
Step-by-step explanation:
3/12 is 0.25
3 divided by 12 when simplified or reduced
The fraction 3/12 is equal to the exact decimal number.
In which quadrant is the point (4, -5)? II I IV III
Answer:
Quadrant IV
Step-by-step explanation:
You can easily find in which quadrant a point lies using this key :
Quadrant I = (+ , +)Quadrant II = (- , +)Quadrant III = (-, -)Quadrant IV = (+, -)We have the coordinate (4, -5)
x-coordinate is positivey-coordinate is negativeIt lies in Quadrant IVAnswer:
Quadrant IV
Step-by-step explanation:
The Cartesian plane is divided into 4 quadrants.
Quadrant I is the top right quadrant, where x and y are positive.
We then move in a counterclockwise direction for quadrants II, III and IV.
Therefore:
Quadrant I: (x, y)Quadrant II: (-x, y)Quadrant III: (-x, -y)Quadrant IV: (x, -y)As point (4, -5) has a positive x-value and a negative y-value, it will lie in Quadrant IV