Answer:
1) The equation for the of the ball in y = a·(x - h)² + k is;
y = -16·(x - 5)² + 25
2) The height of the dock, d = -375 feet below the water level
Step-by-step explanation:
1) The question is with regards to quadratic function representing projectile motion
The given parameters are;
The height the ball reaches 4 seconds after Sarah kicked the ball = 9 feet
The time the ball hits the water = 6 seconds after reaching the 9 feet height
The form of the quadratic equation representing the motion is given as follows;
y = a·(x - h)² + k = a·x² - 2·a·h·x + a·h² + k
Let 'x' represent the time of motion of the ball, and let 'a', represent the acceleration due to gravity, we have;
The equation for the ball, y = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
h = The horizontal component of the vertex coordinate = 0
Therefore, we have;
When x = 0, y = d
d = -16·(0 - h)² + k = -16·h² + k
d = -16·h² + k
When x = 4, y = 9 - d
9 - d = -16(4 - h)² + k = -16(4 - h)² + k
When x = 2, y = d
d = -16(2 - h)² + k
When x = 6, y = 9
9 = -16(6 - 5)² + k
When x = 8, y = d
d = -16(8 - h)² + k
-16(8 - h)² - (-16(2 - h)²) = 0
h = 5
From 9 - d = -16(4 - h)² + k = -16(4 - 4)² + k
d = 9 - k
9 = -16(6 - h)² + k
k = 9 + 16(6 - 5)² = 25
d = 9 - k = 9 - 25 = -16
Therefore, h = 5, k = 25
The equation for the of the ball in y = a·(x - h)² + k is therefore;
y = -16·(x - 5)² + 25
2) When x = 0, y = d, ∴ d = -16(0 - 5)² + 25 = -375 feet below the water
The height of the dock, d = -375 feet below the water level
Anthony had $35 to spend at a fair. He has $21.50 remaining after taking 6 rides with each ride costing the same. How much did Anthony pay for each ride?
Answer:
$3.58
Step-by-step explanation:
Well you do 21.50 ÷ 6 and you have your answer. I hope this helps!
Which of the following terms are considered like terms? Select all that apply. (more than one)
4x^2
6x^4
3x
x^2
5x^2
Answer:
maybe 3x
Step-by-step explanation:
What’s the correct answer?
Answer:
1/7
Step-by-step explanation:
1 - 0 1
------ = -------
0 - ( - 7) 7
In a company, 60% of the workers are men If people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Complete question :
In a company, 60% of the workers are men If 125 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
313
Step-by-step explanation:
Given that :
Percentage of workers who are men = 60%
Number of workers who aren't men = 125
Hence, percentage of workers who aren't men = (100% - 60%) = 40%
Thus;
40% of workers = 125
If ;
0.4 = 125
100% of the workers x
0.4 = 125
1 = x
Cross multiply
0.4x = 125
0.4x / 0.4 = 125 / 0.4
x = 312.5
Hence, total number of workers = 313
PLS NEED HELP ASAP!!!!!!!!
the diagram shows a triangle 3x-1,3x and 4x-1. The perimeter of the triangle is 70 cm. The area of the triangle is a^2 cm. What is the value of a?
Answer:
thanks for your points
In Triangle DEF, e=2.7 inches, angle F=49 degrees and angle D=58 degrees. Find the length of f, to the nearest 10th of an idea.
Answer: 2.1
Step-by-step explanation:
what are the coordinates
PLZ HELP ME
Which is the exponential form of the expanded form shown?
(2/5) (2/5) (2/5) (2/5)
2^{4}/5
2/5^{4}
(tex]\frac{2}{5}[/tex])²
[tex](\frac{4}{5} )[/tex]²
Answer:
c
Step-by-step explanation:
hope this helps
Answer:
answer is c
Step-by-step explanation:
and me know me right. :)
Identify the constants in the expression below.
10x + 19
**ill give brainliest
Answer: look at the picture it have the answer hope you understand this is how I can find the answer...
Step-by-step explanation:
can you guys help plsss
HELPP ASAPPPP on a windy winters day the actual air temps turn is -5C and the wind speed is 15 kilometers per hour. What would the wind chill factor make the temperature feel like to a person outdoors?
A. 1.7C
B. -5C
C. -10.6 C
D. -16.7 C
Answer:
C
Step-by-step explanation:
Anyone can y’all help me. What’s the mistake in this? And what’s N actually equal to?
Answer:
n = -1
Step-by-step explanation:
you've accidently substracted 6n from 12n when you were supposed to be adding them. (-6n becomes +6n when brought to the otherside of the equal sign)
Mr. Emery bought 6 pizzas for the math team. The total cost of the order was $58.50. Each pizza cost the same amount. What is the unit cost per pizza for the order?
Answer:
Each pizza is $9.75
Step-by-step explanation:
$58.50/ 6 pizzas
9.75 / pizza
Answer:
its $9.75
Step-by-step explanation:
59.50/6
1 1/3 x 3/5 and simplify
Answer:
4/5
Step-by-step explanation:
1 1/3 = 4/3
4/3 x 3/5
times the denominator and numerator = 12/15
divide by HCF which is 3
4/5
A concert is attended by2500 people.If 47% are adult females and 32% are adults males,how many children attended?
Answer:
use division
Step-by-step explanation:
Answer:
525
Step-by-step explanation:
first we need to work out the percentage of the children who attended to to do this we need to add 47% with 32% which is 79%. Then you need to take away 79% from 100% which is 21%. After that you now know that 21% is the children who attended but you wanted to know how many children so to work this out you would find 21% of 2500 which would give you 525.
i hope this helps
Use the substitution method to solve the system of equations.
y=-3x+20
y=-2x+12
please I am begging for help
Answer:
(8,-4) hope this helps!! Also yes you can use it
Tameka pilots a hot air balloon. She lowers the balloon five times, going down an equal distance each time. In all, Tameka lowers the balloon 75 m.
Answer:
Step-by-step explanation:
Just divide 75 by 5. Which is 15vso the integer is 15.... gl with the rest
MULTIPLE CHOICE QUESTION
Which is an equivalent ratio for 18 cookies and 4 people?
Select all ratios that are equivalent.
36 cookies for every 8 people
6 cookies for every 1 person
-alue.
each
the same
is, what you
other.
19 cookies for every 5 people
9 cookies for every 2 people
Answer:
36:8, and 9:2
Step-by-step explanation:
8 is 4*2, so 18*2 is 36. that is equivalent so it is one of the answers. 4/2 is 2 and 18/2 is also 2, so the last choice is also an answer.
1. Express 9% as a fraction in simplest form.*
(1 Point)
3/100
9/100
9/10
90/100
9 percent is 9/100.
Brainliest are appreciated! :DD
What is the volume of the rectangular prism
Answer Choices:
a.2/9
b.3 1/3
c.1 1/9
d.10
Answer:
B
Step-by-step explanation:
Just answer it nznnznkskosoaksns
Help me please!!!! I’m super confused
Answer:
8
Step-by-step explanation:
Bert’s age plus twice Ernie’s age is 30. Bert’s age plus 8 times Ernie’s age is 108. How old are Bert and Ernie?
Answer:
They are 12 and 9
Step-by-step explanation:
20 POINTS 20POINTS.........................
Answer:
thank you god bless you
Step-by-step explanation:
:)
Find the mean, median, and mode of this data:
49, 57, 49, 51, 54. If necessary, round to the nearest tenth
Answer:
in this problem
the mean is 49
Answer:
Mean: 52
Median: 51
Mode: 49
Step-by-step explanation:
Mean: (49+57+49+51+54)/2 = 52
Median : 49, 49, 51, 54, 57
the one in the middle is 51, which means that is the median.
Mode: 49 repeats, meaning that 49 is the mode.
what is the value of
Step-by-step explanation:
yes the first option is the correct one.
PLEASE HELP!!!!! AS SOON AS POSSIBLE > WILL GIVE BRAINLY TO CORRECT ANSWER
Answer:
D
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 12² = 13²
a² + 144 = 169 ( subtract 144 from both sides )
a² = 25 ( take the square root of both sides )
a = [tex]\sqrt{25}[/tex] = 5 → D
What is the next fraction in this sequence? Simplify your answer 1/5, 1/3, 7/15, 3/5
How many blocks are needed to make 15 steps
Answer:
15 blocks
Step-by-step explanation:
Nancy bought an energy drink for $4 along with some candy bars that cost $3.50 each. She spent $21.50. How many candy bars did Nancy buy?