Answer:
40 feet (after 1.5 seconds).
Step-by-step explanation:
The height h of the ball after t seconds is modeled by the function:
[tex]h(t)=-16t^2+48t+4[/tex]
And we want to determine the ball's maximum height.
Since the given function is a quadratic, the maximum height occurs at the vertex point.
For quadratics, the vertex point is given by the formulas:
[tex]\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)[/tex]
In this case, a = -16, b = 48, and c = 4.
Therefore, the t-coordinate at which the vertex occurs is:
[tex]\displaystyle t=-\frac{48}{2(-16)}=\frac{48}{32}=\frac{3}{2}[/tex]
So, the maximum height occurs after 1.5 seconds.
Then the maximum height will be:
[tex]\begin{aligned}\displaystyle h\Big(\frac{3}{2}\Big)&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)+4\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)+4\\\\&=-4(9)+72+4\\\\&=40\text{ feet}\end{aligned}[/tex]
So, the maximum of the ball is 40 feet (after 1.5 seconds).
In ANOP, PN = OP and m20 = 32°. Find mZP.
Answer:
m<P = [tex]116^{0}[/tex]
Step-by-step explanation:
The given triangle is an isosceles triangle.
Since PN ≅ OP, then m<O ≅ m<N.
So that,
m<O + m<P + m<N = 180 (sum of angles in a triangle)
But,
m<O = 32 ≅ m<N = 32 (base angles of an isosceles triangle are equal)
32 + 32 + m<P = 180
64 + m<P = 180
m<P = 180 - 64
= 116
m<P = [tex]116^{0}[/tex]
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=53°, and QR = 17 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:
21.2863≈21.3 feet
Step-by-step explanation:
Answer:
21.3
Step-by-step explanation:
A culture of bacteria has an initial population of 7100 bacteria and doubles every 2
hours. Using the formula P+ = Po · 2ả, where P is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 15 hours, to the nearest whole number?
Answer:
Pt=1285237.2855≈ 1285237
YOUR WELCOME :)
Camden is deciding between two parking garages. Garage A charges an initial fee of
$12 to park plus $4 per hour. Garage B charges an initial fee of $8 to park plus $5 per
hour. Let A represent the amount Garage A would charge if Camden parks for t
hours, and let B represent the amount Garage B would charge if Camden parks for t
hours. Write an equation for each situation, in terms of t, and determine the hours
parked, t, that would make the cost of each garage the same.
Answer:
4 hours
Step-by-step explanation:
A = 12 + 4t
B = 8 + 5t
12 + 4t = 8 + 5t
t = 4
The cost of each garage would be the same when Camden parked the car for 4 hours
Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) = f(1) = f(2) = 0. find the factored form of f.
Answer:
I honestly do not know sorry
Is this a function ? :)
Answer:
yes
Step-by-step explanation:
Hey There!
So if you didn't know in order for it to be a function none of the x values can repeat
In the given relation none of the x values repeat, or each input has a different output therefore it is a function
simplify pls with steps 2⁵ x 3⁴ x 5 / 3 x 16
Fill in the missing terms of the arithmetic sequence.
-7, __, 1, 5, __, 13
1. -3, 9
2.-3, 10
3.-4, 9
4.-4, 10
Answer:
the missing terms are x, y
we have:
x + 7 = 4 => x = -3
13 - y = y - 5
<=> 2y = 18
<=> y = 9
so the missing terms are -3; 9
I need help with number 9 please show work how to get the answer.
Answer:
Option B
Step-by-step explanation:
Let 'x' represents the number of miles traveled and 'y' represents the total cost of of the taxi ride.
Cost of ride with a rate of $2.25 per mile = $2.25x
Since, service charge of the taxi = $3 for first mile
Total cost of the ride = 2.25x + 3
Equation for the cost of the ride will be,
y = 2.25x + 3
Since, farthest distance that the taxi can travel = 35 miles
That means value of x may vary between x = 0 to x = 35 (including x = 25)
Therefore, domain for the situation will be,
0 < x ≤ 35
Option B will be the answer.
In 4 minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
Answer:
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
Step-by-step explanation:
Given - In 4 minutes, a conveyor belt moves 800 pounds of recyclable
aluminum from the delivery truck to a storage area. A smaller belt
moves the same quantity of cans the same distance in 6 minutes.
To find - If both belts are used, find how long it takes to move the cans
to the storage area.
Proof -
Given that,
Larger belt take 4 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Larger belt = 4 min/ shifting
Also,
Smaller belt take 6 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Smaller belt = 6 min/ shifting
Now,
As we know that Time is inversely proportional to time, so
Rate of Larger Belt = [tex]\frac{1}{4}[/tex] shifting/min
Rate of Smaller Belt = [tex]\frac{1}{6}[/tex] shifting/min
Now,
Let us assume that , if both belts used then,
Total time taken = x min/shifting
Then, Rate = [tex]\frac{1}{x}[/tex] shifting/min
Now,
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{x}[/tex]
⇒[tex]\frac{6 + 4}{24} = \frac{1}{x}[/tex]
⇒[tex]\frac{10}{24} = \frac{1}{x}[/tex]
⇒10x = 24
⇒x = [tex]\frac{24}{10}[/tex] = 2.4 minutes
∴ we get
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
I really need help with a thing for math if yall can help I would appreciate it. If yall know this comment down below and tell me the answer
Answer:
27
Step-by-step explanation:
3/5of 45 is basically what you are looking for and it in itself is the equation you have to solve
3/5 is 3 divided by and "of" is basically multiply by 45
3/5*45
.6*45
27
Help plz!
The Corresponding Angles Conjecture states that if two
parallel lines are cut by a transversal, the corresponding
angles are congruent. The picture below shows this
relationship
Answer:
B
Step-by-step explanation:
Corresponding angles form a sideways U when you connect the angles.
b is the only one that does that.
1 and 4 are consecutive angles.
1 and 3 are vertical angles
4 and 3 are linear pair angles.
answer the question please
Answer:
sin cos
Step-by-step explanation:
Answer:
hi my dear this is something which i use to remember if to use sin cos or tan u can try it i hope u get the answers
Find the missing angle.
Answer:
90°
Step-by-step explanation:
40+50+x=180
x=90
Which of the following units are units of volume? Select all that apply.
Answer:
we have these we ml and l
Step-by-step explanation:
Here, we want to select the units of volume ;
1. mg
This is a measure of mass and in fact it is called milligrams
2. mm
This is called millimeters and in fact is a measure of distance
3. cm
This is centimeters and it is a measure of distance too
4. ml
Milliliters, this is a measure of volume
5. m
meters;
this is a measure of distance
6. g
grammes
This is a measure of mass
7. l
This is liters
It is actually a measure of volume
8. km
this is kilometers, it is a measure of distance
1) Tommy mows lawns and cleans pools during the summer. He earns $20 per lawn and $9 per
pool. He needs $1500 to buy a car from his friend. If Tommy plans to mow 41 lawns this
summer, how many pools must he clean to earn at least $1500?
Answer:
Step-by-step explanation:
[tex]20L+9P\ge 1500,\ L=41\\ \\ 20(41)+9P\ge 1500\\ \\ 820+9P\ge 1500\\ \\ 9P\ge 680\\ \\ P\ge 75.6\\ \\ P=76[/tex]
It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.
Answer:
300%
Step-by-step explanation:
Given
[tex]y\ \alpha\ \frac{1}{x^2}[/tex]
Required
Find the percentage change in y when x decreased by 50%
First, convert to equation
[tex]y\ = \ \frac{k}{x^2}[/tex]
Where k is the constant of proportionality
When x decreased by 50%
[tex]Y = \frac{k}{(x - 0.5x)^2}[/tex]
[tex]Y = \frac{k}{(0.5x)^2}[/tex]
[tex]Y = \frac{k}{0.25x^2}[/tex]
Expand
[tex]Y = \frac{1}{0.25} * \frac{k}{x^2}[/tex]
Substitute [tex]\frac{k}{x^2}[/tex] for y
[tex]Y = \frac{1}{0.25} * y[/tex]
[tex]Y = 4 * y[/tex]
[tex]Y = 4 y[/tex]
The percentage change is then calculated as:
[tex]\%Change = \frac{Y - y}{y} * 100\%[/tex]
[tex]\%Change = \frac{4y - y}{y} * 100\%[/tex]
[tex]\%Change = \frac{3y}{y} * 100\%[/tex]
[tex]\%Change = 3 * 100\%[/tex]
[tex]\%Change = 300\%[/tex]
The percentage in y is 300%
From the calculation, the percentage change in y is 300%.
From the statement of the question; y α 1/x^2 so introducing the constant of proportionality, we have; y =k/x^2 so k = x^2y.
We are then told that x is decreased by 50% hence;
Y = k/(x - 0.25x)^2
Y = k/(0.5x)^2
Y = 1/0.25 k/x^2
But k/x^2 = y so;
Y = 1/0.25 y
Y = 4y
Change = 4y -y/y * 100/1
= 300%
Learn more about percentage change: https://brainly.com/question/15308590
3х - у = -3
х+у= -1 using elimination
method
Answer:
Your solution is (-1, 0)
Step-by-step explanation:
3x - y = -3
x + y = -1
The elimination method eliminates one variable at a time to find the other variable.
Here we can see that the y variable will naturally be eliminated.
3x - y = -3
x + y = -1
--------------
4x = -4
Divide both sides by 4 to isolate x.
x = -1
Now plug this value back into one of the equations.
3(-1) - y = -3
Multiply.
-3 - y = -3
Add 3 to both sides.
-y = 0
Divide both sides by -1.
y = 0
Your solution is (-1, 0)
Check this solution by plugging these values into the second equation.
-1 + 0 = -1
-1 = -1
Your solution is correct.
Hope this helps!
Answer:
x = -1
y = 0
Step-by-step explanation:
3x - y = -3 -------------------(I)
x + y = -1 ------------------(II)
Add equation (I) & (II). Now, y will be eliminated and you can find the value of x
(I) 3x - y = -3
(I) x + y = -1
4x = -4
x = -4/4
x = -1
Plugin x = -1 in equation (II)
-1 + y = -1
y = -1 +1
y = 0
A fully loaded truck weighed 10 3/5 tons. After unloading, the truck weighed 3 2/3 tons. What was the weight of the load?
Answer:
14
Step-by-step explanation:
A fully loaded truck weighs 10 3/5 tons
After unloading the truck weighed 3 2/3 tons
Therefore the weight of the load can be calculated as follows
= 10 3/5 - 3 2/3
= 53/5 - 11/3
= 265-55/15
= 210/15
= 14
Hence the weight of the load 14
Divide R300 000 between Leona and Janet in the ratio 3:2.
Answer:
let the ratio be in x
a/q. 3x + 2x = 300000
5x = 300000
x = 300000/5
x= 60000
Leona = 60000*3 = 180000
Janet = 60000*2 = 120000
hope it helps
Pls help me!!!! I don't know how to do these.
Answer:
12) Option 3
13) Option 2
Step-by-step explanation:
Add: 2 2/3 + 3 1/12 PLEASE HURRY IM TIMED AND I WILL BE GROUNDED IF I FAIL BECAUSE I FAILED LAST TIME SO PLEASE HURRY AND HELP MEEEEE
Answer: 23/4 is you answer!!
Step-by-step explanation:
Answer: 5 3/4
Step-by-step explanation: I put them in the same denominator to add them
Which of the following is a prime number? Select one: A. 19 B. 20 C. 21 D. 22
Answer: a. 19
Step-by-step explanation:
it only has 1 and itself
Answer:
A. 19
Step-by-step explanation:
The rest wouldn't be considered prime number. Only 19
please help! this is a huge chunk of my grade!!
Answer:
r=8Step-by-step explanation:
3r+4+8r-2 = 90
11r +2 = 90
11r= 88
r= 8You spend $20 to buy supplies for making milky tea, and plan on selling every cup of
milky tea for $1. Write an inequality to find the minimum number of cups of milky tea
you have to sell in order to make a profit.
Answer:
21 savage
Step-by-step explanation:
5 m
10 m
7 m
7 m
I don’t understand this please help me
Answer:
I don't know help me and I will help you
Which of these is the best approximation of
5
to the nearest hundredth?
OA) 0.17
OB) 0.75
OC) 0.83
OD) 1.20
Answer:
oc)0.83
Step-by-step explanation:
have a good day!!!
Will mark brainliest and give thirteen points explanation
Answer:
geyser =groundwater
glacier = freshwater
lake=freshwater
ocean=salt water
Step-by-step explanation:
Which is the graph of y= 2x-3?
Answer:
(A:
Step-by-step explanation:
EXAMPLE:
in Slope Intercept form, the letter x determines the slope of the line, where 0 makes the line horizontal and 1 makes the line at a 45 degree angle, in this case to go from x to x plus 1 you would climb y two times, so it takes two units to go one unit to the right, so x is multiplied by 2
the addition at the end of the formula resembles how high up or down the line crosses the y axis, if the number is positive, then the line crosses that amount higher then 0, if it were a negative number, it would cross that much lower
hope this makes sence, dont worry, once you understand how slope intercept form works, you will never forget it, good luck with ur studies :)
MEGA CREDITS to MisterZeng for double checking our work, thx m8 :D
The graph shows how the cost of flour depends on the amount purchased. image d4e51639499b482e8e204e442f36c002 What is the meaning of the point (0,0) on the graph? A. The cost of 0 pounds of flour is $0. B. The cost of 5 pounds of flour is $7. C. The flour costs 0 dollars per pound. D. The flour costs 00 dollars per pound.
Answer:
A. The cost of 0 pounds of flour is $0.Step-by-step explanation:
The graph is not attached.
But as per description this is a direct relationship.
The formula:
y = kxPoint (0, 0) is the start point when both the domain and range are equal to zero.
Correct option is A