In a kickball game, a ball is kicked and travels along a parabolic path. The height h, in feet, of the kickball t seconds after the kick can be modeled by the equation h(t) = −16 t2 + 24t .
a. A fielder runs a route that will allow him to catch the kickball at about 3 ft above the ground. Write an equation that can be used to find when the fielder will catch the ball.
b. Use graphing technology to find out how long the kickball has been in the air when the fielder catches it on its descent. Round to the nearest hundredth.
Answers
Answer:
(a) h(t) = 3
(b) time = 1.36 seconds
Explanation:
equation: h(t) = -16(t)² + 24t
Part AIf the fielder catches the ball at the height of about 3 ft.
equation: h(t) = 3Part Busing graphing technology, graphed below. (height, y = 3)
Additional *solving part B algebraically*
-16(t)² + 24t = 3
-16(t)² + 24t - 3 = 0
using quadratic equation
[tex]\bold{x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ when \ ax^2 + bx + c = 0}[/tex]
==================================
[tex]\sf t_{1,\:2}=\frac{-24\pm \sqrt{24^2-4\left(-16\right)\left(-3\right)}}{2\left(-16\right)}[/tex]
[tex]\sf t=\frac{3-\sqrt{6}}{4}, \ t=\frac{3+\sqrt{6}}{4}[/tex]
t = 1.36 seconds and 0.14 seconds
The fielder shall catch the ball when the ball is falling, so time : 1.36 s
Answer:
See below ~
Step-by-step explanation:
a. Equation
In place of h(t), substitute 3 in its place3 = -16t² + 24tRearrange by bringing 3 to the other side-16t² + 24t - 3 = 0b. Finding the duration of the kickball in air using graphing technology
Based on the graph (attached), the ball has been in the air for :1.5 seconds
Related Questions
What trigonometric ratio is 6/10?
sinA
cosC
tanC
tanA
Answers
Answer: tanA
Step-by-step explanation:
Yoko made $324 for 18 hours of work.
At the same rate, how much would she make for 12 hours of work?
Answers
Answer:
$216
Step-by-step explanation:
324 / 18 = 18. (Meaning she makes 18 dollars an hour)
18 * 12 = 216
Answer:$216
Step-by-step explanation: Rate per hour is 324/18=18
12hours =18×12
The Rhythm Record Shop orders sixty-minute cassette tapes at $1.49 and CDs at $4.98. A total of 451
items were ordered and the total amount of the invoice is $1240.86. How many of each item were
ordered?
Answers
The number of sixty-minute cassette tapes ordered is 288 and the number of CDs ordered is 163.
What are the linear equations that represent this question?1.49a + 4.98b = $1240.86 equation 1
a + b = 451 equation 2
Where:
a = number of sixty-minute cassette tapes ordered b = number of CDs orderedHow many CDs were ordered?Multiply equation 2 by 1,49
1.49a + 1.49b = 671.99 equation 3
Subtract equation 3 from equation 1
568.87 = 3.49b
Divide both sides of the equation by 3.49
568.87 / 3.49
b = 163
How many sixty-minute cassette tapes were ordered ?Subract 163 deom 451
451- 163 = 288
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Jason is considering two different jobs that he has been offered and he likes the atmosphere and
other employees equally at both companies.
With the first job he would be an apartment property manager for AMLI Company. This job is
offering Jason an hourly rate of $19. 00 an hour plus a weekly bonus of $40 for each new tenant he
sets a one year lease up with. The company expects Jason to work all 52 weeks of the year and 40
hours per week. He was told he could expect to set up an average of 5 lease agreements for each
week that he works.
With the second job he would work as water treatment facility manager in Gwinnett County. He
would be paid an annual salary of $46,000 a year, there are no bonuses by he gets a week off.
Both companies deduct for Social Security (6. 2%), Medicare (1. 2%), State Income Tax (3%), and
Federal Income Tax (14%).
AMLI's individual health insurance costs $115 per month. Gwinnett County's health insurance is
only $25 per month for an individual.
Part A: Determine how much Jason will receive in one year after all deductions have been taken
for each company. Show your work neatly.
Answers
The amount of money that Jason will receive in one year after all deductions have been taken for each company is $30,780.5 and $32562.
What is the final amount?With the first job, he would be an apartment property manager for AMLI Company.
This job is offering Jason an hourly rate of $19. 00 an hour plus a weekly bonus of $40 for each new tenant he sets a one-year lease-up with.
The company expects Jason to work all 52 weeks of the year and 40 hours per week.
He was told he could expect to set up an average of 5 lease agreements for each week that he works.
The amount after one year will be given by an equation
Let y be the amount, x be the number of hours in a week and z be the number of the week.
y = 19x + 40z
The total number of hours in a year will be
x = 2080
Then
y = 19 × 2080 + 40 × 52
y = $ 41,600
The amount after the deduction of Social Security (6. 2%), Medicare (1. 2%), State Income Tax (3%), and Federal Income Tax (14%) will be
→ 41,600 × 0.938 × 0.988 × 0.97 × 0.86
→ $ 32,160.5
The amount after the insurance will be
Amount = 32160.5 - 115 × 12
Amount = $ 30780.5
With the second job, he would work as a water treatment facility manager in Gwinnett County. He would be paid an annual salary of $46,000 a year, there are no bonuses and he gets a week off.
The amount after the deduction of Social Security (6. 2%), Medicare (1. 2%), State Income Tax (3%), and Federal Income Tax (14%) will be
→ 46,000 × 0.938 × 0.988 × 0.97 × 0.86
→ $ 35,562
The amount after the insurance will be
Let the number of the worker be 10. Then
Amount = 35,562 - 10 × 12 × 25
Amount = 35562 - 3000
Amount = $32562
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Pablo sold liters of soda at a baseball game. How much is this in milliliters ?
Answers
Answer:
See below
Step-by-step explanation:
# liters x 1000 = ml sold
Answer this question. There are 3 answers
Answers
Answer:
uh?
Step-by-step explanation:
y=mx+b (-6,-5) and (-4,-4)
Answers
Step-by-step explanation:
We will put this in y=mx +b form so first calculate the slope
m= (-4)-(-5)/(-4)-(-6)
m= 1/2. So y= x/2. +b
Now just substitute the x and y values of either given point to calculate b
I will use (-4,-4)
-4= (1/2)(-4) +b
-4= -2 +b
b=-2
So equation is y= x/2 -2
...................................
I search it.
Answer:
Step-by-step explanation:
Equation of line in slope- y intercept form:
First find the slope.
[tex]\boxed{Slope= \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-4-[-5]}{-4-[-6]}\\\\=\dfrac{-4+5}{-4+6}\\\\=\dfrac{1}{2}[/tex]
Equation:
[tex]y =\dfrac{1}{2}x+b[/tex]
Choose any point and substitute the x and y value in the above equation.
(-6,-5)
[tex]\sf -5=\dfrac{1}{2}*(-6) + b\\\\-5 = -3+b\\\\-5+3=b\\\\-2 = b[/tex]
Equation:
[tex]y = \dfrac{1}{2}x - 2[/tex]
(x+3)(x+2)=0 which technique is most appropriate to use to solve each equation?
A. Zero product property
B. quadratic formula
C. square root property
Answers
The value of x by using the zero product property therefore option A is correct.
We have given that,
(x+3)(x+2)=0
we have to determine the technique that is most appropriate to use to solve each equation
What is the zero product property?The Zero Product Property simply states that if ab = 0, then either a = 0 or b = 0 (or both).
Therefore we have
(x+3)=0 and (x+2)=0
This implies that,
x+3=0
x=-3 and (x+2)=0 this implies that x=-2
Therefore we get the value of x by using the zero product property therefore option A is correct.
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A census was conducted that determined the land area and populations of towns in a certain region. the frequency table displays some of the results. rounded to the nearest hundredth, what values complete the conditional relative frequency table? a = b =
Answers
The value of a in the conditional relative frequency table is 0.58.
The value of b in the conditional relative frequency table is 0.42.
What is a conditional relative frequency table?
A conditional relative frequency table is a two-way table that contains information on the proportion of a population that has a particular characteristic.
a = 32/53 = 0.58
b = 23 / 53 = 0.42
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Answer:
The value of a in the conditional relative frequency table is 0.58.
The value of b in the conditional relative frequency table is 0.42.
Step-by-step explanation:
I need help asp please!!!
Answers
Answer:
Option B, [tex]516.3\ units[/tex]
Step-by-step explanation:
Step 1: Determine the area of the back
[tex]A = l * w[/tex]
[tex]A = 10\ units * 13\ units[/tex]
[tex]A = 130\ units^2[/tex]
Step 2: Determine the hypotenuse
Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]
[tex](10-6)^2\ units + 7^2\ units = c^2[/tex]
[tex]4^2\ units + 7^2\ units=c^2[/tex]
[tex]16\ units+49\ units=c^2[/tex]
[tex]\sqrt{65}=\sqrt{c^2}[/tex]
[tex]8.06 = c[/tex]
Step 3: Determine the area of the top
[tex]A = l * w[/tex]
[tex]A = 13\ units * 8.06\ units[/tex]
[tex]A = 104.81\ units^2[/tex]
Step 4: Determine the area of the front
[tex]A = l * w[/tex]
[tex]A = 13\ units * 6\ units[/tex]
[tex]A = 78\ units^2[/tex]
Step 5: Determine the area of the bottom
[tex]A = l * w[/tex]
[tex]A = 13\ units * 7\ units[/tex]
[tex]A = 91\ units^2[/tex]
Step 6: Determine the area of the trapezoid
[tex]A = \frac{a + b}{2} * h[/tex]
[tex]A = \frac{10\ units\ +\ 6\ units}{2}*7\ units[/tex]
[tex]A = 8\ units*7\ units[/tex]
[tex]A = 56\ units^2[/tex]
Step 7: Determine the total surface area
[tex]130\ units^2 + 104.81\ units^2 + 78\ units^2 + 91\ units^2 + 2(56\ units^2)[/tex]
[tex]515.81\ units^2[/tex]
Answer: Option B, [tex]516.3\ units[/tex]
Use the diagram to determine the length of LJ
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's use distance formula ~
[tex]\qquad \tt \dashrightarrow \:LJ = \sqrt{(x1 - x1) {}^{2} + (y2 - y1) {}^{2} } [/tex]
[tex]\qquad \tt \dashrightarrow \:LJ = \sqrt{(0) {}^{2} + (y2 - y1) {}^{2} } [/tex]
[tex]\qquad \tt \dashrightarrow \:LJ = \sqrt{ {}^{}(y2 - y1) {}^{2} } [/tex]
[tex]\qquad \tt \dashrightarrow \:LJ = { {}^{}y2 - y1 {}^{} } [/tex]
I hope it was easy enough to understand, ask me if you have any doubts ~
What is the distance between the points (-4 , -11) and (-4 , 20) in the coordinate plane?
Answers
10.) Part A: What is the area, in square feet, of the kitchen?
A homeowner created this diagram showing the dimensions of the kitchen
and the family room in his house.
K-5 ft-* 10 ft-
10 ft
kitchen
family
room
To
10 ft
5 ft
דם
- 15 ft
15 ft
Answers
The computation shows that the area of the kitchen that's in the home in square feet is 50ft².
How to calculate the area?It should be noted that an area of a rectangular space is calculated by multiplying the length by the width.
In this case, the area of the kitchen will be:
= 5ft × 10ft
= 50ft²
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companies. After how many miles
are the total costs at the
OI two truck rental
two companies equal?
Company A:
Company B:
$20 per day plus $.70 per mile
$45 per day plus S .25 per mile
Answers
Set up the equation and solve for miles:
20 + 0.70m = 45 + 0.25m
Subtract 20 from both sides
0.70m = 25 + 0.25m
Subtract 0.25m from both sides
0.45m = 25
Divide both sides by 0.45
M = 55.56 miles
answer: 55.56 miles ( rounded to nearest hundredth’s)
A rectangle has sides measuring (6x + 4) units and (2x + 11) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?
Answers
Answer:
Down Here ↓↓↓
Step-by-step explanation:
Hello!
A)
The area of a rectangle is L * W.
Area = (6x + 4)(2x + 11)Area = 12x² + 8x + 66x + 44Area = 12x² + 74x + 44B)
The degree of a polynomial is the value of the highest exponent. The degree of 12x² + 74x + 44 is 2, because 2 is the highest exponent.
C)
This demonstrates the closure property, as adding, subtracting, and or multiplying polynomials will give a polynomial.
A polygon has 8 sides. any line segments connecting any 2 points on the polygon will consist of no points outside of the polygon. complete the statement. the polygon is and is .
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Answer:
an octagon and convex
Step-by-step explanation:
cuz i said so
Answer:
an octagon and convex
Step-by-step explanation:
You put a fence around the dog pen and fill it with gravel. The fence costs $1.75 per foot. One bag of gravel covers 8 square feet and costs $1.50. How much do you spend?
Answers
Answer: Ok so you do 8(1.75+1.50) and then times it by four since it’s a dog fence,I did this on calculator+ so that should be a good answer,the answer is 104
Step-by-step explanation:
I can't remember how to do this
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Answer:
i think it is 12 but i am not sure
Step-by-step explanation:
Find the equation of the circle in standard form.
center (5,-5)
radius = 3 units
Answers
Answer:
(x - 5)² + (y + 5)² = 9
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 5 ) and r = 3 , then
(x - 5)² + (y - (- 5) )² = 3² , that is
(x - 5)² + (y + 5)² = 9
I will give brainliest
Bob's driveway is a rectangular shape with a length of 45 feet and a width
of 18 feet. Yolanda wants to find the area of Bob's driveway in yards. She
made sense of the problem by first finding the area of the driveway in feet
by doing 45(18) = 810 square feet. She then converted the area into yards
by doing 810(3). Her final answer was 2430 square yards. Did Yolanda
correctly make sense of the problem? If not, provide the correct solution
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Answer: she was not correct, she messed up the equation.
A boat traveled 27 miles in 3 hours. At this rate how many mile will the boat travel in 1/2 hour?
Answers
[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 27 & 3\\ x& \frac{1}{2} \end{array} \implies \cfrac{27}{x}=\cfrac{3}{~~ \frac{1}{2}~~}\implies \cfrac{27}{x}=6 \\\\\\ 27=6x\implies \cfrac{27}{6}=x\implies \cfrac{9}{2}=x\implies 4\frac{1}{2}=x[/tex]
If u could help with this I’d really appreciate it
Answers
Answer:
it reflection over the y axis not the x axis
Step-by-step explanation:
Write an equation that represents each diagram and find the value of x.
Answers
[tex]\mathbb{QUESTION:}[/tex]
Write an equation that represents each diagram and find the value of x.
[tex]\mathbb{ANSWER:}[/tex]
A.
Rabbits can exhibit a number of colors in their coats: black, white, tan, brown, red, and grey. A disease randomly kills off most of the population and leaves only black and grey rabbits. Future generations are only black or grey. What is the term used to describe this phenomenon
Answers
Answer:
Genetic drift
Step-by-step explanation:
I took da test
The term used to describe this phenomenon of future generation fluctuations would be Genetic drift.
What is Genetic drift?Genetic drift refers to the random fluctuations in the number of offspring in a population.
Rabbits can exhibit several colors in their coats: black, white, tan, brown, red, and grey.
A disease randomly kills off most of the population and leaves only black and grey rabbits.
Future generations are only black or grey. We can see that the future rabbits have some common colors that are given by their parents.
So, this must be Genetic drift.
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a polygon is graphed on a coordinate plane the coordinates of the polygon vertices are listed (2,2,-6,-5,-6,-4,-1,-7,0,0
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(-1,4) • 13.-1)
Step-by-step explanation:
I need help please !!!!!!!
Answers
Answer: The answer is C
If a customer’s total is $9. 02 and he/she gives you a $10. 00 bill and 2 pennies, how much do you have to give back in change? *
Answers
3. Kyle starts with $15.00 and saves $3.50
each day. What expression represents
the total amount Kyle saves?
A $3.50
B $15.00
C 3.5t + 15, where t is the number
of days
D 15t + 3.5, where t is the number
of days
Answers
Answer:
C 3.5t + 15, where t is the number
of days
x, miles y, cost ($) 0 2.00 1 2.75 2 3.50 3 4.25 4 5.00 13) The cost of a cab trip, y, is given by the table, where x is the number of miles traveled. Which THREE statements are correct? A) The rate of change is $0.75. B) A ten-mile trip would cost $12.00. C) The initial passenger fee is $2.00. D) A twenty-mile trip would cost $17.00. E) The cost of a cab trip can be modeled by the function y = 1x + 2. Help
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Answer: A, C, D
Step-by-step explanation: Lot's of brain stuffs
the fraction of girls at the dance is
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